DOCUMENT RESUME ED 053 978 · Final Report Office of Education (DHEW) , Washington, D.C. 65 116p....
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ED 053 978 AUTHOR TITLE INSTITUTION PUB DATE NOTE AVAILABLE FROM EDRS PRICE DESCRIPTORS ABSTRACT DOCUMENT RESUME SE 012 301 Lindquist, Clarence B. Mathematics in Colleges and Universities. A Comprehensive Survey of Graduate and Undergraduate Programs. Final Report Office of Education (DHEW) , Washington, D.C. 65 116p. Superintendent of Documents, Government Printing Office, Washington, D.C. 20402 ($0.60) EDRS Price MF-$0.65 HC-$6.58 Bachelors Degrees, *College Mathematics, College Programs, *Curriculum, *Degree Requirements, Doctoral Programs, Enrollment, Masters Degrees, *Mathematics Education, *Surveys Presented is a comprehensive survey of graduate and undergraduate programs in mathematics in effect during Winter and Spring of 1961. Questionnaires were mailed to 1,069 institutions which awarded degrees in mathematics or offered substantial programs in mathematics. Junior colleges and such specialized schools as Bible Colleges and seminaries, schools of art or music, law schools, and schools of business were not included. Data for the statistical analysis were taken from the 877 questionnaires which were returned. Information is reported on curricula, degrees, course offerings, enrollments, credit requirements, examination requirements, special features, innovations, and trends. The appendices provide specific information about graduate programs at individual institutions which were available in 1961. (RS)
Transcript of DOCUMENT RESUME ED 053 978 · Final Report Office of Education (DHEW) , Washington, D.C. 65 116p....
ED 053 978
AUTHORTITLE
INSTITUTIONPUB DATENOTEAVAILABLE FROM
EDRS PRICEDESCRIPTORS
ABSTRACT
DOCUMENT RESUME
SE 012 301
Lindquist, Clarence B.Mathematics in Colleges and Universities. AComprehensive Survey of Graduate and UndergraduatePrograms. Final ReportOffice of Education (DHEW) , Washington, D.C.65116p.Superintendent of Documents, Government PrintingOffice, Washington, D.C. 20402 ($0.60)
EDRS Price MF-$0.65 HC-$6.58Bachelors Degrees, *College Mathematics, CollegePrograms, *Curriculum, *Degree Requirements,Doctoral Programs, Enrollment, Masters Degrees,*Mathematics Education, *Surveys
Presented is a comprehensive survey of graduate andundergraduate programs in mathematics in effect during Winter andSpring of 1961. Questionnaires were mailed to 1,069 institutionswhich awarded degrees in mathematics or offered substantial programsin mathematics. Junior colleges and such specialized schools as BibleColleges and seminaries, schools of art or music, law schools, andschools of business were not included. Data for the statisticalanalysis were taken from the 877 questionnaires which were returned.Information is reported on curricula, degrees, course offerings,enrollments, credit requirements, examination requirements, specialfeatures, innovations, and trends. The appendices provide specificinformation about graduate programs at individual institutions whichwere available in 1961. (RS)
U.S. DEPARTMENT OF HEALTH.EDUCATION & WELFAREOFFICE OF EDUCATION
THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIG-INATING IT POINTS OF VIEW OR OPIN
CO IONS STATED DO NOT NECESSARILYREPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR POLICY
C)
w
r".1
OE - 56018
1mi CsIN COLLEGES &UNIVERSITIESA COMPREHENSIVE SURVEY OF GRADUATE AND UNDERGRADUATE PROGRAMS (FINAL REPORT)
U. S. DEPARTMENT OF HEALTH, EDUCTION, AND WELFARE - Office of Education
OBI MIMI
OE - 56018Cir. #765
HEM. CsIN COLLEGES &UNIVERSITIESA COMPREHENSIVE SURVEY OF GRADUATE AND UNDERGRADUATE PROGRAMS (FINAL REPORT)
By
Clarence B. LindquistSpecialist in Mathematics and Physical Sciences
Division of Educational Research
U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
Anthony J. Celebrezze, Secretary
Office of EducationFrancis Keppel, Commissioner
2
Superintendent of Documents Catalog No. FS 5.256:56018
U.S. Government Printing OfficeWashington : 1965
For sale by the Superintendent of Documents, U.S. Government Printing OfficeWashington, D.C., 20402 - Price 60 cents
3
FOREWORD
In recent years there has been no discipline in whichcurriculum analysis and development have aroused greaterinterest and activity than in mathematics. Furthermore,mathematics and the mathematics-based fields of statisticsand computing have been undergoing tremendous expansionin enrollments and degrees. Whereas 4,034 bachelor'sdegrees in the mathematical sciences were awarded in1954-55 by U.S. colleges and universities, 14,610 wereawarded in 1961-62. The Office of Education predicts thatthis number will increase to about 39,000 by 1969-70. Byway of comparison, the corresponding data for all thephysical sciences combined are 11,202 degrees for 1954-55;17,040 for 1961-62; and 29,100 for 1969-70, figures whichgive ample evidence of the growing importance of mathe-matics.
The survey of mathematics programs reported herewas the most comprehensive depth study of programswithin a discipline ever undertaken in the United States.A total of 877 colleges and universities granting bachelor'sor higher degrees, or about 82 percent of the 1,069 to whichquestionnaires were sent, responded. Both undergraduateand 'graduate programs were surveyed, and informationwas solicited on curriculums, degrees, course offerings,enrollments, credit requirements, examination require-ments, special features, innovations, and trends.
This report is expected to be valuable not only tomathematics educators, but also to deans and others re-sponsible for curriculum development in colleges anduniversities. In addition, the appendixes, which providespecific information about master's and doctor's programsat individual institutions, should be a helpful guide for pro-spective graduate mathematics students and their advisers.
The Office of Education wishes particularly to acknowl-edge for their advice and counsel Professor G. Baley Priceof the University of Kansas, Professor Harry M. Gehman ofthe State University of New York at Buffalo (formerly Uni-versity of Buffalo), Professor John W. Cell of the StateCollege of the University of North Carolina at Raleigh,Professor Howard F. Fehr of Teachers College of ColumbiaUniversity, and Dr. C. Russell Phelps of the National
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Science Foundation. We express gratitude also to membersof the Committee on the Undergraduate Program in Mathe-matics (CUPM) of the Mathematical Association of Americafor their helpful suggestions. Finally, we wish to expressour appreciation to the hundreds of persons in colleges anduniversities who filled out the lengthy questionnaire andto the mathematicians who assisted in the conception ofthe survey and the questionnaire instrument.
RALPH C. M. FLYNTAssociate Commissioner forEducational Research andDevelopment
FRANCIS A. J. IANNI, DIRECTORDivision of Educational Research
CONTENTS
Page
FOREWORD iii
CHAPTER I. INTRODUCTION 1
RECENT MATHEMATICS CURRICULUM STUDIES 2
PREPARATION OF THIS SURVEY 2
Pretest of the Questionnaire 2
Determination of the Universe 2
Categories Used for Analysis 3Response Rate 3Copy of the Questionnaire Form 4
CHAPTER II. UNDERGRADUATE PROGRAMS 15
ENTERING FRESHMAN LEVELS IN MATHEMATICS 15Comparisons by Type of Institution 16Comparisons by Control 16Comparisons by Region 16Comparisons by Enrollment Size 16
CHARACTERISTICS OF CURRICULUMS FOR THE MATHEMATICS "MAJOR" 16Kinds of Curriculum 16Credit-Hour Requirements for the Mathematics Major 18
Liberal arts or general curriculum 18Mathematics-teaching curriculum 18Statistical, actuarial, applied, and "other" curriculums 20
Credit-Hour Requirements in Professional Education 20Kinds of Degrees Awarded 21
Liberal arts or general curriculum. 21Mathematics-teaching curriculum 22Statistical, actuarial, applied, and "other" curriculums 23
Distribution of Degrees in Various Curriculums 24
COURSE OrTERINGS AND ENROLLMENTS 25Freshman Year 25Sophomore Year 26Junior Year and Senior Year 27
PREREQUISITE INSTRUCTION 29Extent of Prerequisite Instruction and Provision for Credit 29Enrollments in Prerequisite Instruction 30Where Prerequisite Instruction Is Given 31Discontinuance of Prerequisite Instruction from 1951 to 1961 31
Page
REQUIRED ADMISSIONS EXAMINATIONS THAT INCLUDED MATHEMATICS 32Comparisons by Type of Institution 33Comparisons by Control 33
Comparisons by Region 33
Comparisons by Enrollment Size 34
PLACEMENT EXAMINATIONS IN MATHEMATICS 34Statistical Findings 36
All institutions 36Principal differences, by category of institution 36
PROGRAMS OF ADVANCED STANDING IN MATHEMATICS 36Comparisons by Type of Institution 37Comparisons by Control 38Comparisons by Region 38Comparisons by Enrollment Size 38
UNDERGRADUATE HONORS PROGRAMS IN MATHEMATICS 39Statistical Findings 39Types of Program 39
Independent Study 39Admission Criteria 40General Observations 40The Program at Carleton College 40The Program at Wesleyan University 42The Program at Dartmouth College 43The Program at the University of Maryland 43
UNDERGRADUATE THESIS REQUIREMENTS 44Comparisons by Category of Institution 44
A COLLEGE-LEVEL MATHEMATICS COURSE AS A GRADUATION REQUIRE-MENT 46
INNOVATIONS IN MATHEMATICS PROGRAMS FROM 1950 TO 1961 46Comparisons by Type of Institution 47Comparisons by Control 47Comparisons by Region 48Comparisons by Enrollment Size. 48Frequency of Innovations per Institution 48
COMMENTS AND OBSERVATIONS ON UNDERGRADUATE PROGRAMS 48Number of Comments 48The Mathematics Department as a Service Department 48Updating the Mathematics Curriculum 49The Quality of Entering Freshmen 50Providing Suitable Mathematics Courses for General Education 52The Mathematics Faculty 52
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CHAPTER III. GRADUATE PROGRAMS
Page
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MASTER'S PROGRAMS IN MATHEMATICS 54Kinds of Degrees Awarded 54Credit Requirements in Mathematics 54Total Credit Requirements for the Degree 55Thesis Requirements 55Foreign Language Requirements 55Special Methods of Obtaining Degrees 55Final Comprehensive Examination Requirements 55"Minor" Requirements 56Provisions for a Minor in Mathematics 56Variations in Programs 56
MASTER'S PROGRAMS SPECIALLY DESIGNED FOR THE TEACHING OF MATHE-MATICS 57
Kinds of Degrees Awarded 57Credit Requirements in Mathematics 58Credit Requirements in Education Courses 58Total Credit Requirements for the Degree 58Thesis Requirements 58Foreign Language Requirements 59Special Methods of Obtaining Degrees 59Final Comprehensive Examination Requirements 59"Minor" Requirements 59Provisions for a Minor in Mathematics 59Variations in Programs 59
DOCTORAL PROGRAMS IN MATHEMATICS 60Kinds of Degrees Awarded 61Credit Requirements in Mathematics 61Total Credit Requirements for the Degree 61Examination Requirements 61Foreign Language Requirements 62"Minor" Requirements 62Special Methods of Obtaining Degrees 62Areas of Specialization and Numbers of Degrees 63
DOCTORAL PROGRAMS SPECIALLY DESIGNED FOR THE TEACHING OF MATHE-MATICS 63
Kinds of Degrees Awarded 63Credit Requirements in Mathematics 63Credit Requirements in Education Courses 64Total Credit Requirements for the Degree 64Examination Requirements 64Foreign Language Requirements 64"Minor" Requirements 65Special Methods of Obtaining Degrees 65Number of Degrees 65Special Programs for Preparing College Teachers of Mathematics 65Additional Preparation for Teaching Mathematics in College 65
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Statistical Findings 66Variations in Programs 66Teachers for Junior Colleges 66Kinds of Courses and Programs 66
CHAPTER IV. SOME RELATED FACTORS 68
ACTIVITIES DESIGNED TO STIMULATE INTEREST IN MATHEMATICS 68The Undergraduate Mathematics Club 68
Comparisons by category of institution 68Characteristics of club programs 68
Activities Other Than Clubs 69Comparisons by category of institution 69
INSTRUCTIONAL TECHNIQUES OTHER THAN THE STANDARD LECTURE 70Comparisons by Type of Institution 70Comparisons by Control 71Comparisons by Region 71Comparisons by Enrollment Size 71Less Frequently Used Techniques 72
INSERVICE EDUCATION OF MATHEMATICS TEACHERS 72National Science Foundation Institutes 72Other Institutes 72
Kind's of institutes and sponsorship 72Comparisons by category of institution 72
LIBRARY ORGANIZATION FOR MATHEMATICS 73Extent of Separate Libraries, by Categories 73Attitudes Toward Separate Libraries by Those Who Do Not Have Them 74General Comments 74
DIGITAL COMPUTERS ON COLLEGE CAMPUSES 74
CHAPTER V. SUMMARY 76
UNDERGRADUATE PROGRAMS 76
GRADUATE PROGRAMS 78Master's Programs in Mathematics 78Master's Programs Specially Designed Ior Teaching 79Doctoral Programs in Mathematics 79Doctoral Programs Specially Designed for Teaching 80Additional Preparation for College Teaching 81
SOME RELATED FACTORS 81
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APPENDIXESPage
APPENDIX A. MASTER'S PROGRAMS 84
In Mathematics: Institutions, program requirements, program characteristics, 196 L 84
Programs specially designed for teaching: Institutions, program requirements,program characteristics, 1961 90
Institutions with master's programs in statistics, 1961 95
APPENDIX B. DOCTOR'S PROGRAMS 96
In Mathematics: Institutions, credit requirements, areas of specialization, and num-ber of degrees, January 1958 to January 1961, inclusive 96
Programs specially designed for teaching: Institutions, kinds of degrees awarded,credit and foreign language requirements, and numbers of degrees from January1958 to January 1961, inclusive 99
Institutions at which doctor's degrees in mathematics may be earned through eveningand/or Saturday study, or through summer study 100
Institutions at which doctor's degrees specially designed for the teaching of mathe-matics may be earned through evening and/or Saturday study, or through summerstudy 100
APPENDIX C. COMPUTERS 101
Institutions with digital computers on campus in 1961; make and model number ofeach computer, and year of installation, if known 101
TABLESCHAPTER I
1.--Number of institutions to whicn questionnaires were mailed and percent ofusable responses; by type, control, region, and enrollment size: AggregateUnited States, 1960-61
CHAPTER II2.--Number and percent of entering freshmen enrolled in mathematics courses;
by level of courses, and by type, control, region, and enrollment size of in-stitution: Aggregate United States, Fall 1960
3.--Number and percent of institutions having specified curriculums with a majorin mathematics; by type, control, region, and enrollment size: AggregateUnited States, 1960-61
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10
4
15
17
4.--Percent of institutions having specified semester credit-hour requirementsin mathematics for a mathematics major in a liberal arts or general cur-riculum; by type, control, region, and enrollment size: Aggregate UnitedStates, 1960-61
Page
19
5.--Percent of institutions having specified semester credit-hour requirements inmathematics for a mathematics major in a mathematics-teaching curriculum;by type, control, region, and enrollment size: Aggregate United States, 1960 -61.. 19
6.--Percent of institutions having specified semester credit-hour requirements inmathematics for a mathematics major in statistical, actuarial, applied, and"other" curriculums; all institutions: Aggregate United States, 1960-61 20
7.--Percent of institutions having specified semester-hour requirements in pro-fessional education (education courses) for a mathematics-teaching curriculum;by type, control, region, and enrollment size: Aggregate United States, 1960 -61.. 20
8.--Percent of institutions awarding specified degrees in liberal arts or generalcurriculums with a major in mathematics; by type, control, region, and en-rollment size: Aggregate United States, 1960-61
9.--Percent of institutions awarding specified degrees in mathematics-teachingcurriculums with a major in mathematics; by type, control, region, and en-rollment size: Aggregate United States, 1960-61
10.--Percent of institutions awarding specified degrees in statistical, actuarial, ap-plied, and "other" curriculums with a major in mathematics; all institutions:Aggregate United States, 1960-61
11.--Percent of bachelor's degrees awarded in specified curriculums with a majorin mathematics; by type, control, region, and enrollment size: AggregateUnited States, July 1, 1959 to June 30, 1960
12. -- Number and percent of institutions offering freshman-year mathematicscourses, and number and percent of students enrolled in them: AggregateUnited States, Fall 1960
13.--Number and percent of institutions offering sophomore-year mathematicscourses, and number and percent of students enrolled in them: AggregateUnited States, Fall 1960
14.--Number and percent of institutions offering junior-year and senior-year mathe-matics courses, and number and percent of students enrolled in them: AggregateUnited States, Fall 1960
15.--Number and percent of institutions offering prerequisite instruction and per-cent offering specified courses; by type, control, region, and enrollment size:Aggregate United States, 1960-61
16.--Percent of institutions giving specified prerequisite courses that also gavecollege credit for them; by type, control, region, and enrollment size: Ag-gregate United States, 1960-61
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22
23
23
25
26
27
28
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30
17.--Number of students enrolled in prerequisite instruction and percent distribu-tion in specified courses in fall of 1960; by type, control, region, and enroll-ment size: Aggregate United States
18.--Number and percent of institutions requiring admissions examinations that in-clude mathematics and percent of usage of different examinations; by type,control, region, and enrollment size: Aggregate United States, 1960-61
Page
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33
19.--Number and percent of institutions administering a placement examination inmathematics, and percents related to pertinent characteristics of these exami-natt-its; by type, Fontrol, region, and enrollment size: Aggregate United States,1960-61 35
20.--Number and percent of institutions with programs of advanced standing in mathe-matics, extent to which credit is given for courses skipped, and factors uponwhich advanced standing is based; by type, control, region, and enrollment size:Aggregate United States, 1960-61
21.--Number and percent of institutions which require undergraduate theses of atleast some mathematics majors, and percent requiring them of specifiedcategories of students; by type, control, region, and enrollment size: Aggre-gate United States, 1960-61
22.--Percent of institutions making specified innovations in undergraduate mathe-matics programs between 1950 and 1961; by type, control, region, and enroll-ment size: Aggregate United States
CHAPTER III23.--Number of institutions offering particular doctoral specializations in mathe-
matics, and number of doctoral degrees awarded in each: January 1958 toJanuary 1961, inclusive
CHAPTER IV24.--Number and percent of institutions having undergraduate mathematics clubs on
campus, and percent of these institutions having specified clubs; by type, con-trol, region, and enrollment size: Aggregate United States, 1960-61
37
45
47
63
69
25.--Number and percent of institutions sponsoring one or more activities otherthan mathematics clubs, to stimulate interest in mathematics at the under-graduate level and percent of these institutions sponsoring specified activities;by type, control, region, and enrollment sip: Aggregate United States, 1960-61. 70
26.--Number and percent of institutions using one or more instructional techniquesother than the standard lecture, and percent using specific techniques; by type,control, region, and enrollment size: Aggregate United States, 1960-61
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71
CHAPTER I. INTRODUCTION
Mathematics represents the highest level ofabstract thought. To the mathematician, it isthe essence of orderliness, form, beauty, andelegance. Like the musician and the painter,the mathematician obtains from his work anemotional and esthetic satisfaction. For thisreason there is a considerable body of mathe-maticians who wish to be "pure mathemati-cians," that is, to study mathematics for itsown sake, with no immediate concern forpractical or useful results. Yet, history hasproved that many discoveries made throughpure study are later the basis for practicalresults.
Beyond its esthetic qualities, the utilitarianimportance of mathematics is so great that onlya country with a strong base in mathematicscan produce the technology that places anation among the leaders of the contemporaryworld. At present, when the United States andthe Soviet Union are vying for world leader-ship in space and nuclear energy, the im-portance of mathematics to both nations isenormous. Accordingly, in the Soviet Union,mathematics is a major part of the generalschool curriculum. It takes' up about one-sixthof the entire school curriculum and hastraditionally been a required subject in thegeneral education of all Soviet pupils in eachgrade. Although mathematics is equally es-sential to the defense, welfare, and prosperityof the United States, it receives less emphasisin the total school curriculum; it is not evena required subject in most senior high schools.
Traditionally, mathematics has been re-garded as a necessary basic tool for physicalscience and engineering. More recently, thevalue of mathematics in the biological sciences,the social sciences, and business has been in-creasingly recognized. For example, the 1960Annual Review of Physiology reported: 1
1Published by Annual Reviews, Inc., and the AmericanPhysiological Society. Vol. 22, Preface, pg. v.
1
"In 1929, of 76 papers selected at randomfrom the American Journal of Physiology,only 10.4 percent used mathematicalequations of any sort, the most complexofwhich had four variables. In 1959, of 91similar papers, 17.6 percent used equa-tions, two with six and one with thirteenvariables. Similar trends are to be seeneverywhere in the literature."
Statistics and, particularly, computing, bothheavily rooted in mathematics, are fields whichhave been undergoing tremendous expansion inrecent years. For the computing field alone,an official of the Association for ComputingMachinery recently estimated that 300,000computer programers would be needed inthe next 8- to 10-year period. Many ofthe positions will require college-levelmathematics, and for some of the dositionsa degree in mathematics will be highly desir-able.
In recent years, in terms of bachelor'sdegrees, mathematics has been the mostrapidly growing discipline among the majorfields of study. (See statistical data on mathe-matics degrees in the Foreword.) Concomi-tantly, there has been ferment in the mathe-matics curriculum at all levels. Many mathe-maticians feel that the traditional curriculumis outmoded and not in tune with newer ideasand emphases in mathematics. This feeling wasalready so strong in 1952 that the MathematicalAssociation of American established in thatyear a Committee on the Undergraduate pro-gram in Mathematics (CUPM). This Commit-tee has been active since its inception in de-veloping guidelines and recommendations formathematics programs for (1) teacher train-ing; (2) the physical sciences and engineering;(3) the biological, management, and socialsciences; and (4) pregraduate training forgraduate study in mathematics.
RECENT MATHEMATICSCURRICULUM STUDIES
In 1959, CU PM authorized Frederick Mostel-ler, Keewhan Choi, and Joseph Sedransk atHarvard University to survey the availabilityof mathematics courses to undergraduates inthe United States. 2 The survey was a catalogstudy of a stratified sample of institutions ofhigher education consisting of 216 four-yearcolleges and 54 junior colleges. The surveyattempted to answer the following questions:
1. What mathematics courses were avail-able to undergraduates throughout theUnited States?
2. What "modern" mathematics courseswere available to undergraduates?
3. What elementary mathematics courseswere available to undergraduates?
4. What were the mathematics prereq-uisites for enrollment in various phys-ics courses?
5. What were the regional differences inthe availability of mathematics coursesto undergraduates?
A second study, carried out in 1961 underthe sponsorship of CUPM and with financialsupport from the Ford Foundation, was re-ported in Undergraduate Mathematics Teach-ing: Settings and Staff, by Patricia Collette. 3A sample of 135 baccalaureate-granting schoolswas studied, with primary emphasis on in-stitutions which did not grant the Ph.D. inmathematics or statistics. The report containsinformation on certain characteristics ofundergraduate mathematics curriculums.
In 1959, John A. Schumaker conducted astudy of trends in the education of secondaryschool mathematics teachers for the period1920-58.4 His study involved 140 institutionsthroughout the United States that had programsfor the preparation of secondary school mathe-matics teachers. The principal sources of datawere the catalogs of the selected institutions.Schumaker's study reported the percentage of
2A Catalogue Survey of College Mathematics Courses,
CUPM, Mathematical Association of America, ReportNo. 4, December 1961. 37 pp.
3 Report No. 94, National Opinion Research Center,University of Chicago, October 1963. 252 pp.
4 "Trends in the Education of Secondary-School Mathe-matics Teachers," The Mathematics Teacher, Vol. 54,No. 6, October 1961. pp. 413-22.
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teacher-training institutions offering mathe-matics courses in selected years; the medianminimum number of semester-hours requiredof prospective mathematics teachers inselected years; and the percentage of institu-tions requiring various specified mathematicscourses of prospective teachers majoring inmathematics in selected years.
In the early 1960's, Lehi T. Smith soughtdata on curriculums for teacher-trainingthrough a questionnaire sent to the chairmanof the mathematics department at 213 collegesand universities engaged in teacher-training. 5His report gives data on the preparation ofmathematics teachers for elementary andsecondary schools; curriculums for teachersreturning for graduate work; and the influenceof curriculum-study groups on programs forteacher education.
PREPARATION OF THIS SURVEY
Pretest of the Questionnaire
A pretest of the questionnaire for the surveyreported in this book was made in a sample of90 institutions in May and June of 1960, andsome modifications were then made: open-ended questions were replaced by items whichwere more objective and simpler to answer,in most cases, by a "yes" or "no."
Determination of the Universe
It was decided early in the planning stagethat a universe rather than a sample studywould be made of institutions offering bache-lor's and higher degrees in mathematics.Junior colleges and such specialized schoolsas Bible colleges and seminaries, schools ofart or music, law schools, and schools ofbusiness were eliminated from the start. Thereport on Earned Degrees Conferred, 1958-59,issued by the U.S. Office of Education, pro-vided the list of most of the institutions towhich questionnaires were to be sent. The
5 "Curricula for Education of Teachers," The Ameri-can Mathematical Monthly, Vol. 70, No. 2, February 1963.pp. 202 -03.
remaining institutions, which were not in thislist because they did not grant a bachelor'sdegree in mathematics in 1958-59 or becausethey were not yet in existence, were deter-mined by examination of the Education Direc-tory, 1960-61: Part 3, Higher Education, alsoa publication of the U.S. Office of Education.The Directory was scanned for other institu-tions which should possibly be in the study,and college bulletins were checked to see ifinstitutions in question offered degrees inmathematics.
In this way, a total of 1,014 institutions(counting the 4-year degree-granting branchesof complex institutions as separate institu-tions) was obtained. In addition to these 1,014institutions, 55 others that did not awarddegrees in mathematics but that offered sub-stantial programs in mathematics were in-cluded, making a total of 1,069 institutions.
The questionnaire forms became availablefor distribution in the middle of January 1961.This caused a slight inconvenience for respon-dents at institutions that were on a quarterbasis; the questionnaire sought data on en-rollments in various courses as of Fall 1960,but these institutions were already in the Winterquarter. Except for enrollments, the data ofthis survey reflect programs in effect duringWinter and Spring of 1961.
Response Rate
The questionnaires were mailed out inJanuary 1961. In March and April, follow-upletters were mailed to non-respondents. Atthe same time, questionnaires which had beenreceived incompletely answered or in need ofcorrection were returned to the respondentsfor further attention (unless the questionableresponses could be obviated by reference tothe appropriate college catalog). June 15, 1961,was made the final cutoff date. By that time atotal of 877 usable questionnaires--out of the1,069 mailed out--had been received. These877 questionnaires provided the data for thestatistical analyses in this report.
A check of all graduate institutions in theEducation Directory, 1960-61: Part 3. HigherEducation, revealed that data on graduateprograms in mathematics were received frombetter than 95 percent of institutions having
3
master's programs in straight mathematics orin mathematics for teaching. A 100-percentcoverage was achieved for institutions offeringdoctoral programs in mathematics or in mathe-matics for teaching.
Categories Used for Analysis
To make the statisticalplete and comprehensivesurvey data were analyzedtion, by control, by region,size, as follows:
Type of Institution
UniversitiesLiberal arts collegesTeachers collegesTechnological schools
Control
Public institutionsPrivate institutions
Region
analysis as com-as possible, theby type of institu-and by enrollment
North Atlantic (Connecticut, Delaware,District of Colombia, Maine, Maryland,Massachusetts, New Hampshire, NewJersey, New York, Pennsylvania, RhodeIsland, and Vermont)
Great Lakes and Plains (Illinois, Indiana,Iowa, Kansas, Michigan, Minnesota,Missouri, Nebraska, North Dakota,Ohio, South Dakota, and Wisconsin)
Southeast (Alabama, Arkansas, Florida,Georgia, Kentucky, Louisiana, Missis-sippi, North Carolina, South Carolina,Tennessee, Virginia, West Virginia, andPuerto Rico)
West and Southwest (Alaska, Arizona,California, Colorado, Hawaii, Idaho,Montana, Nevada, New Mexico, Okla-homa, Oregon, Texas, Utah, Washing-ton, and Wyoming)
Enrollment size
Over 5,000 students1,500 to 5,000 students700 to 1,499 studentsUnder 700 students
The response rate for each of these clas-sifications is shown in table 1, which indicatesthat there were no significant variations. Thelowest response rate occurred among thesmallest institutions, particularly in the South-east region.
All the data relating to the graduate portionof the questionnaire and part of the under-graduate portion were processed manually.The rest of the data, which pertained chieflyto enrollments, were put on punch cards andprocessed by machine.
Copy of the Questionnaire Form
Note. Wherever possible, the :Major topicheadings in this book bear a cross-reference
4
Table 1.--Number of insti tUtions to which questionnaires were mailed andpercent of usable responses, by type, control, region, aM enrollmentsize: Aggregate United States, 1960-61
Category of lnntltutlon
Number ofinstitutions
to whichquestionnaireswere mailed'
Number ofinstitutions
whichreturned usablequestionnaires
Rate ofresponse
(1) (2) (3) (4)
All institutions 1,069 877 82
Type
Universities 158 139 88
Liberal arts colleges 701 570 81Teachers colleges 173 136 79Technological schools 37 32 86
ControlPublic 366 291 80Private 703 586 83
RegionNorth Atlantic 296 256 86Great Lakes and Plains 311 270 87Southeast 268 198 74Went end Southwest 194 153 79
Enrollment sizeOver 5,000 163 143 881,500-5,000 261 221 85700-1,499 306 250 82Under 700 339 263 78
1 For purposes of this survey 4-year brdnchee of complex institutionshave been counted as separate institutions.
to the relevant questionnaire item or sec-tion. The book does not take up all the itemsin the same order in which they appear onthe questionnaire.
OEOHE239 It0/001 DUDGET BUREAU NO. 5100321451479 APPROVAL EXPIRES 0/30/01
U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFAREOFFICE OF EDUCATION - DIVISION OF HIGHER EDUCATION
WASHINGTON 25, D. C.
r
SURVEY OF MATHEMATICS PROGRAMS IN INSTITUTIONSGRANTING BACHELOR AND HIGHER DEGREES
1 1 PLEASE COMPLETE
THIS COPY FOR YOUR FILE
AND RETURN BY JAN. 6;
if not, as soon thereafter
as possible
L
DATE: DEC. 15, 1960TO: HEAD OF MATHEMATICS INSTRUCTION
In recent years our country has become increasingly aware of the importance of mathematics in our nationalwelfare. The passage of the National Defense Education Act of 1958 and the expanded programs of the NationalScience Foundation are evidences that the Federal Government is interested in the strengthening and improvementof mathematics instruction in our educational institutions.
There has been a growing concern regarding the character and content of mathematics programs in collegesand universities. There has been a serious lack of information on a national basis relative to the status of, andtrends in, these programs. Among others, the Committee on the Undergraduate Program, The Mathematical Asso-ciation of America, has underscored the need for information of this kind. It is for these reosons that this study,Survey of Mathematics Programs in Institutions Granting Bachelor and Higher Degrees, is being undertaken. Thefindings should be useful to the mathematics community, to institutions in evaluating their own programs, tolegislative bodies, and to educators generally.
The members of the Committee on the Undergraduate Program as well as a number of chairmen of depart-ments of mathematics have assisted in the planning of this study. In the belief that the information sought isneeded and will serve a useful purpose, they have offered many valuable suggestions in the preparation of thequestionnaire instrument.
The questionnaire has been designed to facilitate responses as much as possible. Part One of the ques-tionnaire deals with undergraduate programs and general information about mathematics and mathematics educa-tion, and will involve all institutions. Part Two concerns graduate programs in mathematics and mathematicseducation, and will involve only the institutions which offer such programs.
Please complete the attached questionnaire at your earliest convenience. Two copies are enclosed, one tobe returned in the franked envelope which has been provided you, and the other for your files. Your cooperationwill be much appreciated. Each respondent will receive a copy of the report when it is published.
Please note that we would like to receive the enclosed Acknowledgment Card upon your receipt of thisquestionnaire. The Acknowledgment Card also affords you an opportunity to advise us of other persons in yourinstitution who should be contacted regarding its programs in mathematics (including mathematical statistics).
Enclosures
Sincerely yours,
Clarence B. LindquistChief for Natural Sciences and Mathematics
Division of Higher Education
GENERAL INSTRUCTIONSYou are to report on mathematics mograms (including
mathematical statistics) under your cognizance. Dota on pro.groms under the cognizance of other heads of your or othercompuses (if ony) of your institution will b. reported by theseother heads.
For the most part questions are asked relative to yourdepartment. In some institutions mathematics may not have odepartmental status. Even though this may be true in yourcose, respond as if your octivity had deportmentol status.
In case your answer to a question requires qualification,write it as near to the question as possible. Answer questionsaccording to practices and programs (curriculums) as they
exist at the time you fill out this questionnaire. However,indicate, where applicoble, any new developments under con-sideration which ore likely to be approved in the near future.
Please send along any descriptive moterial (printed orotherwise) about your mathemotics programs. It is plonned todescribe a sample of promising and interesting programs inthe bulletin forthcoming from this survey, as examples of whatcan be done and what is being done.
Coding numbers appear on many of the questions anditems. These ore used merely for the convenience of theOffice of Education in tabulating the returns.
5
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veal
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pret
est o
f thi
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estio
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ours
es li
sted
in c
olum
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the
follo
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g fo
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) of
the
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s) u
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and
Me
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sen
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) of
its
auth
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col
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(3)
...10
the
num
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iven
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the
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tota
l num
ber
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the
fifth
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five
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ven
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two
or m
ore
part
s).
In c
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rite
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toto
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of s
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nts
who
enr
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som
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all
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our
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in th
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pace
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ts w
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nrol
led
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cou
rse)
.w
rite
in 1
1.17
e. o
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ot fa
lling
into
thes
e ca
tego
ries.
For
the
purp
os o
f thi
s su
rvey
oon
side
t as
a si
ngle
For
6 G
OU
ts n
ot b
eing
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e .0
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cour
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stru
ctio
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o p
artic
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woo
of m
athe
mat
ics
whi
ch y
ou h
ove
divi
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up in
to tw
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mor
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rts.
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s gi
ven
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r pr
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stru
ctio
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the
fres
hman
yea
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hese
cou
rses
are
cov
ered
in in
fes
C. P
lace
a c
heck
(V
) in
thos
e re
moi
ning
col
umns
, (5)
thro
ugh
(12)
, whe
re s
uch
caur
ss a
re u
sual
ly to
ken
by
tion
9.st
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ts w
hose
prin
cipa
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dica
ted
by th
e he
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t the
top
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PIC
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ES
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OM
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RR
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S IN
MA
TH
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CE ..f /11 - Z . Ul A ci
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SE
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inst
ead
cif
chm
il
(1)
(2)
131
(Al
151
16)
(7)
(a)
(9)
(10)
It))
(12)
1C
olle
ge A
lgeb
ra
2T
rigon
omet
ry
3A
naly
tic G
eom
etry
IA
naly
tic G
eom
etry
and
Cal
culu
s
5M
oth.
Ana
lysi
s (A
com
bine
r/en
of d
e.,
trig
., Ic
.)
6B
asic
Con
cept
s (S
tecu
re, N
V, o
mM
c)
Gen
eral
Mo/
hern
enic
(B
aste
slti
lls,
oper
atio
ns, I
c.)
9E
a Ic
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9M
athe
mat
ics
of F
inan
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10E
lem
enta
ry S
tatis
tics
11M
oth.
for
Ele
men
tary
Sch
ool T
each
ers
Oth
er (
Spe
d ty
)
13
Oth
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Spe
cify
)
14O
ther
(S
pec+
Fr)
Tt < tu 3- to to 0 0 I 9 -";
1C
alco
los
2A
naly
tic G
eom
etry
and
Col
culo
t
3D
iffer
entia
l Equ
atio
ns
4S
tatis
tics
5M
athe
mat
ics
al F
inan
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6O
ther
(S
pec!
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Oth
er (
Spe
c+ ty
)
Oth
er (
Spe
c! ly
)
1A
dvan
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culo
s
2O
rdin
ary
Dill
lel E
quat
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3P
artia
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tial E
quat
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4T
heor
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Equ
atio
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5T
heor
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Mem
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6P
roba
bilit
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7le
athe
r...M
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. 'M
oder
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ontin
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rs
9C
ontin
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atrix
The
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11V
ecto
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naly
sis
St < or 2-
ce o E u,
t:t i St 0 E m
12 Complex Variables
13 College Cameo,
II Solid Ano lytic Geometry
15 Synthetic Proiect Iva Geometry
16 Analytic Protective Geometry
17 Hero Euclidean Geometry
18 Differential Geometry
19 Topology
20 Math. for Teachers filetheele, etc.)
21 Fours:lotions of Mathematics
22 liletory of Mathematics
23 Arithmetic for College Students
21 Numerical Analys'e
25 Programming far Digital COTFI.f
26 Calculus of Finite Difference.
27 Slothematic of Finance
28 Advanced Math. for Cosine." nn, Physic' me
29 Fourier Series 6 Bounday Veto* N.M...
30 Theoretical or Analytical Mechanics
31 Meows Thesis
32 Independent Study or Homes Course
33 Other (Specify)
II Other (Speclhl
35 Other (Specify)
(I) (2) (3) (dl' 15) (6) (7) (8) (9) (ID) (11) (12)
PAGE 2
DO
ES
YO
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INS
TIT
UT
ION
RE
QU
IRE
AN
AD
MIS
SIO
NS
EX
AM
INA
TIO
N O
F S
OM
E S
OR
T W
HIC
H IN
CLU
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SM
AT
HE
MA
TIC
S A
S A
PA
RT
OF
IT?
(Che
ck N
o at
Yes
boa
at r
ight
, and
If Y
es 1
. che
cked
, cho
ck a
pvIL
cotd
Item
s be
low
)
YE
S
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fo.g
., N
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ork
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te R
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AL
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Spo
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016
6D
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EN
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DM
INIS
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PLA
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ME
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N IN
YA
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EM
AT
ICS
? If
Yes
, cho
ck a
ppre
plof
e H
arm
end
ive
O th
roug
h': f
ollo
win
g:
NO
YE
S
PLA
CE
ME
NT
EX
AM
INA
TIO
N IS
TA
KE
N B
Y:
1/1
19A
LL E
NT
ER
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FR
ES
HM
EN
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YO
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TIT
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HA
VE
A P
RO
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AM
OF
AD
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NC
ED
ST
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DIN
G IN
MA
TH
. (Lc
., . p
rogr
amw
here
by e
stu
dent
, by
Ittoo
of h
oein
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mat
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f col
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hig
h sc
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of b
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sing
p...
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per
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em
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fhom
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a no
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ced
'hen
cour
se In
whi
ch 'h
ety
pica
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uden
t Is
perm
itted
to o
ntol
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yrm
, ...p
ond
to (
blen
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)
IS C
OLL
EG
E C
RE
DIT
, CO
UN
TIN
G T
OW
AR
D G
RA
DU
AT
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CR
ED
IT R
EQ
UIR
EM
EN
TS
, an
on th
eun
dent
's m
aned
for
five
in c
olle
ge w
hich
'he
shal
om w
as p
enei
ned
to .k
ip?
If ye
., ch
ock
belo
w,
o oP
Pro
foro
rm
NO
CO
UR
SE
S C
RE
DIT
S A
RE
GIV
EN
IN:
11)
40 C
OLL
EG
E A
LGE
BR
A
at T
RH
ON
OM
ET
RY
2A
NA
LYT
IC G
EO
ME
TR
Y
5C
ALC
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S
OT
HE
R (
Spe
cify
)
AD
VA
NC
ED
ST
AN
DIN
G IS
BA
SE
D U
PO
N:
YE
S
YE
S
(I)
3R
EC
OM
ME
NO
AT
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OF
HIG
H S
CH
OO
L
PR
OF
ICIE
NC
Y E
XA
M. M
AD
EA
DM
INIS
TE
RE
D L
OC
ALL
Y
47P
RO
FIC
IEN
CY
EX
AM
. BY
NA
TIO
NA
L A
GE
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Y. I
DE
NT
IFY
:
BO
TH
ER
(S
poci
fel
20 21
ST
UD
EN
TS
TA
KIN
G M
AT
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MA
TIC
S IN
CO
LLE
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FO
R T
HE
FIR
ST
TIM
E
ST
UD
EN
TS
In s
peci
al c
orvi
culu
nts
only
(o.
g., n
g1no
teln
g, p
hyni
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clon
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etc
OT
HE
R (
Spe
cify
)22 23 24 23
PLA
CE
ME
NT
EX
AM
INA
TIO
N T
ES
TS
FO
R A
KN
OW
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GE
OF
:
ALG
EB
RA
GE
OM
ET
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TR
IGO
NO
ME
TR
Y
OT
HE
R (
Spe
cify
)26
OB
JEC
TIV
ES
OR
PU
RP
OS
ES
OF
PLA
CE
ME
NT
EX
AM
INA
TIO
N A
RL:
27T
o de
term
ine
whi
ch u
ndo.
. hov
e O
w n
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srm
y m
athe
rnaN
cal k
is...
Ced
es to
und
erta
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egul
ar c
allin
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oot s
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ndw
hich
are
inad
oqua
mly
pre
pare
d to
do
BO
.
2aT
o du
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in. r
ho r
earh
emat
ica
I apt
itude
of t
he *
rado
n,
25 10
To
*got
ten
endu
e. in
to g
roup
s ha
ving
abo
ut th
e sa
me
abIll
ry le
vel
To
de4r
InIn
e rb
e sp
ocIll
c co
w. I
n w
hich
the
mel
on, w
ill b
o po
rmItt
ed to
em
ail
OT
HE
R (
Spe
clh.
)31
AR
E S
TA
ND
AR
DIZ
ED
OR
NA
TIO
NA
LLY
DIS
TR
IBU
TE
D E
XA
MS
US
ED
?
ON
OO
YE
S
IF Y
ES
, GIV
E N
AM
E O
F T
HIS
EX
AM
.
FU
RT
HE
R C
OM
ME
NT
, IF
AN
Y, O
N T
HE
PLA
CE
ME
NT
EX
AM
INA
TIO
N
9I
prer
eoul
nira
iner
ocrI
on In
mar
l.. (
for
cred
it w
with
out .
.div
er o
ff...1
by
your
inar
it.rt
ion
to c
anna
, the
dolic
lonc
ien
of s
tude
nt .h
o ar
e be
ginn
ing
to to
k co
llege
inot
hem
aric
s fo
r th
e fir
st r
im.?
(W
ho, c
onsH
mto
p om
aulIt
e In
urus
Hon
ear
l.. fr
om in
eiha
fion
to In
. Ind
ian.
Res
pond
acc
ordi
ng to
you
r pr
oclic
a in
this
reg
ard.
)I
nos,
...a
rm to
(e)
and
(b)
bel
ow:
NO
YE
S
CO
UR
SE
S G
IVE
N A
S P
RE
RE
QU
ISIT
EIN
ST
RU
CT
ION
CH
EC
K (
1)IF
OF
FE
RE
D
NU
MB
ER
OF
CR
ED
IT H
OU
RS
GIV
EN
TO
TA
L N
O O
FS
TU
DE
NT
S E
NR
OLL
ED
(F.1
1 19
60)
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r/9
PR
ER
EQ
UIS
ITE
INS
TR
UC
TIO
N IS
GIV
EN
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heck
app
ropr
iate
ono
( .)
1:
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0uA
RR
cEE
G, .
1./A
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IVi T
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s .7
050
If w
oman
ish.
iner
ucvi
on in
no,
offe
red
now
, hos
it b
een
offe
red
or a
ny ti
nvo
darin
g fiv
e pe
at m
n yo
ars
apa
rt o
f the
colle
ge in
arhe
arm
ic p
rogr
am?
NO
YE
S
If an
.... t
o "c
" I.
Ye.
, In
Ulu
yea
r an
d fo
r U
lu r
easo
n vr
m o
uch
prer
eosi
rmt.
inst
rocr
ion
an o
par
r of
rho
reg
ular
col
lege
mat
h pr
ogra
m d
isco
ntin
ued?
7D
OE
S Y
OU
R IN
ST
ITU
TIO
N H
AV
E A
SP
EC
IAL
PR
OG
RA
M, S
UC
H A
S A
N H
ON
OR
S P
RO
GR
AM
, FO
R S
IJP
EO
R U
ND
ER
GR
AD
UA
TE
MA
TH
EM
AT
ICS
ST
UD
EN
TS
?
NO
YE
S
IF Y
ES
, brie
fly d
escr
ibe
Al.
roam
, nam
ing
team
use
d, If
any
. Als
o, s
end
any
drm
ulpf
Ive
mat
eria
l you
may
hov
e on
rho
10D
OE
S Y
OU
R IN
ST
ITU
TIO
N H
AV
E A
RE
QU
IRE
ME
NT
TH
AT
EV
ER
Y S
TU
DE
NT
. In
orde
r to
gra
ds..
with
aba
ccol
owoo
m d
ean.
, mos
, hov
e to
ken
at h
oar
one
colle
ge -
leve
l nor
heaw
ric c
aws.
?(I
v I.
wel
l kno
wn,
of
LOO
M, f
hot I
nIn
siitu
lans
rep
air.
..em
sca
llego
and
in d
iffer
enr
prog
ram
. war
y. W
hat'
dI o
dto
be
know
n ha
re I.
who
thar
or
net t
hem
..lo
ts a
n In
orito
tionr
mid
e m
osim
men
t tha
t nen
. col
lege
-leve
lm
oIlm
maN
c be
'Ota
ni
NO
YE
S
11D
OE
S Y
OU
R D
EP
AR
TM
EN
T R
EQ
UIR
E A
N U
ND
ER
GR
AD
UA
TE
TH
ES
IS O
F A
NY
OF
YO
UR
MA
JOR
S?
(If Y
chec
k be
low
to o
ppro
pria
ro r
ho k
inds
of y
our
unifo
rm m
ajor
. for
who
m th
i, is
o r
orm
irom
enth
NO
YE
S
19A
LL M
AT
HE
MA
TIC
S S
TU
DE
NT
S
20H
ON
OR
ST
UD
EN
TS
ON
LY
31 O
TH
ER
(S
pset
s)
Is th
ere
an u
nder
grad
uate
mat
hem
atic
. clu
b on
you
r ca
mpu
s? If
yew
, Is
the
club
(C
heck
one
):N
DT
ES
2.
AF
FIL
IAT
ED
WIT
H P
I MU
EP
SIL
ON
?
25A
FF
ILIA
TE
D W
ITH
KA
PP
A M
UE
PS
ILO
N'
26A
LO
CA
L C
LUB
WIT
. NO
AF
FIL
IAT
ION
?
27O
TH
ER
(S
peci
fy)
TY
PE
S O
F P
RO
GR
AM
S (
Che
ck a
. (m
any
4800
(I)
NO
. OF
ME
ET
ING
S P
ER
AC
AO
. YR
.
28P
AP
ER
S G
IVE
N B
Y C
LUB
ME
MB
ER
S12
1 T
O
29T
ALK
S B
Y F
AC
ULT
Y M
EM
BE
RS
5 T
O 7
10S
PE
AK
ER
S F
RO
M O
UT
SIO
E T
HE
INS
TIT
UT
ION
14T
O 1
0
OT
HE
R (
Spe
cify
)15
MO
RE
TH
AN
10
One
s."
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wg
17:1
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":,.;
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)361
14;:3
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ot1.
:111
7:31
:Ze1
rg.:(
L'In
I,
YE
S
AT
HE
MA
TIC
S C
ON
TE
ST
S (
Spe
cs /0
VIS
ITIN
G L
EC
TU
RE
RS
NE
WS
LET
TE
RS
OR
BU
LLE
TIN
S T
O H
IGH
SC
HO
OLS
TO
PR
OV
IOE
LE
AO
ER
SH
IP A
NO
CR
EA
TE
INT
ER
ES
TIS
MA
TH
EM
AT
ICS
(5.
nd ..
.Pi.)
OT
HE
R (
Spe
cify
)
13D
oes
your
dep
artm
ent m
ake
us. o
f any
tech
niqu
e. e
ther
than
the
stan
dard
ar
trad
ition
al lo
ctut
e-re
cita
tion
tyst
ern?
If ye
s, p
lace
o c
heck
in th
e bo
o at
the
right
far
each
tech
niqu
e yo
u us
e:
OY
ES
LAR
GE
LE
CT
UR
E C
LAS
SE
S W
ITH
SM
ALL
QU
IZ S
EC
TIO
NS
tO 11 12 13 1. 15 16
LAR
GE
LE
CT
UR
E C
LAS
SE
S W
ITH
HE
LP S
ES
SIO
NS
Doe
s yo
ur d
epor
tmen
t hav
e an
y sp
ecia
l equ
ipm
ent a
. fac
ilitie
s fo
r m
athe
mat
ics
iner
uctio
n, th
e sc
hedu
li g
of w
hich
Is th
e re
spon
sibi
lity
of y
our
deP
ootm
oM?
If 74
, giv
e `n
lotm
etio
rt b
elow
:
YE
S
carn
pute
r(s)
. (H
ow m
any,
mak
e an
d no
de)
na.,
and
year
of i
nsta
llatio
n.If
none
, so
indi
ceta
.)
NO
. OF
DE
SK
CA
LCU
LAT
OR
S. I
F N
ON
ES
O IN
DIC
AT
E.
OT
HE
R fS
pect
irl
Doe
s yo
ur d
epor
tmen
t hav
e av
aila
ble
Ieq
uipa
mnt
or
fogi
litie
for
loat
het.
in tr
Con
thsc
hedu
ling
of w
hich
Is n
ot th
e re
spon
sibi
lity
of y
our
depa
rtm
ent?
If ye
s, g
ive
info
rmat
ion
belo
w.
YE
S
Hig
h-ag
ed c
ompu
ter(
s). (
How
man
y, m
aim
and
mod
el r
e., a
nd y
ear
of in
stal
latio
n.II
none
, so
indi
cate
.)
NO
. OF
DE
SK
CA
LCU
LAT
OR
S. I
F N
ON
E.
50 IN
DIC
AT
EO
TH
ER
(S
peci
fy)
hat e
peci
al e
quip
men
t or
faci
litie
do
you
not n
ow h
ove
but w
hich
ore
in y
aw im
iget
ent d
esire
d an
d ne
eded
?
OR
GA
NIZ
EO
PR
OG
RA
M O
F IN
OE
PE
NO
EN
T S
TU
OY
'CO
NT
INE
NT
AL
CLA
SS
RO
OM
. CO
UR
SE
BY
TE
LEV
ISIO
N
OT
HE
R B
RO
AO
CA
ST
TE
LEV
ISIO
N C
OU
RS
ES
CO
UR
SE
S B
Y C
LOS
ED
- C
IRC
UIT
TE
LEV
ISIO
N
CO
UR
SE
S B
Y F
ILM
OT
HE
R (
3844
,(7)
14D
oes
your
intti
tutio
n ha
ve a
libr
ary
sepa
rate
hor
n th
e m
ain
libra
ry?
(Che
ck o
ne o
f the
follo
win
g):
(I)
17Y
ES
, FO
R M
AT
HE
MA
TIC
S A
LON
E
YE
S. F
OR
MA
TH
EM
AT
ICS
AN
O (
E.G
.. S
CIE
NC
E. P
HY
SIC
S, E
TC
.)
(Whi
ch)
ALO
NE
NO
SE
PA
RA
TE
LIB
RA
RY
FO
R M
AT
HE
MA
TIC
S A
LON
E O
R M
AT
HE
MA
TIC
S IN
CO
MB
INA
TIO
N W
ITH
ON
EO
R M
OR
E O
F T
HE
SC
IEN
CE
S A
LON
E
If th
e Ite
m im
med
lote
ly p
rece
ding
I. c
hock
ed. d
oes
your
dep
ortm
ent d
esire
a li
brar
y ...
aort
ae fr
om th
e m
ain
libra
ry?
(Che
ck o
ne):
(I)
20Y
ES
. FO
R M
AT
HE
MA
TIC
S A
LON
E
21Y
ES
. FO
R M
AT
H. I
N C
OM
BIN
AT
ION
WIT
H O
NE
OR
MO
RE
OF
TH
E S
CIE
NC
ES
ALO
NE
22Y
ES
, BU
T N
O P
AR
TIC
ULA
R P
RE
FE
RE
NC
E B
ET
WE
EN
A S
EP
AR
AT
E L
IBR
AR
Y F
OR
MA
TH
EM
AT
ICS
ALO
NE
OR
ON
E F
OR
MA
TH
. IN
CO
MB
INA
TIO
N W
ITH
ON
E O
R M
OR
E O
F T
HE
SC
IEN
CE
S A
LON
E
23D
O N
OT
OE
SIR
E A
LIB
RA
RY
SE
PA
RA
TE
FR
OM
TH
E M
AIN
LIB
RA
RY
16O
mitt
ing
Nat
iona
l Sci
ence
Fou
ndat
ion
Inst
itute
s, d
id y
our
depa
rtm
ent o
ffer
any
prog
ram
, of a
t lea
st tw
o .w
oks
dura
tion,
eas
el**
d.ig
ned
for
the
in.:o
rric
e ed
ucat
ion
of m
athe
mat
ics
teac
hers
dur
ing
the
sum
mer
of 1
960
and
for
the
acad
emic
yea
r 19
59-6
0? (
Info
rmat
ion
on N
SF
Inst
itute
s w
ill b
. obt
aine
d ho
m th
e F
osm
dat'o
mak
i git
unne
cess
ary
for
you
to s
uppl
y 'h
i. in
form
atio
n-)
YE
S
If ye
s, c
heck
levI
(s)
for
whi
ch s
uch
iic
e
FO
R E
LEM
EN
TA
RY
TE
AC
HE
RS
ON
LY
35F
OR
JU
NIO
R H
IGH
TE
AC
HE
RS
ON
LY
9F
OR
SE
NIO
R H
IGH
TE
AC
HE
RS
ON
LY
%IL
O 42 43
b
46
FO
R E
LEM
EN
TA
RY
AN
O J
UN
IOR
HIG
H T
EA
CH
ER
S O
NLY
FO
R J
UN
IOR
HIG
H A
ND
SE
NIO
R H
IGH
TE
AC
HE
RS
ON
LY
FO
R E
LEM
EN
TA
RY
JU
NIO
R H
IGH
, AN
O S
EN
IOR
HIG
H T
EA
CH
ER
S
FO
R C
OLL
EG
IAT
E T
EA
CH
ER
S O
NLY
FO
R H
IGH
SC
HO
OL
AN
O C
OLL
EG
IAT
E T
EA
CH
ER
S
Che
ck th
e fin
anci
al s
ponr
hip
of th
e ;tr
ait,.
(Che
ck 0
. may
44
only
):
YO
UR
OW
N IN
ST
ITU
TIO
N
PR
IVA
TE
CO
RP
OR
AT
ION
OR
FO
UN
OA
TIO
N. G
rua
m. o
r re
nt o
f spo
nsor
ing
orga
nixa
tions
:
OT
HE
R (
Spe
c/8)
Che
ck ty
pe(s
) of
pro
grot
o(s)
°tie
red:
SU
MM
ER
INS
TIT
UT
E
2LA
TE
AF
TE
RN
OO
NS
. EV
EN
ING
S. O
R S
AT
UR
OA
YS
AC
AO
IC-Y
EA
R. F
ULL
-T
IME
INS
TIT
UT
OT
HE
R (
3444
1r0
PA
GE
3
17IN
NO
VA
TIO
NS
IN U
ND
ER
GR
AD
UA
TE
MA
TH
EM
AT
ICS
PR
OG
RA
MS
MC
P .0
50
It I.
deire
d to
kno
w th
e in
nova
tions
in u
nder
grad
uate
mat
hem
atic
s pr
ogra
ms
at y
our
intit
utio
n ei
ne. 1
950.
Bel
e,. e
relim
ed B
erne
paB
sibl
e ch
ange
s w
hich
may
hov
e oc
curr
ed.
Pla
ce a
che
ck (
) in
the
appr
opria
te b
oo fo
r ea
ch s
uch
inno
vatio
noc
curr
ing
at y
our
inst
itutio
n si
nce
1950
. AN
r go
ing
thro
ugh
the
chec
klis
t you
on
invi
ted
to m
ake
any
com
men
t you
des
ire r
egar
d:lo
g th
ee. i
nnov
atio
n, o
n on
e no
t con
tain
ed in
the
chec
klis
t bel
ow.
It w
ill n
ot h
o B
BB
BB
B 0
17 to
com
m.,'
on
hono
r an
d ad
vanc
ed
stan
ding
pro
gram
s si
nce
they
hav
e al
read
y be
en c
over
ed.
16O
BS
ER
VA
TIO
NS
AN
D C
OM
ME
NT
S
In th
e sp
oc b
elow
you
are
Invi
ted
to in
ok a
ny o
bser
eatio
n an
d co
mm
ents
you
wis
h ab
out t
he u
nder
grad
uate
mat
h-er
atite
pro
gram
of y
our
inst
itutio
n. P
artic
ular
ly d
..h.d
are
com
men
ts o
n su
cces
sful
met
hods
in d
ealin
g w
ith c
urric
ulum
prob
lem
s w
hich
cou
ld b
e of
hel
p to
eth
er.,
unso
lved
pro
blem
s, n
eede
d im
prav
erne
nts,
and
sug
gstr
ed w
ays
of b
ringi
ng a
bout
thes
e im
prov
emen
ts. (
Ext
end
thes
e re
read
. on
addi
tiona
l pag
e on
sub
mit
pert
inen
t sta
ff pa
pers
.)
Che
ck in
Dm
rig
htha
nd b
ox n
o ap
plic
able
:()
SN
AV
E IN
TR
OD
UC
ED
NE
W D
EG
RE
E P
RO
GR
AM
S
6N
AV
E S
UB
ST
AN
TIA
LLY
EX
PA
ND
ED
CO
UR
SE
OF
FE
RIN
GS
7H
AV
E IN
TR
OD
UC
ED
FR
ES
HM
AN
CO
UR
SE
S E
MP
HA
SIZ
ING
SU
CH
CO
NC
EP
TS
AS
ST
RU
CT
UR
E. L
OG
IC. S
ET
TH
EO
RY
. ET
C.
.H
AV
E P
RO
VID
ED
NE
W C
OU
RS
ES
CO
NS
IDE
RE
D A
PP
RO
PR
IAT
E F
OR
BIO
LOG
ICA
L A
NO
SO
CIA
L S
CIE
NC
EM
AJO
RS
aH
AV
E IN
TR
OD
UC
ED
A N
EW
PR
OG
RA
M. O
R H
AV
E S
UB
ST
AN
TIA
LLY
ALT
ER
ED
A P
RE
VIO
US
PR
OG
RA
M. F
OR
TH
E U
ND
ER
GR
AD
UA
TE
PR
EP
AR
AT
ION
OF
MA
TH
EM
AT
ICS
TE
AC
HE
RS
10N
AV
E P
RO
VID
ED
CO
UR
SE
S A
ND
INS
TR
UC
TIO
N L
EA
DIN
G T
O C
AR
EE
RS
IN D
AT
A P
RO
CE
SS
ING
AN
DC
OM
PU
TIN
G
IIN
AV
E IN
TR
OD
UC
ED
AN
HO
NO
RS
PR
OG
RA
M
12H
AV
E IN
TR
OD
UC
ED
AN
AD
VA
NC
ED
ST
AN
DIN
G P
RO
GR
AM
CO
MM
EN
TS
, IF
AN
Y, O
N IN
NO
VA
TIO
NS
CH
EC
KE
D A
BO
VE
. ALS
O M
EN
TIO
N A
ND
DIS
CU
SS
AN
Y IN
NO
VA
TIO
NS
INT
RO
-O
LIC
ED
SIN
CE
195
0 A
ND
NO
T L
IST
ED
AB
OV
E.
FO
R O
FF
ICE
US
E O
NLY
ISIt
ISIS
1716
1920
2122
2324
2526
2720
29D
O31
SD
A..
INF
OR
MA
TIO
N S
UP
PLI
ED
BY
NA
ME
AN
D T
ITLE
DA
TE
...
PA
RT
IIG
RA
DU
AT
E P
RO
GR
AM
S (
If yo
ur d
epar
tmen
t has
no
grad
uate
pro
gram
lead
ing
to a
deg
ree
in m
athe
mat
ics
or th
e te
achi
ng o
f mat
hem
atic
s, c
heck
her
e 0
and
OM
IT th
e re
mai
nder
of t
his
ques
tionn
aire
.
Pio
.ch
ock
In th
e bo
a at
the
right
hel
ow ta
r ea
ch ty
of p
rogr
am y
our
inst
itutio
n of
fer.
:(1
)G
EN
ER
AL
INS
TR
UC
TIO
NS
Far
eac
h ty
po o
f pro
gram
you
ha.
. cho
cked
at r
ho lo
ft,fo
r on
o pr
ogra
m .
rmlu
esto
d. T
han,
In th
e ...
pro
vide
d In
(111
.1n,
whe
re a
ppro
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SECTION C - DOCTORAL PROGRAM WITH A MAJOR INMATHEMATICS
SECTION D - DOCTORAL PROGRAM SPECIALLY DESIGNED FORTEACHING OF MATHEMATICS
NAME OF DOCTOR'S DEGREE CONFERRED (.g. PhD.. Sc.0.1 NAME OF DOCTOR'S DEGREE CONFERRED (.g, Ed.D., Ph.D.)
2NUMBER OF CREDIT HOURS IN MATHEMATICSREQUIRED BEYOND THE BACCALAUREATEI
NUMBER OF CREDIT HOURS IN MATHEMATICS2 REQUIRED BEYOND THE BACCALAUREATEI
MINIMUM TOTAL NUMBER OF CREDIT HOURS REQUIREDFOR THE DEGREE BEYOND THE BACCALAUREATEI
NUMBER OF CREDIT HOURS IN PROFESSIONAL EDUCATION (Education Course.)REQUIRED BEYOND THE BACCALAUREATE:
4EXAMINATIONS YOUR DEPARTMENT REQUIRES IN THE PARTIAL FULFILLMENT OFTHE DOCTORAL DEGREE (Check appropriate ons)
MINIMUM TOTAL NUMBER OF CREDIT HOURS REQUIREDFOR THE DEGREE BEYOND THE BACCALAUREATE:
29 ORAL PRELIMINARY OR QUALIFYING EXAMINATION
30 WRIT TEN PRELIMINARY OR QUALIFYING EXAMINATION
31 FINAL COMPREHENSIVE ORAL EXAMINATION
32 FINAL COMPREHENSIVE WRIT TEN EXAMINATION
33 ORAL EXAMINATION ON THESIS
3 OTHER (Specify)
IS COMPETENCY IN ONE OR MORE FOREIGN LANGUAGES REQUIRED?IF YES. GIVE INFORMATION REQUESTED BELOW: " NO "D.
EXAMINATIONS YOUR DEPARTMENT REQUIRES IN THE PARTIAL FULFILLMENT OFTHE DOCTORAL DEGREE (Check q3propriat ons)
29 ORAL PRELIMINARY OR QUALIFYING EXAMINATION
30 WRITTEN PRELIMINARY OR QUALIFYING EXAMINATION
3 I FINAL COMPREHENSIVE ORAL EXAMINATION
32 FINAL COMPREHENSIVE WRIT TEN EXAMINATION
33 ORAL EXAMINATION DN THESIS
3 OTHER (Specify)
37IN HOW MANY LANGUAGES ISCOMPETENCY REQUIRED,
In the table below are listed several foreign langtroges. Blank speedos ar provided forwriting the name of other languages not listed. Check each language which your departmentaccepts toward meeting language requirements and each langvag which in additionacceptable, Is also preferred.
LANGUAGEACCEPT- PRE
ABLE FERRED()
LEVEL OF FOREIGNLANGUAGE COMPETENCY
REQUIRED OF THE STUDENT ()o GERMAN 40 S 50 READING COMPREHENSION
b FRENCH 1 5 SI LISTENING COMPREHENSION
C RUSSIAN 2 7 52 ABILITY TO SPEAK
3 8 53 ABILITY TO WRITE
9 5 OTHER (Sr...CHO
COMMENTS, IF ANY, ON FOREIGN LANGUAGE REQUIREMENTS, INCLUDING POSSIBLESUBSTITUTIONS. IF THEY ARE PERMITTED:
6IN THE REQUIREMENTS FOR THE DEGREE IS A MINOR OR MINORS:Checkpn: REOUIREO p OPTIONAL 40 NOT PROVIDED FOR
6IS COMPETENCY IN ONE OR MORE FOREIGN LANGUAGES REQUIRED?IF YES, GIVE INFORMATION REQUESTEO BELOW: " "0 YES
37IN HOW MANY LANGUAGES ISCOMPETENCY REOUIREOT
In the table below ore listed several foreign languages. Blank spaces am provided farwriting the name of other languages not listed. Check each language which your deportmentaccepts toward meeting language requirements and each language which in addition to beingacceptable. Is also preferred.
LANGUAGEACCEPT
ABLE()PRE
FERRED(/LEVEL OF FOREIGN
LANGUAGE COMPETENCYREQUIRED OF THE STUDENT
GERMAN 40 5 50 READING COMPREHENSION
FRENCH 1 5 51 LISTENING COMPREHENSION
RUSSIAN 2 7 32 ABILITY TO SPEAK
3 e 53 ABILITY TO WRITE
9 5 OTHER (Specify)
COMMENTS, IF ANY, ON FOREIGN LANGUAGE REQUIREMENTS, INCLUDING POSSIBLESUBSTITUTIONS, IF THEY ARE PERMITTED:
7IS THIS DEGREE OBTAINABLE BY EITHER OR BOTH OF THE FOLLOWING METIIDOS?(Check If se)
'El RALONEcEzirc,ruf=CILCZ.SdAIT,U,R.O..ALgyZnfA.:1.-fre:,,(1.7.51Yds
7
AREAS OF SPECIALIZATION IN MATHEMATICS AND DOCTORAL DEGREES GRANTEDBY YOUR DEPARTMENT SINCE THE BEGINNING OF JANUARY 1958. (Check and givenumber of doctoral davits. granted In each rem, In space provided below):
IN THE REQUIREMENTS FOR THE DEGREE IS A MINOR OR MINORS:
oCn",,,ek REQUIRED p OPTIONAL NOT PROVIDED FOR
IS THIS DEGREE OBTAINABLE BY EITHER OR BOTH OF THE FOLLOWING METHODS?(Chock If so)
SUMMER EVENINGeEfV.IN,offered by
pS.TfU.13.Y. fAc1,-,01c4:.(ptcLud
AREA OF SPECIALIZATION () IF OFFEREI)1 NO. OF DR. DEGREES
7 ALGEBRA
8 ANALYSIS
9HOW MANY DEGREES IN DOCTORAL PROGRAMS SPECIALLY DESIGNED FOR THETEACHING OF MATHEMATICS HAVE BEEN GRANTED BY YOUR INST. SINCE THEBEGINNING OF JANUARY 195B?
NO. OF DEGREES
APPLIED MATHEMATICS
10 GEOMETRY
LOG IC
12 STATISTICS
13 TOPOLOGY
1 OTHER (Specify)
VARIATIONS, IF ANY. IN DOCTORAL DEGREE PROGRAMS IN MATHEMATICS
VARIATIONS, IF ANY, IN DOCTORAL DEGREE PROGRAMS SPECIALLY DESIGNED FOR THETEACHING OF MATHEMATICS
13
2
DOES YOUR INSTITUTION OFFER COURSES OR SEMINARS IN COLLEGE TEACHING OR OTHER ASPECTS OF HIGHER EDUCATION(..11-. hew In leash In cono9or problems of Moller sclueorloh, rho college curriculum, .4.)7 E NO ' YE5
IF YES,(Chock ono):
WITH REGARD TO STUDENTS MAJORING IN YOUR DEPARTMENT AND CONSIDERING CAREERS
REQUIRED OUT ENCOURAGED
IN COLLEGE TEACHING, ARE SUCH COURSES OR SEMINARS
REQUIRED AND NOT PARTICULARLY ENCOURAGED'M REQUIRED M NOT =NOT
IF SUCH COURSES OR SEMINARS ARE OFFERED, BRIEFLY DESCRIBE, THE PROGRAM OFFERED:
F Describe any innovations In products programs In mathematle and in Ow feachlno of officers. With lb. recent Increased emphasis an improved preponolon of teachers, If ismothernItica which bare taken place at your insfltutien Mace 1950. For In/ample, a new particularly desired to haw Information on any new programs which have been Introduced InPKISFIN. Of doctoral program mty hays bean aaponded to Include optIoni not offered before, or WIN area. Printed and mimeographed dscrIptions, II they exist, will ha much aOlwaclatml andsame optIons any hove boon terminated, or you may hare a special program for retired military may convnlently be ubstItuted In lieu of your written accounts of them.
FOR THE OFFICE OF EDUCATION USE ONLY
6 7 a s to It 17 IS 14 15 16 17 I. 19 go
CHAPTER II. UNDERGRADUATE PROGRAMS(Part I of the Questionnaire)
ENTERING FRESHMEN LEVELS INMATHEMATICS (ITEM 2)
The kind of preparation that students receivein high school has always concerned collegeauthorities, since they must gear their pro-grams to the level of the entering students. Inrecent years the importance of the level ofprevious training in mathematics has greatlyincreased because of the substantial changesin mathematics curriculums.
Of the 877 institutions that returned ques-
tionnaires, 855 answered the question of thenumbers of freshmen enrolled in Fall 1960 inthe three levels of introductory mathematics.Table 2 shows the data for all the respondinginstitutions, as well as for institutions in thevarious categories. Slightly over half (52 per-cent) of the entering freshmen in all 855institutions were enrolled at the level of collegealgebra, trigonometry, and courses of equiva-lent level. One-fourth were enrolled in coursesof lower level, and slightly fewer than one-fourth (23 percent) in courses of higher level.
Table 2.--Number and percent of entering freshmen enrolled in mathematics courses, by level of courses,and by type, control,, region, and enrollment size of institution: Aggregate United States,Fall 1960
(NOTE. 22 institutions of the 877 in the survey were unable to give the breakdown by level.)
Category of institutionNumber of
institutionsproviding
data
Entering freshmen enrolled in --
Courses of levelpreceding college
algebra andtrigonometry
College algebra,trigonometry,
and courses ofequivalent level
Analytic geometry,calculus, and
courses of equivalentlevel and above
Number Percent Number Percent Number Percent
(1) (2) (3) (4) (5) (6) (7) (8)
All institutions 855 76,161 25 159,183 52 70,324 23
TypeUniversities 134 25,972 20 71,962 55 32,724 25Liberal arts colleges 566 29,162 25 63,239 55 23,534 20Teachers colleges 125 18,192 47 16,994 44 3,863 10Technological schools 30 2,835 14 6,988 35 10,203 51
ControlPublic 274 55,283 31 96,774 53 29,124 16Private 581 20,878 17 62,409 50 41,200 33
RegionNorth Atlantic 247 14,274 18 32,036 41 31,170 40Great Lakes and Plains 267 21,930 24 51,227 55 19,459 21Southeast 191 23,069 30 45,314 58 9,279 12
West and Southwest 150 16,888 29 30,606 53 10,416 18
Enrollment sizeOver 5,000 140 31,418 22 75,247 53 36,174 25
1,500-5,000 214 26,264 28 46,088 50 20,593 22700-1,499 243 12,125 27 23,680 52 9,693 21Under 700 258 6,354 26 14,168 58 3,864 16
15
2
Comparisons by Type of Institution
In the universities more than half (55 per-cent) of the freshmen were enrolled in basiccollege algebra and trigonometry or in coursesof equivalent level; a quarter were enrolled inmore advanced courses, and a fifth in lessadvanced courses. At liberal arts colleges thepercentages were about the same, except thata quarter of the freshmen were enrolled inthe less advanced mathematics and a fifth inthe more advanced. Fewer than 10 percent ofthe freshmen at teachers colleges were en-rolled in courses of a level equivalent toanalytic geometry and calculus, whereas nearlya half (47 percent) were in courses at a levelbelow college algebra and trigonometry and 44percent were enrolled in basic college courses.At the technological institutions, as would beexpected, 51 percent of the entering freshmentook advanced mathematics courses, 35 per-cent took basic college courses, and only 14percent took the lower-level courses.
There seem to be several reasons for thevariations among the different types of insti-tution. Undoubtedly the large number of stu-dents who are preparing to be elementaryschool teachers and who consequently take onlyelementary mathematics accounts for the highpercentage of students at the lowest level ofmathematics at the teachers colleges. On theother hand, higher admission requirements inmathematics at technological institutions elim-inate many who are only qualified to take thelower-level courses. Furthermore, these in-stitutions, as well as the colleges of engineer-ing and technology within universities, natu-rally attract those who are both gifted andrelatively well-educated in mathematics.
Comparisons by Control
Variations between public and private in-stitutions may stem from the fact that thereare so many teachers colleges among thepublic institutions reporting. The teacherscolleges, as we have seen, had the highestpercentage of freshmen in the lower-levelcourses and the lowest percentage in thehigher-level ones. Private universities as agroup have far higher admissions require-ments than public universities, which are
often compelled by law to take almost anyapplicant.
A little over half (53 percent) of the enteringfreshmen at public colleges were enrolled incourses at the college algebra-trigonometrylevel, about a third in the lower-level courses,and a sixth in higher-level courses. Privateinstitutions showed just the reverse--a thirdof the entering freshmen were in the higher-level courses, a sixth in the lower-level.
16
28
Comparisons by Region
Geographic regions showed striking differ-erences. The North Atlantic region had rela-tively low percentages of freshmen in coursesat the lower and basic college levels: 40 per-cent of freshmen entering colleges in thisregion took advanced courses. In fact, 32institutions (mostly private), or about 1 out ofevery 8, in the region offered no courseslower than analytic geometry or calculus.This is in striking contrast to the Southeastregion, where only 12 percent of enteringfreshmen took advanced courses. Only 2 in-stitutions in this region offered no mathe-matics below the level of analytic geometryand calculus.
Comparisons by Enrollment Size
The size of enrollment seems important onlyat the extremes. In 1960, the largest schoolsenrolled only 22 percent of their incomingfreshmen in the lower level courses. On theother hand, the smallest schools enrolled 58percent of their freshmen in the basic collegecourses and only 16 percent in advancedcourses. These were the largest and thesmallest for all four enrollment-size groups.
CHARACTERISTICS OF CURRIC-ULUMS FOR THE MATHEMATICS
"MAJOR" (ITEM 3)
Kinds of Curriculum
Since a liberal arts curriculum and a gen-eral curriculum serve basically the samepurpose and are accordingly essentially the
same, the two were combined on the question-naire into the one category "liberal arts orgeneral. "
Table 3 gives the number and percent ofvarious categories of institutions having thedifferent curriculums, as reported by therespondents, who were themselves the judgesof whether they offered the curriculums listed.Thus, in interpreting the table, one shouldallow for possible lack of uniformity in re-porting. For example, one institution mightoffer what it calls an applied mathematics cur-riculum; another institution might offer ap-proximately the same curriculum, but mightconsider it an option within the liberal artsor general curriculum. The "mathematics-teaching" curriculum is another case in point.Some institutuions offer a unique curriculumfor teaching mathematics which is differentfrom their liberal arts or general curriculum.
Undoubtedly, such a curriculum was listed asmathematics-teaching by these respondents.On the other hand, some institutions, princi-pally liberal arts schools, that offer a liberalarts or general curriculum that is frequentlytaken by teacher trainees apparently alsolist it as a mathematics-teaching curriculum.
The liberal arts or general curriculum wasby far the most common kind, being offeredby 87 percent of the 877 participating institu-tions. Fifty-nine percent reported having amathematics-teaching curriculum. At mostof the institutions that did not report havingsuch a curriculum, students could neverthe-less prepare to be mathematics teachers bytaking the regular mathematics curriculumand the required number of education coursesfor teacher certification. Of all the types ofparticipating institutions, the only type atwhich a student generally could not study to
Table 3.--Number and percent of institutions having specified curriculums with a major in mathematics, by type, control, region, andenrollment size: Aggregate United States, 1960-61
(Note. L = less than 0.5 but not zero percent)
Category of
institutions
Number ofinstitutionsin category
Number and percent of institutions offering:
Liberal arts orgeneral
curriculums
Mathematics-teaching
curriculums
Statisticalcurriculums
Actuarialcurriculums
Appliedcurriculums
Othercurriculums
No. Percent No. Percent No. Percent No. Percent No. Percent No. Percent
All institutions 877 759 87 521 59 27 3 7 1 36 4 16 2
TypeUniversities 139 126 91 83 60 22 16 5 4 16 12 8 6
Liberal arts colleges 570 545 96 329 58 5 1 2 L 13 2 6 1
Teachers colleges 136 68 50 103 76 0 0 0 0 1 1 1 1
Technological schools 32 20 63 6 19 0 0 0 0 6 19 1 3
ControlPublic 291 214 74 219 75 17 6 5 2 18 6 9 3
Private 586 545 93 302 52 10 2 2 L 18 3 7 1
RegionNorth Atlantic 256 195 76 120 47 7 3 1 L 15 6 7 3
Great Lakes and plains 270 245 91 197 73 11 4 5 2 8 3 4 1
Southeast 198 181 91 110 56 3 2 0 0 2 1 1 1
West and Southwest 153 138 90 94 61 6 4 1 1 11 7 4 3
Enrollment sizeOver 5,000 263 125 87 93 65 23 9 5 2 18 7 9 3
1,500-5,000 250 185 84 143 65 1 L 1 L 11 4 4 2
700-1,499 221 222 89 146 58 2 1 0 0 4 2 2 1
Under 700 143 227 86 139 53 1 1 1 1 3 2 1 1
17
29
become a secondary school mathematicsteacher was the college devoted exclusivelyto engineering.
Statistical, actuarial, and applied curric-ulums are not common. They were offered byonly 3 percent, 1 percent, and 4 percent,respectively, of the reporting institutions. Six-teen institutions reported having curriculumsother than those specifically listed in thequestionnaire. These were identified for themost part as "engineering mathematics."
Liberal arts or general curriculums, whichwere of course more common in liberal artscolleges than -in other types of institutions,were also more common in private than inpublic institutions. Mathematics-teaching cur-riculums were most popular among teacherscolleges, public institutions, institutions ofthe Great Lakes and Plains region, and thelarger institutions. Most of the statisticaland actuarial curriculums reported were of-fered in large universities. Such specializedcurriculums as statistics, actuarial science,and applied mathematics are probably difficultto offer in a small institution.
Credit-Hour Requirements for aMathematics Major
This survey revealed that colleges anduniversities differ greatly in credit-hour re-quirements for a major in mathematics. Often,when there was more than one curriculum atan institution, the requirement for a mathe-matics major differed between curriculums.Institutions commonly specified certain re-quired courses for a major, while allowingthe remaining credits to be earned from aselection of additional courses. A few institu-tions reported requirements of a specificnumber of credits beyond a certain level, suchas calculus.
Credit units varied among the colleges anduniversities. A majority of them operated onthe semester-hour basis, a considerable num-ber on the quarter-hour basis, and a muchsmaller number on some other basis such ascourse unit or trimester unit. Since thesemester-hour unit was by far the most com-mon, the data reported in other units wereconverted by the author to semester-hourswherever possible. In the case of quarter-
18
30
hours, this was done by multiplying by two-thirds and then rounding to the nearest integer.Data that could not be converted were re-ceived from only a few institutions, and wereomitted from the tabulations.
Liberal arts or general curriculum.--Table4 shows that the most common mathematicsrequirement for a liberal arts or generalcurriculum was in the category of 29-31semester-hours (usually the requirement is30). Of all the institutions that providedusable data, 27 percent had this requirement,35 percent required less than this, and 38percent required more. A little less thanone-fifth (19 percent) of the institutions had arequirement in the 23-25 range and about one-seventh (14 percent) in each of the 26-28 and32-34 ranges. Sixteen (2 percent) of 716 in-stitutions required 22 or fewer semester-hours and 9 (1 percent) 47 or more.
An analysis of the data by type of institutionshows that technological institutions and uni-versities had generally higher requirementsfor the major. than did liberal arts collegesor teachers colleges. Seventy-eight percentof the technological schools and 52 percentof the universities had requirements of 32 ormore credits, compared to 35 percent of theliberal arts colleges and 33 percent of theteachers colleges.
Private institutions tended to have lowercredit requirements than did public institu-tions. Thirty-nine percent of the liberal artscolleges had a requirement of 28 or fewercredits compared to 24 percent of the publicinstitutions. The North Atlantic region and theWest and Southwest region had generallylarger requirements than did the Great Lakesand Plains region or the Southeast region.Comparisons by enrollment size of institutionsshow a direct relationship between size ofinstitution and number of credits required forthe mathematics major. Generally speaking,the largest institutions had the larger creditrequirements, and the smallest institutions,smaller credit requirements.
Mathematics-teaching curriculum.--A totalof 521, or 59 percent, of the 877 respondinginstitutions reported having a mathematics-teaching curriculum, although, as mentionedearlier, these were not the only schools at
Table 4.--Percent of institutions having specified semester credit-hour requirements in mathematics for n mnthemntics major in n liberal arta or generalcurriculum, by type, control, region, and enrollment size: Aggregate United States, 1960-61
(NOTE. Credit-hour requirements reported in quarter-hours have been converted to semester-hours by multiplying by two-thirds and rounding to the nearestinteger. Data from institutions using courses as credit units were not usable.)
Category ofinstitution
Number ofinstitutionshaving thiscurriculum
Number incolumn 2 asn percentof all
institutionsin category
Number ofinstitutionsprovidingusable data
Percent ofinstitutionsprovidingusable data(column 4 +column 2)
Percent' of institutions in column 4 having a semestercredit-hour requirement in mathematics of:
22
orlean
23-25 26-28 29-31 32-34 35 -37 38-40 41-43 44-4647orover
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
All institutions 759 87 716 94 2 19 14 27 14 12 6 3 2 1
UniversitiesType
126 91 120 95 2 14 10 23 18 8 15 6 3 2
Liberal arts colleges 545 96 512 94 2 21 14 29 14 13 4 2 1 1
Teachers colleges 68 50 66 97 6 14 17 30 10 20 2 0 0 1
Technological schools 20 63 18 90 0 6 17 0 0 6 22 17 22 11
ControlPublic 214 74 208 97 2 11 11 30 15 15 10 4 1 1
Private 545 93 508 93 2 22 15 26 14 11 5 2 2 1
RegionNorth Atlantic 195 76 184 94 3 14 11 24 14 15 8 5 4 3
Great Lakes and Plains 245 91 230 94 3 25 15 29 14 10 2 0 1 2
Southeast 181 91 175 97 2 19 18 29 14 13 3 2 0 1
West and Southwest 138 90 127 92 2 13 9 27 13 12 17 4 2 1
Enrollment sizeOver 5,000 125 87 119 95 2 13 8 24 20 8 15 3 4 3
1,500-5,000 185 84 182 98 1 12 15 24 14 20 7 4 1 1
700-1,499 222 89 207 93 3 22 14 30 13 12 2 1 1 1
Under 700 227 86 208 92 3 25 15 29 12 8 5 1 1 1
Detail may not add to 100 because of rounding.
which a student could prepare to become asecondary school mathematics teacher.
Table 5 shows a bimodal distribution in thesemester-hour requirements in mathematics.For all institutions combined, 28 percent hada requirement in the 29-31 credit range, and26 percent in the 23-25 credit range. Com-pared to liberal arts of general curriculums,
mathematics-teaching curriculums had gen-erally less credit-hour requirements. Only 21percent of the mathematics-teaching curric-ulums had a semester-hour requirement of32 hours or more, compared to 38 percent ofthe liberal arts or general curriculums.
Excluding the few (6) technological schools,teachers co 11 eges as a group had the
Table 5.--Percent of institutions having specified semester credit-hour requirements in mathematics for a mathematics major in a mathematics-teaching curri-culum, by type, control, region, and enrollment size: Aggregate United States, 1960-61
(NOTE. Credit hour requirements reported in quarter -hours have been converted to semester-hours by multiplying by two-thirds and rounding to the nearestinteger. Data from institutions using courses as credit units were nt usable.)
Category ofinstitutions
Number ofinstitutionshaving thiscurriculum
Number incolumn 2 asa percentof all
institutions
in category
Number ofinstitutionsprovidingusable data
Percent ofinstitutionsprovidingusable data(column 4 4-column 2)
Percent' of institutions in column 4 having a semestercredit-hour requirement in mathematics of:
22or
less23-25 26-28 29-31 32-34 35-37 38-40 41-43 44-46
47orover
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
All institutions 521 59 495 95 11 26 15 28 10 7 2 1 1 0
TypeUniversities' 83 60 76 92 12 21 22 25 11 5 1 0 1 1
Liberal arts colleges 329 58 313 95 11 28 14 27 10 6 2 1 1 0Teachers colleges 103 76 100 97 9 22 12 33 12 10 2 0 0 0Technological schools 6 19 6 100 17 . 0 0 0 0 0 33 0 50 0
ControlPublic 219 75 208 95 10 .20 14 33 9 9 3 0 1 1
Private 302 52 287 95 11 30 15 24 12 5 1 1 1 0
RegionNorth Atlantic 120 47 111 93 9 23 13 36 9 7 1 1 2 0
Great Lakes and Plains 197 73 190 96 9 27 17 25 13 6 2 0 1 1
Southeast 110 56 107 97 16 31 14 22 9 6 0 2 0 0
West and Southwest 94 61 87 93 10 18 13 30 8 9 7 1 3 0
Enrollment sizeOver 5,000 93 65 86 93 9 15 21 27 11 8 5 0 3 1
1,500 -5,000 143 65 137 96 11 22 14 30 7 12 2 1 2 0
700-1,499 146 58 139 95 11 32 11 31 9 4 1 1 0 0
Under 700 139 53 133 96 10 30 15 23 15 4 2 1 0 0
' Detail may not add to 100 because of rounding.' More than 83 of the 139 responding universities actually had a mathematics-teaching curriculum. Many of these curriculums were not reported because they
were under the control of the school of education, not of the mathematics department.
19
31
Table O.Percent. of institutions having specified semester credit-hour requirements in mathematics for a mathematics major in ntatintienl, nctunrinl,applied, and "other" curriculums, all institutions: Aggregate United States, 1960-61
(NOTE. Credit-hour requirements reported in quarter-hours have been converted to semester -hours by multiplying by two-thirds and rounding to the nearestinteger. Dnta from institutions using courses an credit units were not unable.)
Kind ofcurriculum
Number ofinstitutionshaving, thiscurriculum
Number incolumn 2 ana percentof all
institutions
Number ofinstitutionsprovidingusable data
Percent ofinstitutionsprovidingunable datacolumn 4 -i-
column 2)
Percent' of institutions in column / having n semestercredit-hour requirement in mathematien of:
22or
less23-25 26-28 29-31 32-34 35-37 38-40 41-43 44-46
47or
over
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
SU:Untie:11ActuarialAppliedOther (Engineering,
etc.)
27736
16
3
1
4
2
226
32
15
828689
94
14
173
0
9176
0
14
176
27
5
013
7
273313
0
006
13
14
1722
20
14
013
7
006
20
5
013
7
' Detail may not add to 100 because of rounding.
highest credit requirements for mathematics-teaching curriculums. Public institutions gen-erally had slightly higher requirements thandid private institutions. In a comparison byregions, the North Atlantic region was highestand the Southeast region lowest. In a com-parison by enrollment size, the largest in-stitutions generally had the largest require-ments and the smallest institutions the lowestsemester-hour requirements in mathematics.
Statistical, actuarial, applied, and "other"curriculums.--Relatively few institutions re-ported having statistical, actuarial, applied,or "other" curriculums (see table 6). The few"other" curriculums were primarily "engi-neering mathematics." Because the numbersof statistical, actuarial, applied, or "other"
curriculums were rather small, breakdownof data by various categories of institutionsis not given as in the case of the liberalarts and mathematics-teaching curriculums.Credit-hour requirements in mathematicswere generally higher in applied or engineer-ing mathematics curriculums than in any otherkind of curriculum with a major in mathe-matics.
Credit-Hour Requirements inProfessional Education
The statistical findings representing 469mathematics-teaching curriculums are pre-sented in table 7. Because the semester-houris the most common type of credit unit, other
Table 7.--Percent of institutions having specified semester-hour requirements in professional education (education courses) for a mathematics-teachingcurriculum, by type, control, region, and enrollment size: Aggregate United States, 1960-61
(NOTE. Credit-hour requirements reported in quarter-hours have been converted to semester-hours by multiplying by two-thirds and rounding to the nearestinteger. Data from Institutions using courses as credit units were not usable.)
Categoryof
institution
Number ofinstitutionshaving thiscurriculum
Number incolumn 2 asa percentof all
institutionsin category
Number ofinstitutionsprovidingusable data
Percent ofinstitutionsproviding
usable data(column 44-column 2)
Percent' of institutions in column 4 having a semestercredit-hour requirement in professional education of:
7or
less8-10 11-13 14-16 17-19 20-22 23-25 25 -28 29-31
32or
over
(1) (2) (3) (4) (5) i (6) (7) (8) (9) (10) (11) (12) (13) (14) (lb)
All institutions 521 59 469 90 1 2 2 4 32 25 22 6 3 4
Type
Universities' 83 60 73 88 0 6 4 4 25 22 22 4 7 7Liberal arts colleges 329 58 297 90 1 1 2 5 38 25 19 5 3 2Teachers colleges-- 103 76 93 90 0 0 2 1 15 28 29 14 3 8Technological schools 6 19 6 100 0 17 0 17 50 0 17 0 0 0
ControlPublic 219 75 198 90 1 3 2 3 17 27 26 10 7 6Private 302 52 271 90 1 1 2 6 42 23 19 4 1 2
RegionNorth Atlantic 120 47 101 84 0 2 2 5 47 14 10 8 5 8Great Lakes and Plains 197 73 182 92 1 1 2 4 39 34 15 3 1 1Southeast 110 56 102 93 2 0 2 4 21 22 36 5 4 5West and Southwest 94 61 84 89 0 5 2 4 11 21 33 14 6 4
Enrollment sizeOver 5,000 93 65 81 87 0 7 4 6 26 25 17 5 5 51,500 -5,000 143 65 132 92 1 1 3 1 22 20 30 11 6 5700-1,499 146 58 130 89 0 0 1 6 32 31 19 6 3 2Under 700 139 53 126 91 2 0 2 5 44 23 19 2 0 2
'Detail may not add to 100 because of rounding.' More than 83 of the 139 responding universities actually had a mathematics-teaching curriculum. Many of these curriculum were not reported because they
were under the control of the school of education, and not of the mathematics department.
20
32
credits were converted, if possible, tosemester-hours. As in credit-hour require-ments in mathematics, there was variationamong the institutions in the credit require-ments in professional education. For thelatter, however, there was a concentration;almost four-fifths (79 percent) of all institu-tions had a requirement in the range of 17 to25 credits. Almost one-third (32 percent) hada requirement in the 17-19 range (usually 18semester-hours). The median requirement forall institutions was in the 20-22 range.
Comparison of the institutions by type,shows that teachers colleges, as expected, hadgenerally the highest professional educationrequirements. In fact, the mode for teacherscolleges was in the 23-25 range, whereas themodes for universities and liberal arts col-leges were both in the 17-19 range. Public in-stitutions had, on the average, higher pro-fessional education requirements than didprivate institutions. Institutions in the South-east region and in the West and Southwestregion generally had higher requirements thandid institutions in the North Atlantic regionand in the Great Lakes and Plains region.Institutions with enrollments between 1,500and 5,000 students had generally higher re-quirements in professional education than didinstitutions of any other size - category.
A total of 120 respondents, 97 of themliberal arts institutions, reported their pro-fessional education requirements for prospec-tive teachers following a liberal arts curric-ulum. Because of this small number a tablewith detailed breakdowns, like table 7, is notpresented here. Suffice it to say, the require-ment associated with liberal arts or generalcurriculums tended to be lower than the re-quirement associated with the mathematics-teaching curriculum. Twenty-six percent ofinstitutions reporting on the liberal arts ofgeneral curriculum, reported a requirementof 16 semester-hours or less of professionaleducation, compared to a corresponding figureof 9 percent for institutions reporting on amathematics-teaching curriculum.
Kinds of Degrees Awarded
There is no uniformity among colleges anduniversities in the kinds of degrees awarded tostudents majoring in mathematics. For onething mathematics has the attributes of both ahumanity and a science. Consequently, someregard the bachelor of arts, and some thebachelor of science, as the more appropriatedegree. Many institutions decree only one:and of degree for the whole institution, andat some public institutions the kind of degreethat may be awarded is determined by statute.
While the bachelor of arts (B. A.) and thebachelor of science (B.S.) are the mostcommonly offered, the degree of bachelor ofscience in education (B.S. in Educ.) is notuncommon for mathematics-teaching curric-ulums.
Liberal arts or general curriculum.--Atotal of 746 institutions, or 98 percent of thosehaving a liberal arts or general curriculum,identified the degree to which the curriculumled (see table 8). More than half (55 percent)of the institutions awarded only a B.A. degreefor such a curriculum; 21 percent, only a B.S.;and 24 percent, either a B.A. or B.S.
As would be expected, the B.A. degreepredominated at the liberal arts colleges; at61 percent of them, this was the only under-graduate degree awarded. Similarly, at 16, or80 percent, of the technological schools re-porting, the B.S. was the only degree awarded.Because so many liberal arts institutions areprivately controlled, the percentage of privateinstitutions conferring B.A. degrees only (60percent) was much higher than the corre-sponding percentage of public institutions (42percent). Awarding of only the B.A. degree forthis curriculum was most prevalent in theNorth Atlantic region (66 percent) and leastso in the Southeast region (42 percent). Com-parison of institutions by enrollment sizeshows that the smaller institutions tended tooffer only the B.A. degree more commonly thandid the larger institutions.
21
33
Table 8.--Percent of institutions awarding specified degrees in liberal arts or general
curriculums with a major in mathematics; by type, control, region, and enrollmentsize: Aggregate United States, 1960-61
Category of institution
Number ofinstitutionsproviding
data
Response rate(number incolumn 2 -:-
number ofinstitutionshaving thiscurriculum)
Percents of institutions in column2 in which this curriculum leE...1s
to a--
B.A. only B.S. only B.A. or B.S.
(1) (2) (3) (4) (5) (6)
All institutions 746 98 55 21 24
TypeUniversities 124 98 41 24 32Liberal arts colleges 534 98 61 18 21Teachers colleges 68 100 44 23 33Technological schools 20 100 10 80 10
ControlPublic 211 99 42 28 28Private 535 98 60 19 21
RegionNorth Atlantic 192 98 66 18 16Great Lakes and Plains 239 98 57 17 26Southeast 179 99 42 32 26West and Southwest 136 99 54 20 26
Enrollment sizeOver 5,000 121 97 45 21 341,500-5,000 ....... 185 100 45 29 24700-1,499 219 99 57 18 25Under 700 221 97 66 19 15
1 Instead of either a B.A. or B.S. degree, two institutions awarded a B.S. in Educa-tion degree and another institution, a degree which was not identified. Because ofthese three curriculums and rounding, the percents in columns 4, 5, and 6 do not alwaysadd up to 100.
Mathematics-teaching curriculum.--Infor-
mation on the kinds of degrees awarded for this
curriculum was received from 495 institutions,
or about 95 percent of those having such a
curriculum. About one-third of the 495 of-fered a B.A. only (33 percent); about one-third,
a B.S. only (32 percent); about one-seventh, a
B.A. or B.S. (15 percent); and one-fifth, a
bachelor's degree with designation of educa-
non in it (20 percent). (See table 9).
Teachers colleges (34 percent) and univer-
sities (32 percent) tended, much more than
liberal arts colleges (12 percent), to offer
a degree with the designation of education,
22
the bachelor of science in education being by
far the most popular. Even for teachers col-
leges, however, the straight B.S. degree, with
no allowance for other kinds of degrees, was
most common (40 percent). On the other hand,
43 percent of the liberal arts colleges offered
a straight B.A. degree exclusively, a fact
which accounted for the relatively higher per-
centages of both private institutions and in-
stitutions with enrollments under 700 thatoffered only a straight B.A. The Southeast
region offered only the B.A. degree consic'
ably less than did other regions. Larger in-
stitutions tended to offer degrees with the
Table 9.--Percent of institutions awarding specified degrees in mathematics-teaching curriculums with amajor in mathematics; by type, control, region, and enrollment size: Aggregate United States, 1960-61
Category ofinstitution
Number ofinstitutionsprovidingdata
Response rate(number incolumn 2:4-number of
institutionshaving thiscurriculum)
Percent' of institutions in col. 2 in whichthis curriculum leads to a--
B.A.
only
B.S.
onlyB.A. or
B.S.
B.S.
in Educ.BA
in Educ.B. Ed.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
All institutions 495 95 33 32 15 15 3 2
TypeUniversities 77 93 14 34 20 21 7 4Liberal arts colleges 313 95 43 28 16 10 1 1
Teachers colleges 99 96 15 40 10 47 4 3
Technological Schools 6 100 0 100 0 0 0 0
ControlPublic 208 95 18 38 12 25Private 287 95 44 28 18 8
RegionNorth Atlantic 110 92 36 35 16 12 1 1
Great Lakes and Plains 190 96 34 29 16 17 2 2
Southeast 107 97 22 40 15 15 5 3
West and Southwest 88 98 39 26 14 14 5 2
Enrollment sizeOver 5,000 85 91 17 33 19 22 5 41,500-5,000 137 96 26 37 10 20 4 3
700-1,499 141 97 36 28 20 13 3 1
Under 700 132 95 46 32 14 7 0 1
Two institutions offered degrees other than those given in columns 4 through 9. Because of these twocurriculums and rounding, the percents do not add up to 100 percent for some categories.
designation of education more frequently thandid smaller institutions. In fact, there was adirect relationship between degrees with thisdesignation and the size-category of institu-tions.
Statistical, actuarial, applied, and "other"
curriculum s.--Except for actuarial science, inwhich only five curriculums were reportedon, the most commonly awarded degrees byfar in these curriculums was the B.S. degree.(See table 10). In 25 applied mathematics cur-riculums, or about 71 percent of the 36 re-ported, the B.S. was the only degree offered.
Table 10.--Percent of institutions awarding specified degrees in statistical, actuarial,applied, and "other" curriculums with a major in mathematics; all institutions:Aggregate United States.? 1960-61
Kind ofcurriculum
Number ofinstitutions
providing dataon kinds of
degrees awardedin this
curriculum
Response rate(number incolumn 2-i-
number ofinstitutionshaving thiscurriculum)
Percent of institutions in column 2in which this .curriculum leads to a --
B.A.only
B.S.only
B.A. orB.S.
Degree otherthan B.A.or B.S.
(1) (2) (3) (4) (5) (6) (7)
StatisticalActuarialAppliedOther
235
3516
858397
100
26601412
52
407163
2206
12
0
09
12
23
3b
In statistical curriculums, the B.S. was themost common degree awarded, yet the B.A.was the only degree offered in 6 of the 23'curriculums reported.
Distribution of Degrees in VariousCurriculums
Since 1947-48, the U.S. Office of Educationhas annually surveyed the numbers of degreesearned in mathematics at the bachelor's,master's, and doctor's levels; the results havebeen reported in the annual editions of EarnedDegrees Conferred. From 1947-48 through1954-55, the category "mathematics" appearedon the survey form without subcategories.Since the 1955-56 survey, the category "math-ematical subjects," with subcategories "math-ematics" and "statistics," has appeared. Re-spondents have been asked to include degreesin actuarial science with degrees in statistics.
Despite the innovation of 1955-56, nothingwas known on a national scale of the distribu-tion of degrees within the several curriculumsof mathematics until this present survey wasconducted. The survey on Earned DegreesConferred distinguished between degrees instatistics and mathematics, but not, for ex-ample, between degrees in statistics andactuarial science, or between liberal artsdegrees in mathematics and mathematics-teaching degrees.
In order to discover the distribution ofbachelor's degrees in the various mathematicscurriculums, respondents in this survey wereasked to report the number of degrees awardedin each curriculum from July 1, 1959, toJune 30, 1960. Not all institutions could givethis information. Out of 759 institutions havinga liberal arts or general curriculum, 130 didnot provide the requested data. For mathe-matics-teaching, the comparable figures were88 out of 521; for statistics, 9 out of 27; foractuarial science, 1 out of 7; for appliedmathematics, 6 out of 36; and for "other"curriculums, 5 out of 16.
The data received are shown in table 11. Atotal of 8,847 degrees were classified andreported by the respondents. According toEarned Degrees Conferred, 1959-60, an Office
of Education survey of all institutions, 1 a totalof 11,361 bachelor's degrees in mathematicsand 76 bachelor's degrees in statistics (in-cluding actuarial science) were conferred. Forstatistical purposes, however, the Office ofEducation counts a major in mathematics thatis carried on with a co-major in another fieldonly as one-half degree in mathematics andone-half degree in the other field. Hence, therewere more graduates with majors in mathe-matics or statistics than indicated by the Officeof Education survey data for that year. It isestimated that the 8,847 degrees in mathe-matics reported in this present survey werebetween two-thirds and three-fourths of allthe degrees in mathematics awarded in1959-60.
As table 11 shows, the liberal arts orgeneral curriculum was by far the mostpopular curriculum, accounting for 58 percentof the bachelor's degree awarded by all in-stitutions. The mathematics-teaching curric-ulum accounted for 36 percent of the degrees;applied mathematics, 4 percent; and statistics,1 percent.
As was expected, degrees earned in liberalarts curriculums predominated at liberal artscolleges and hence at private colleges sinceso many liberal arts colleges are private.Degrees in mathematics-teaching curriculumsaccounted for 75 percent of the bachelor'sdegree in mathematics at the teachers colleges,and at the technological schools applied math-ematics and "other" (principally, engineeringmathematics) accounted for 61 percent of thedegrees.
In comparisons by region, the Great Lakasand Plains region was the highest in percentof degrees awarded in the mathematics-teach-ing curriculum (43 percent of the degreesawarded) and lowest in percent awarded in theliberal arts or general curriculum (52 per-cent). In comparisons by enrollment size, thesmall colleges--those with enrollments offewer than 700--awarded almost two-thirds(65 percent) of their degrees in the liberalarts or general curriculum. Institutions withenrollments between 1,500 and 5,000 studentsawarded a little less than half (46 percent) of
1 Washirgton: Government Printing Office, 1962.
Table 11.--Percent of bachelor's degrees awarded in specified curriculums with a major in mathematics; bytype, control, region, and enrollment size: Aggregate United States, July 1, 1959 to June 30, 1960
(NOTE. L = less than 0.5 but not zero percent.)
Category of institutionCategory
Total number ofdegreesamarded.Mathe-
in allcurriculums
Percent distribution of degrees in college (2) among:
arts ormaticsteachingcurricu-
lums
Statis-tical
curricu-lums
Actu-arial
curricu-lums
Appliedcurricu-lums
Othercurricu-lums
(1) (2) (3) (4) (5) (6) (7) (8)
All institutions 8,847 58 36 1 L 4 2
TYPeUniversities 2,945 67 24 2 L 6 2
Liberal arts colleges 3,752 70 27 L L 2 LTeachers colleges 1,892 25 75 0 0 L 0
Technological schools 258 31 7 0 0 36 25
ControlPublic 4,754 44 49 1 L 5 1
Private 4,093 75 20 1 L '2 2
RegionNorth Atlantic 2,111 61 30 1 L 4 4
:seat Lakes and Plains 2,974 52 43 1 L 3 1
Southeast 2,083 62 36 L 0 2 LWest and Southwest 1,679 61 29 1 L 7 2
Enrollment sizeOver 5,000 3,255 59 27 2 L 8 3
1,500-5,000 2,804 52 46 0 0 1 1
700-1,499 1,788 62 35 L 0 1 1
Under 700 1,000 65 34 L L L L
their degrees in mathematics-teaching cur-riculums. For reasons explained earlier, itcan be assumed that somewhere between 40and 50 percent of all recipients of bachelor'sdegrees in mathematics are fully qualified toteach mathematics in secondary schools, eventhough only 36 percent of all mathematicsdegrees awarded were in mathematics-teach-ing curriculums.
COURSE OFFERINGS ANDENROLLMENTS (ITEM 4)
In considering data on enrollment in anygiven course, the reader should keep in mindthat some courses, such as analytic geometryand ordinary differential equations are typi-cally given at the end of the school year;hence, the enrollments cited here, based uponautumn data, are lower for such courses thanthey would be if they were based on springdata.
The readei should also keep in mind thatmany subjects that are given separate listingat one institution are combined into a singlecomprehensive course at another. At someinstitutions, for example, freshman mathe-matical analysis is a year-long integratedcourse consisting of algebra, trigonometry,and analytic geometry; similarly, higher math-ematics for engineers often consists of ad-vanced calculus, some advanced algebra,vector analysis, and complex variables.
25
347
Freshman Year
Table 12 gives the 16 different freshmancourses that were cited with sufficient fre-quency and enrollment to be listed separately.All other courses were lumped into the "other"category.
Table 12.--Number and percent of institutions offering freshman-year mathematics courses, and numberand percent of students enrolled in them: Aggregate United States, Fall 1960
Course
Institutionsofferingcourse
at some time
Of institutionsin column 2,
number and percentoffering course in
Fall 1960
Enrollment: Fall 1960
Number
Percent of totalfreshman
mathematicsenrollment
Number Percent Number Percent
1 2 3 4 5 6 7
Total -- -- -- -- 374,830 100.0
Plane geometry 145 17 84 58 3,277 0.9
Solid geometry 96 11 50 52 1,429 0.4
Elementary algebra 148 17 109 74 9,183 2.4Intermediate algebra 303 35 256 84 27,907 7.4
College algebra 572 65 544 95 82,125 21.9Trigonometry 552 63 408 74 35,926 9.6Analytic geometry 332 38 228 69 17,957 4.8Analytic geometry and calculus 360 41 318 88 50,874 13.6Mathematical analysis 376 43 354 94 46,151 12.3
Basic concepts (includingfinite mathematics) 246 28 228 93 27,512 7.3
General mathematics 233 27 216 93 32,461 8.7Calculus 91 10 72 79 5,212 1.4Mathematics of finance 148 17 93 63 8,026 2.1Elementary statistics 105 12 61 59 3,827 1.0
Mathematics for elementaryschool teachers 153 17 117 76 9,761 2.6
Business mathematics 45 5 40 89 5,886 1.6
Other -- -- -- -- 7,316 2.0
The courses most frequently given in thefirst year were college algebra, trigonom-etry, and mathematical analysis. They weregiven by 65 percent, 63 percent, and 43 percent,respectively, of the institutions replying. En-rollment figures showed that college algebra,with an enrollment of 82,125 students, or21.9 percent of the freshman mathematicsenrollment, was the most popular single fresh-man course, and that analytic geometry andcalculus (offered by 41 percent of the institu-dons) was second with 50,874 students, or13.6 percent of the total. Mathematical analysiswas next with 46,151 students, or 12.3 percentof the total enrollment.
A total of 246 institutions, or 28 percent ofthose responding, reported that they offered abasic concepts course in mathematics, with atotal enrollment of 27,512 students, or 7.3percent of the total freshman mathematicsenrollment. This enrollment reflects a trend,for in recent years more and more Collegesand universities have been offering suchcourses. In fact, many institutions are offering
26
3r)
a new course called finite mathematics. Thetopics covered in a basic concepts courseinclude elementary set theory, logic, andmathematical structure. These courses areoften recommended to students to meet generaleducation requirements because they focus onbasic understanding of mathematics ratherthan on the acquisition of skills or techniqueswhich the student not majoring in mathematicsor science will soon forget.
The data cited here on business mathematicsdo not reflect a true picture. Since businessmathematics is often taught in the businessdepartment rather than the mathematics de-partment, undoubtedly some business mathe-matics enrollments went unreported. A similarsituation exists in elementary statistics, whichis sometimes taught in departments other thanmathematics.
Sophomore Year
The number and percent of institutionsoffering various sophomore-year mathematics
Table 13.--Number and percent of institutions offering sophomore-year mathematics courses, and numberand percent of students enrolled in them: Aggregate United States, Fall 1960
Course
Institutionsoffering courseat some time
Of institutionsin column 2,
number and percentoffering course in
Enrollment: Fall 1960
Percent of total
Fall 1960 Numbersophomore-yearmathematics
Number Percent Number Percentenrollment
1 2 3 4 5 6 7
Total -- -- -- -- 92,847 100.0
Calculus 530 60 501 95 31,144 34.9
Analytic geometry and calculus 370 42 345 93 37,015 39.0
Differential equations 176 20 118 67 9,771 10.3
Statistics 210 24 127 60 5,624 5.9
Mathematics of finance 98 11 45 46 1,771 1.9
Mathematics for elementary schoolteachers 23 3 18 78 1,396 1.5
Analytic geometry 48 5 44 92 1,304 1.4
Other -- -- -- -- 4,822 5.1
courses and the enrollment in these coursesare given in table 13. Only seven courses wereoffered with sufficient frequency to be listedseparately in the table.
Although the straight calculus course wasthe one given by the greatest percentage ofinstitutions (60 percent), the integrated course,analytic geometry and calculus, offered by 42percent of the institutions, had the largestenrollment, accounting for 39.0 percent of thetotal sophomore-year enrollment during Fall1960.
The fact that differential equations is anend-of-year course at many institutions ex-plains why it accounted for only 10.3 percentof the Fall 1960 enrollment. Statistics andmathematics of finance are offered with lessfrequency than is calculus in the sophomoreyear, and this is why these courses account fora lower percentage of the total enrollment.
Junior Year and Senior Year
A great number of different mathematicscourses were offered at the junior and seniorlevels. The course offered by the most insti-tutions (74 percent of them) was advancedcalculus, but the greatest enrollment was inordinary differential equations, which ac-
27
counted for 15.0 percent of the total mathe-matics enrollment at this level. (See table 14.)
Other commonly given courses were modernalgebra (64 percent of the institutions), mathe-matical statistics (47 percent), theory ofequations (47 percent), college geometry (42percent), and mathematics for secondaryschool teachers (40 percent). These courses,along with the two mentioned in the precedingparagraph, generally accounted for the largestenrollments. A significant exception was ad-vanced mathematics for engineers and physi-cists, a course offered by only 19 percent ofthe institutions but one which accounted for6.7 percent of the total mathematics enroll-ment at this level. Independent study or honorscourses were offered by 20 percent of theinstitutions but accounted for only 0.5 percentof the enrollment. Perhaps the individualattention needed for the supervision of suchstudents accounted in part for the small en-rollment.
The data on programing for digital com-puters do not reflect the full picture, becausethe respondents were heads of mathematicsdepartments or persons whom they designatedto respond. At many universities, however,instruction in digital computing is given in aseparate department of digital computing, notin the mathematics department. There is goodreason to believe that some respondents failed
Table 14.--Number and percent of institutions offering Junior-year and senior-year mathematics courses,and number and percent of students enrolled in them: Aggregate United States, Fall 1960
Course
Institutionsoffering courseat sometime
Of institutions
in column 2, number and percent of-fering course in
Fall 1960
Enrollment: Fall 1960
Number
Percent of totalJunior- and senior-year mathematics
enrollmentNumber Percent Number Percent
1 2 3 4 5 6 7
Total -- -- -- -- 101,277 100.0
Advanced calculus 647 74 461 71 12,976 12.8Oridnary differential equations. 631 72 410 65 15,144 15.0Partial differential equations 93 11 45 48 1,621 1.6Theory of equations 409 47 195 48 3,724 3.7Theory of numbers 196 22 74 38 1,486 1.5probability 192 22 92 48 2,233 2.2Mathematical statistics 410 47 224 55 5,496 5.4Modern algebra 559 64 334 60 6,824 6.7"Continental Classroom" 147 17 137 93 1,756 1.7Matrix theory 186 21 100 54 2,671, 2.6Vector analysis.. 232 26 120 52 3,626 3.6Complex variables 199 23 104 52 2,676 2.6College geometry 368 42 156 42 2,958 2.9Solid analytic geometry 167 19 70 42 1,124 1.1Projective geometry 171 19 56 33 789 0.8Non-Euclidean geometry 66 8 19 29 412 0.4Differential geometry 69 8 21 30 322 0.3Higher geometry and modern
geometry 70 8 26 37 438 0.4
Topology 126 14 69 55 789 0.8
Mathematics for secondaryschool teachers 354 40 182 51 3,506 3.5
Mathematics for elementaryschool teachers 49 6 38 78 1,614 1.6
Foundations of mathematics 182 21 89 49 1,862 1.8
History of mathematics 206 23 69 33 1,141 1.1
Arithmetic for college students. 35 4 21 60 1,225 1.2
Numerical analysis 173 20 94 54 2,178 2.2
Programing for digital computers 102 12 75 74 2,665, 2.6Calculus of finite differences 37 4 14 38 189 0.2
Mathematics of finance 69 8 29 42 1,021 1.0
Advanced mathematics forengineers and physicists 170 19 121 71 6,750 6.7
Fourier series and boundaryvalue problems 66 8 27 41 865 0.9
Theoretical or analyticalmechanics 61 7 36 59 960 0.9
Honors thesis 54 6 43 80 168 0.2
Independent study or honorscourse 179 20 120 67 552 0.5
Finite mathematics 29 3 17 59 263 0.3Linear algebra 23 3 13 57 376 0.4Senior seminar 87 10 56 64 41111 0.4Applied statistics 27 3 19 70 1,428 1.4Logic 32 4 14 44 280 0.3
Differential and integralcalculus 73 8 61 84 1,517 1.5
Higher analysis, theory offunctions, real variables 66 8 35 53 897 0.9
Operational mathematics 14 2 6 43 216 0.2Set theory 11 1 6 55 101 0.1Higher algebra 26 3 18 69 414 0.4Other --- --- --- --- 3,580 3.5
28
40
to obtain the pertinent data from the com-puting department. Since theoretical and ana-lytical mechanics is often taught in a physicsdepartment or an engineering department,enrollment data for this subject are also notbelieved to have been universally reported.
PREREQUISITE INSTRUCTION(ITEM 9)
Each college and university has what itconsiders its regular freshman mathematicscourses. For students who do not possess thenecessary prerequisite courses, many institu-tions offer courses lower in level than theregular freshman courses. These remedialcourses are sometimes given on a creditbasis and sometimes without credit.
What is considered prerequisite instructionvaries among institutions. Plane geometry,solid geometry, elementary algebra, and in-termediate algebra, if they are offered at all,are usually considered remedial. On the otherhand, although college algebra and trigonom-etry are usually regarded as regular courses,
at come institutions they are given as pre-requisite instruction.
Extent of Prerequisite Instructionand Provision for Credit
Table 15 shows the number and percent ofinstitutions in each category which offeredone or more courses of prerequisite instructionand the percent of institutions, based on thetotal number of institutions in each category,which offered various specific courses. Table16 shows the percent of institutions amongthose giving various prerequisite courses thatgave college credit for them.
Fifty-eight percent of all institutions offeredat least one course in what they consideredremedial mathematics. Almost three-fourthsof the public institutions offered such instruc-tion whereas only one-half of the private in-stitutions did so. Prerequisite instruction wasrelatively more than twice as common in theWest and Southwest region as in the NorthAtlantic region, where only 36 percent of theinstitutions offered any kind of remedial mathe-
Table 15.--Number and percent of institutions offering prerequisite instruction and percent offering specified courses; bytype, control, region, and enrollment size: Aggregate United States, 1960-61
Category of institution
Number ofinstitutionsoffering
prerequisiteinstruction
Percent offeringnumber in column2 :number of
institutions incategory
Percent' offering- -
Planegeometry
Solidgeom-etry
Element-ary
algebra
Inter-mediatealgebra
Collegealgebra
Trigo-nometry
Othercourses
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
All institutions 508 58 17 10 17 34 4 6 8
TypeUniversities 100 72 25 12 29 45 8 10 5
Liberal arts colleges 308 54 13 8 14 30 4 6 8
Teachers colleges 82 60 25 19 15 40 1 0 13
Technological schools 18 56 17 10 22 39 5 12 5
ControlPublic 217 74 28 20 28 47 2 4 12
Private 291 50 11 6 11 27 5 6 6
Region'North Atlantic 92 36 6 2 9 16 5 7 6
Great Lakes and Plains 168 62 17 9 19 38 4 5 7
Southeast 131 66 22 19 19 36 3 3 10West and Southwest 117 76 27 17 24 52 5 8 10
Enrollment sizeOver 5,000 111 78 26 11 32 51 9 11 8
1,500-5,000 135 61 24 16 22 42 4 5 8
700-1,499 136 54 12 8 13 30 3 6 5
Under 700 126 48 10 7 9 22 3 3 10
Each percent is based on the total number of institutions in each category, not Just on the number offering prerequisiteinstruction.
29
41
Table 16.--Percent of institutions giving specified prerequisite courses that also gavecollege credit for them; by type, control, region, and enrollment size: AggregateUnited States, 1960-61
Category ofinstitution
Of those institutions offering the course,percent which gave college credit for:
Planegeometry
Solidgeometry
Elemen-taryalgebra
Inter-mediatealgebra
Collegealgebra
Trigo-nometry
Othercourses
(1) (2) (3) (4) (5) (6) (7) (8)
All institutions 31 68 36 73 77 58 55
TypeUniversities 18 50 35 67 60 54 33Liberal arts colleges 29 69 35 74 86 63 59Teachers colleges 53 80 55 92 100 0 59Technological schools 14 50 0 31 50 40 0
ControlPublic 38 70 41 82 50 75 56
Private 23 64 30 67 83 53 54
RegionNorth Atlantic 7 50 22 44 58 22 43
Great Lakes and Plains 36 60 42 74 80 67 75
Southeast 21 69 24 73 100 60 40West and Southwest 44 76 47 87 88 100 60
Enrollment sizeOver 5,000 19 47 36 66 50 53 461,500-5,000 33 67 36 76 100 90 65
700-1,499 45 86 39 78 75 31 57
Under 700 27 67 29 72 100 78 52
matics. The largest institutions, principally theuniversities, tended to offer prerequisitecourses much more than did the smallerinstitutions. Perhaps the smaller institutionsfound it more difficult to provide the additionalstaff for prerequisite instruction.
Intermediate algebra was the subject mostfrequently given as prerequisite instruction;34 percent of all 877 responding institutionsoffered it. Only a small number of collegesand universities offered college algebra ortrigonometry as subfreshman courses. Aboutone-sixth of all the institutions gave planegeometry, and about one-sixth gave elementaryalgebra.
Except for plane geometry and elementaryalgebra, college credit was given for pre-requisite instruction more often than not; only31 percent and 36 percent of all institutions,respectively, offered credit for these courses.
30
42
(See table 16.) Teachers colleges tended togive credit more than did other types ofinstitutions; public institutions, more thanprivate institutions; and the West and Southwestregion, more than other regions. Although thelargest institutions offered prerequisite in-struction more frequently than did the smallerinstitutions, they gave college credit for it lessfrequently.
Enrollments in PrerequisiteInstruction
Table 17 gives the total number of studentsenrolled in Fall 1960 in courses of prerequisiteinstruction, in all institutions and in variouscategories of institutions. The 50,899 studentsin all institutions represent almost 14 percentof the 374,830 students enrolled in freshman-year mathematics courses in the 877 partici-pating colleges and universities. In other
Table 17.--Number of .:Ludents enrolled in prerequisite instruction and percent distribution in specified courses in Lhe fallof 1960; by type, control, region, and enrollment size: Aggregate United :ltaLes
Cntegory ofinstitution
Total enrollment
in prerequisiteinstruction
Percent distribution of total enrollment in prerequisite--
Planegeometry
Solidgeometry
Elementaryalgebra
Inter-mediatealgebra
Collegealgebra
Trigo-nomeLry
Othersubjects.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
All institutions 50,899 6 3 18 53 5 4 10
TypeUniversities 22,382 3 3 20 57 6 6 6
Liberal arts college:1 19,416 8 3 19 48 6 3 13
Teachers colleges 6,394 11 2 12 53 1 0 21
Technological schools 2,707 15 2 12 57 1 6 7
ControlPublic 37,641 5 3 19 55 4 4 11
Private 13,258 10 3 16 48 9 6 9
RegionNorth Atlantic 6,121 4 1 24 40 9 7 14
Great Lakes and Plains 17,908 8 2 16 58 4 4 9
Southeast 10,829 9 5 19 49 1 1 15
West and Southwest 16,041 4 2 17 55 7 6 8
Enrollment sizeOver 5,000 28,374 3 1 18 59 6 6 6
1,500-5,000 14,206 9 5 19 47 3 3 15
700-1,499 5,403 13 2 16 47 4 4 14
Under 700 2,916 5 4 14 36 12 2 26
words, about one student in seven was enrolledin a course which the institution regarded asremedial.
Table 17 also shows in percentages thedistribution of enrollment in prerequisitecourses for each category of institution aswell as for all institutions. More than half(53 percent) of the students in all institutionswho were taking courses considered subfresh-man were enrolled in intermediate algebra.The only other course with a fairly highpercentage was elementary algebra (18percent).
Public institutions had almost three timesas many students enrolled in prerequisiteinstruction as did private institutions. For themost part, private institutions, which canestablish higher admissions requirements, donot feel obligated to give such courses. En-rollments in prerequisite instruction weremuch lower in the North Atlantic region thanin other regions. As would be expected, thelargest institutions, as a category, had thelargest enrollments. Very few teachers col-leges offered college algebra or trigonometryas prerequisite instruction. More than one infive students in remedial, courses in thesecolleges were enrolled in mathematics coursesother than those specified in the questionnaire- -often in basic mathematics or arithmetic.
Where Prerequisite Instruction IsGiven
A total of 447 colleges and universities, or88 percent of the 508 offering prerequisiteinstruction, offered it as a regular service ofthe mathematics department. Forty-eight, or9 percent, provided the service through anextension activity of their institution, and 19,or 4 percent, used other means. A few insti-tutions indicated that they used more than oneof these methods. The pattern was similaramong the various categories of institution.
Discontinuance of PrerequisiteInstruction from 1951 to 1961
A total of 84, or 23 percent, of the 369institutions which were not at the time of thesurvey offering prerequisite instruction, hadoffered it some time in the preceding 10 years.Liberal arts colleges accounted for 77percentof the institutions that had discontinued it,although they constituted only 66 percent ofthe responding institutions. On the other hand,teachers colleges contributed only 6 percentof the discontinuances, although they repre-sented 15 percent of the 877 institutions in thesurvey.
In dropping remedial mathematics, privateinstitutions were 14 percent higher than the
percentage they represented of public andprivate institutions combined, and conversely,the public institutions were 14 percent lower.By the standards applied in this survey, therewere no important regional differences. En-rollment size was a controlling factor: thelargest institutions, representing only 16 per-cent of the universe of institutions, constituted36 percent of those discontinuing remedialinstruction, whereas the smallest institutions,representing 30 percent of the universe, madeup only 10 percent of those dropping suchinstruction.
The principal reasons given by respondentsfor the discontinuance of prerequisite instruc-tion, together with some selected comments,appear below:
1. Better high school preparationA small private liberal arts school in the
East: "1958--Trigonometry, and solid geom-etry were discontinued. Entering students whoare prospective math majors take trig in highschool, and a complete course in solid geom-etry is no longer considered necessary evenfor prospective teachers."
A very small private liberal arts college inthe Southeast: "We have not altogether dis-continued this service, but find it hard to fitinto schedule. More students offer 2 1/2 yearsof high-school math."
Another small private liberal arts institu-tion in the Southeast: "Discontinued 3 yearsago - insufficient demand."
A fairly large private liberal arts school inthe Far West: "Discontinued 1950--No longernecessary. High school preparation adequate."
A small private liberal arts college in theGreat Lakes area: "In 1957-58, we had threefreshmen who did not offer plane geometry asan entrance unit, so we provided such acourse for them. Since that time, prospectivestudents have been told to get it off campus."
2. Staffing problemsA small private liberal arts school in the
Great Lakes area: "Discontinued in 1960- -shortage in regular staff."
A small public liberal arts college in theGreat Lakes area: "Lack of teaching person-nel."
A fairly large private liberal arts collegein the Southeast: "Staff needed for regular
32
4 4
instruction plus decreasing need for coursesdue to higher entrance standards."
3. Preference for giving remedial help with-out formal courses
A small private liberal arts school in theEast: "Faculty members are quite readilyavailable for help and students are in chargeof problem sessions which may be attendedvoluntarily by those in difficulty."
4. Belief that remedial courses are not alegitimate part of college curriculum
A small private liberal arts college in theNorth Atlantic area: "When I arrived here in1953 such courses were being given as regularcollege credit courses. I junked the wholemess, got new faculty, and put in all newcourses by 1955. Of course, college algebraand trigonometry are a part, in a sense, ofthe Allendoerfer and Oakley text."
A fairly large private liberal arts collegein the Great Lakes area: "1958. It was feltthat high-school mathematics was improving;also that college professors should not usevaluable time for prerequisite instruction."
A fairly large private liberal arts school inthe West: "Remedial instruction is beingcurtailed as rapidly as possible as beingwasteful of staff time."
REQUIRED ADMISSIONSEXAMINATIONS THAT INCLUDED
MATHEMATICS (ITEM 5)
A total of 657, or 75 percent, of the 877responding institutions reported that they hadan admissions examination which includedmathematics (see table 18). The College En-trance Examination Board (C.E.E.B.) testwas by far the most commonly used. Of theinstitutions requiring mathematics examina-tions for admissions, 57 percent either re-quired the C.E.E.B. test permitted it as oneof two or more alternatives. The C.E.E.B.Achievement examination was used by 25percent of the institutions .requiring mathe-matics examinations for admission; a Stateexamination (mostly New York State RegentsExamination), by 6 percent; a local, institu-tional examination, by 20 percent; and "other"examinations, by 25 percent. The "other"examinations consisted principally of tests
Tatie 18.--Number and percent of institutions requiring admisiens examinations that include machemntica, and percent of usageof different cxaminations; by type, control, region, rota enrollment size: Aggregate United States, 1960-61
Category of
institution
Number ofinstitutions
requiringsuch exami-nations
Percent requiringnumber in column
2: number ofinstitutions in
category
Percent' of institutions In columnroquiremenl can be met
2 in whi2h theby:
Institutional
examinationother
examinationAptitude0.E.E.R.2
AchievementState
examination
(1) (2) (3) (4) (5) (6) (7) (8)
All institutions 657 75 57 25 6 ,20 25
TypeUniversities 103 75 61 32 7 22 L8
Liberal arts colleges 433 76 61 25 17 23Teachers colleges 92 68 32 15 10 28 37
Technological schools. 29 9.1 59 34 14 24 24
ControlPublic. 192 66 36 18 8 29 32Private 465 79 66 29 5 16 21.
RegionNorth Atlantic 229 77 39 11 15 11Great Lakes and Plains 181 67 43 18 1 27 36Southeast 136 69 51 21 6 21 22West and Southwest 111 73 46 14 4 LE 35
Enrollment s'zeOver 5,000 106 74 50 31 8 24 271,500-5,000 165 75 52 22 9 25 22700-1,499 202 81 65 27 3 16 22Under 700 184 70 57 23 5 17 27
1 Some institutions permit more than one examination to meet their admissions requirement. Hence, the percents in columns4 through 8 add up to more than 100 percent.
2 College Entrance Examination Hoard.
issued by the American College Testing Pro-gram (ACT), the School and College AbilityTest (SCAT), and Sequential Tests of Educa-tional Progress (STEP).
Comparisons by Type of InstitutionTechnological schools as a group required
admissions examinations including mathe-matics more frequently than any other type ofinstitution, with 91 percent of them requiringthem. Teachers colleges, with 68 percent,required them least among the four types ofinstitutions surveyed.
The C.E.E.B. Aptitude examination was byfar the most commonly employed test, exceptin the teachers colleges. Fewer than one-third(32 percent) of the teachers colleges used thistest, but teachers colleges were highest in theuse of "other" examinations (37 percent) andinstitutional examinations (28 percent).
Comparisons by Control
Private institutions (79 percent) requiredadmissions examinations involving mathe-
33
4 1--
matics more than did public institutions (66percent). The difference between the privateand public institutions in the frequency of useof the C.E.E.B. Aptitude examination wasparticularly striking. This examination metthe requirement in 66 percent of the privateinstitutions, but only in 36 percent of thepublic ones. Institutional and "other" examina-tions were more commonly used in public thanin private institutions.
Comparisons by RegionThe North Atlantic region (89 percent)
required admissions examinations involvingmathematics far more than did the other threeregions, which clustered around 70 percent.The C.E.E.B. Aptitude examination was espe-cially popular in the North Atlantic region,where it met the requirement of 77 percent ofthe institutions. Because of the New York StateRegents examination, the North Atlantic regionalso led in the use of State examinations(11 percent). The Great Lakes and Plainsregion was highest in the use of institutionalexaminations (27 percent) and "other" exami-nations (36 percent).
Comparisons by Enrollment Size
Institutions with enrollments of 700 to 1,499
students required admissions examinationsinvolving mathematics (81 percent) slightlymore than did other size-categories of insti-tutions. The same category also led in requiringor permitting the use of C.E.E.B. Aptitute test(65 percent). Institutional examinations weremore commonly used in larger institutionsthan in smaller ones. Perhaps the largerstaffs at larger institutions are helpful factorsin the preparation of examinations locally.
PLACEMENT EXAMINATIONSIN MATHEMATICS (ITEM 6)
Because of the diversity of mathematicalbackground and ability among entering fresh-men, many institutions administer placementexaminations in mathematics. Sometimes theseexaminations are given to determine, on thebasis of the student's knowledge of mathe-matics, the proper course for him to enter.At other times, they are given to measurethe mathematical aptitude of the student or tohelp divide the students into appropriatecourse-sections. A list of the various stand-ardized, or nationally distributed, examina-tions used for placement are shown in thefollowing listing, and the statistical findingson the use of placement examinations gen-erally, in table 19.
Nationally Distributed orStandardized Mathematics
Examinations Used for Placement*
The Educational Testing Service CooperativeSeries
The Cooperative Mathematics Pretest forCollege Students
The Cooperative High School MathematicsTests: Elementary Algebra (throughquadratics)
The Cooperative High School MathematicsTests: Intermediate Algebra (quad-ratics and beyond)
"Does not include psychological examinations put outby colleges or the armed services. Also, some of theexaminations indicated on the questionnaire were un-identifiable.
The Cooperative High School MathematicsTests: Plane Trigonometry
The Cooperative High School MathematicsTests: Plane Geometry
The .Cooperative General Culture Test,Mathematics Section
The Cooperative General Achievement Tests:Test 3, Mathematics
The Educational Testing Service, Other Exam-inations
College Entrance Examination Board Ad-vanced Placement Program: Mathematics
College Entrance Examination Board Scho-lastic Aptitude Test
Pre-engineering Ability TestSchool and College Ability Tests, Level 1
or Level 2Sequential Tests of Educational Progress:
Mathematics Section, Level 1 or Level 2
Harcourt, Brace, and World, Inc. Examinations
Blyth Second-Year Algebra TestDavis Test of Functional Competence in
Mathematics, Grades 9-13
Essential High School Content Battery: Math-ematics Section, Grades 10-12
Lankton First-Year Algebra TestMadden-Peak Arithmetic Computation TestMetropolitan Achievement Tests, Grades 7-9
Snader General Mathematics Test, Grades9-13
Stanford Achievement Test: Arithmetic,Grades 7-9
Other Examinations
34
413
Algebra Prognosis Test-- Bobbs Merrill Co.,Inc.
Algebra Test for Engineering and Science- -Acorn Publishing Company
American College Testing Program- -Science Research Associates, Inc.
California Achievement Tests: Mathemat-icsCalifornia. Test Bureau
College Qualification Tests-- Numerical --The Psychological Corporation
Differential Aptitude Test--Numeri-cal Ability--The Psychological Corpora-tion
Table 19.--Number and percent of institutions administering a placement examination in mathematics, and percents related to pertinent characteristics of these
examinations; by type, control, region, and enrollment size:
Aggregate Unit.ad States, 1960-61
Category
of
institution
Institutions
administering
placement
examinations
Percent of
institutions
administering
placement
exams which use
standardized or
nationally
distributed
exans
Percent' of institutions at
which placement examinations
are taken by--
Percent' of institutions at
which placement examination
tests for knowledge of--
Percent' of institutions at which the
objective of the placement exam is to--
All
enter-
ing
fresh-
men
Students
taking
math in
college
for first
tine
Students
in
special
curricu-
lums
only
Other
Alge-
bra
Geom-
etry
Trigo-
nom-
etry
Other
Determine
math
knowledge
of
students
Determine
math
aptitude
of
students
Section
students
into
equal
ability
levels
Determine
specific
course
f,:q. stu-
cent to
enter
Other
Number
Percent
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
All institutions
Type
Universities
Liberal arts colleges
Teachers colleges
Technological schools
Control
Public
Private
Region
North Atlantic
Great Lakes and Plains
Southeast
West and Southwest
Enrollment size
Over 5,000
1,500-5,000
700-1,499
Under 700
517
59
61
54
29
14
12
88
50
49
20
58
26
24
70
6
104
315
81
17
75
55
60
53
42
65
72
47
47 54
57
71
23
31
33
18
26
12 7 6
20
10
10
18
9290
77
82
51
50
48 35
68
46
40
41
15
20
30
18
58
57
60
71.
16
28
2641
17
26
2512
7970
60
47
7 5
10 0
207
310
71 53
62
60
56
53
24
33
2210
12
13
85
90
43 54
48 50
30
14
63
55
19
30
21
25
69
70
7 5
112
163
136
106
44
60 69
69
60 50
74 60
41
51
68
54
26
34
24
33
17
11
11
20
13 12
10
16
82
88
91
91
57
51
4546
60 57
31 50
2320
18
20
45
55
65
70
27
23
29
24
2126
31
13
61
75
67
75
11 7 2 3
105
142
139
131
73 64
56 50
43 63
65
68
47
51
53
63
2230
32
31
2717 9 6
20
1110
11
9590
8880
47
48
55
47
69
45
46
42
3318
19
14
61
62
54
57
12
25
2439
17
25
25
23
78 66
68
66
9 3 3 8
1 Totals do not add up to 100 because more than one item could be checked by a respondent.
Engineering and Physical Science AptitudeTest--The Psychological Corporation
Iowa Placement Examinations: MathematicsAptitude, Grades 12-13--Bureau of Ed-ucational Research and Service, StateUniversity of Iowa
Iowa Placement Examinations: MathematicsTraining, Grades 12-13--Bureau of Ed-ucational Research and Service, StateUniversity of Iowa
Kansas Mathematics Test, Grades 9-13- -Kansas State Teachers College
Kentucky Classification Battery, Grades 12and 13--Kentucky Cooperative Counsel-ing and Testing Service
The Purdue Mathematics Training Test:Arithmetic and Algebra, Grade 13 --University Book Store, West Lafayette,Indiana
Statistical Findings
All institutions.--A total of 517 institutions,or 59 percent of all respondents, reportedadministering a mathematics placement exam-ination. Of these institutions, more than hall(54 percent) administered them to all enteringfreshmen. Twenty-nine percent administeredthem only to students taking mathematics incollege for the first time, and 14 percent onlyto students in such special curriculums asengineering. Algebra (88 percent) is the subjectmost commonly tested for, and geometry andtrigonometry next, with about hall the institu-tions testing for the former and hall for thelatter. The most common objective was todetermine the specific course in which toenroll the student. Seventy percent of theinstitutions used the placement examinationfor this purpose, while 58 percent used it todiscover the mathematical knowledge of thestudent.
Principal differences, by category of in-stitution.--Three-fourths of the universities,but only slightly more than half the liberalarts colleges or technological schools, re-quired placement examinations. Among insti-tutions that administered such examinations,technological schools required them mostfrequently (71 percent) of all entering fresh-men, and universities required them mostfrequently (26 percent) for students takingspecial curriculums.
Public institutions required placement ex-aminations much more (71 percent) than didprivate institutions (53 percent). The latterwere more prone to require them for studentstaking mathematics in college for the firsttime (33 percent to 24 percent), but lessprone to require them only of students inspecial curriculums (10 percent to 22 percent).
Institutions in the North Atlantic regionrequired placement examinations less often(44 percent) than did institutions in otherregions of the country. They were also lowestin the percentage (41 percent) requiring suchexaminations of all entering freshmen.
The percentage of institutions requiringplacement examinations varied directly ac-cording to size, ranging from 73 percent forinstitutions with enrollments of more than5,000 down to 50 percent for institutions withenrollments of less than 700. There was aninverse relationship, however, between thesize category of institutions and the percentagerequiring placement examinations for all en-tering freshmen, with the range extendingfrom 47 percent to 63 percent.
PROGRAMS OF ADVANCEDSTANDING IN MATHEMATICS
(ITEM 8)
In recent years there has been increasinginterest in programs of advanced standing incolleges and universities. Factors contributingto the growth of such programs include (1) theintroduction, by some of the better highschools, of some work of college grade in thesenior year; (2) the recognition by manyeducators that repetition in college of worktaken in high school is wasteful of a student'stime; and (3) burgeoning college enrollments,which are putting heavy strains on college anduniversity staffs and facilities.
As used in this report, "advanced standing"refers to a program whereby a college oruniversity permits a student to receive appro-priate placement, with or without credit, onthe basis of college-level courses taken inhigh school. It must be remembered, however,that because of differing standards, what isconsidered to be of college level in oneinstitution may not be so regarded in another.The statistical findings on advanced standingare shown in table 20.
36
4
Table 20.--Number and percent of Institutions with programs of advanced standing in mathematics, extent to which credit is given for courses skipped, andfactors upon which advanced standing is based; by type, control, region, and enrollment size; Aggregate United States, 1960-61
Category of institution
Number ofinstitutionshaving such
Percent having
(column 2-eallinstitutionsin category)
Institutions
giving collegecredit for
od,,,,,,,d
Percent'
algebra
of institutions
course
Trigo-
nom-
in
credits
geometry
column 4
in--
Calculus
giving
Other
Percent' of institutions in coliimn 2baning advanced standing on --
R"°m"mends-Lion of
hig.'school
locally
constructedproficiency
examination
NationallydistrIbUledproficiencyexamination
Other
Number Percent Number Percent
(1) (2) (3) (4) (5) (6) (7) (A) (9) (10) (11) (12) (13) (14)
All institutions 589 67 310 53 55 54 52 51 14 20 48 37 17
TypeUniversities 125 90 92 74 51 50 55 65 5 13 62 43 10
Liberal arts colleges 388 68 181 47 55 54 53 46 17 22 45 36 18
Teachers colleges 60 44 28 47 75 68 39 36 2 22 40 20 20
Technological schools 6 50 9 56 33 44 44 56 11 38 31 63 25
ControlPublic 180 62 113 63 65 65 50 50 15 12 54 26 16
Private 409 70 19'/ 48 49 47 54 52 13 24 45 41 17
RegionNorth Atlantic 171 67 90 53 29 28 57 72 19 25 29 57 16
Great Lakes and Plains L96 73 113 58 56 56 55 49 14 18 53 33 17
outheast 118 60 56 47 84 SO 43 47 9 19 58 19 22
West and Southwest 104 68 51 49 69 65 49 47 10 D 56 29 13
Enrollment sizeOver 5,000 124 87 92 74 53 53 63 66 8 11 61 44 13
1,500-5,000 153 69 74 48 55 53 53 53 14 20 44 34 17
700-1,499 166 66 87 52 49 47 46 47 18 23 46 38 16
Under 700 146 56 57 39 67 65 44 32 18 25 40 31 22
1 The sum of the percents exceeds 100 percent, since many colleges give advanced standing credit for more than one kind of mathematics course.' The sum of the percents exceeds 100 percent, since many colleges base advanced standing on more than one method.
Institutions differ greatly in their policieson advanced placement. Some that grant place-ment in an advanced course give credit for theprerequisite and some do not. Some givecredit for one semester of the freshmancourse or credit for a parallel course..Someaward credit toward the general educationrequirements or merely grant exemption fromthem without giving credit. Some set a limiton the amount of credit awarded, and somegive unlimited credit.,
Of the 877 institutions reporting in thesurvey, 589, or 67 percent, fiad programs ofadvanced standing. Of these, 310, or 53 per-cent, gave credit for courses for which studentshad already met the requirements throughprevious study. Fifty-five percent of these310 gave credit for college algebra in suchinstances; 54 percent, for trigonometry; 52percent, for analytic geometry; 51 percent,for calculus; and 14 percent, for some othersubject.
Twenty percent of the institutions havingprograms of advanced standing admitted stu-dents to these programs on the basis of therecommendations of the high school; 48 per-cent, on the basis of a proficiency examinationconstructed locally; 37 percent, on the basisof a nationally distributed proficiency exami-nation; and 17 percent, by some other measure.As is apparent from the total of the preceding
37
percentages, a number of institutions usedmore than one of these means.
Comparisons by Type of Institution
Ninety percent of the universities offeredprograms of advanced standing, but only 44percent of the teachers colleges did. Universi-ties took the lead in giving college credit forcourses skipped. Seventy-four percent of themgave such credit, as compared to 47 percentof both liberal arts and teachers colleges.
Universities tended to give credit for analyticgeometry and calculus more than for collegealgebra, trigonometry, or any other mathe-matics subject; liberal arts colleges, forcollege algebra, trigonometry, and analyticgeometry more than for calculus or any othermathematics subject; teachers colleges, forcollege algebra and trigonometry more than forany other mathematics subject; and techno-logical schools, for calculus more than anyother mathematics subject.
The type of institution also seemed to havesome bearing on the means used to determineadvanced standing, although again it is im-portant to remember that institutions frequentlyused more than one means. Universitiesseemed to base advanced standing on profi-ciency examinations more frequently than on
other means, particularly locally constructedexams, but also on nationally distributed ones;the percentages of universities using eachwere 62 percent and 43 percent, respectively.Only 13 percent relied on the recommendationof the high school; and 10 percent, on someother measure.
Liberal arts colleges, like universities,relied more on proficiency examinations: 45percent based advanced standing on locallyconstructed examinations; and 36 percent, onnationally distributed ones. They tended morethan universities but less than technologicalschools to rely on the recommendation of thehigh school.
Forty percent of the teachers collegesbased advanced standing upon a locally con-structed proficiency examination. Approxi-mately 22 percent accepted the recommendationof the high school; 20 percent, a nationalproficiency examination; and 20 percent, someother measure.
Technological schools favored national pro-ficiency examinations, which were used tomeasure eligibility for advanced standing in63 percent of the schools. Thirty-eight per-cent allowed advanced standing on the basis ofhigh school recommendations; 31 percent, ona locally constructed proficiency test; and25 percent, on some other measure.
Comparisons by Control
A slightly higher percentage of privatelycontrolled institutions had programs of ad-vanced standing than did publicly controlledschools. Among the private institutions 409,or 70 percent, had such programs as comparedwith 180, or 62 percent, of the public colleges.Public institutions with programs of advancedstanding, however, were more prone to givecollege credit for courses skipped, with 63percent doing so, as compared with 48 percentof private colleges.
Type of administrative control seemed notto have any significant effect on the kinds ofcourses for which credit was given, exceptthat credit was granted for college algebraand trigonometry more frequently in publicinstitutions than in private ones. This dif-ference is due principally to the teacherscolleges, which are mostly public institutions.
In determining advanced standing, public in-stitutions used locally constructed proficiencyexaminations more often than any other means;and private institutions used both locallyconstructed and national examinations aboutequally.
Comparisons by Region
A slightly higher proportion of schools inthe Great Lakes and Plains region both offeredprograms of advanced standing and also gavecollege credit for courses skipped. One hundredninety-six, or 73 percent, of the institutionsin the Great Lakes and plains region hadprograms of advanced standing; 104, or 68percent, in the West and Southwest region; 171,or 67 percent, in the North Atlantic region;and 118, or 60 percent, in the Southeast region.
Of the institutions having programs of ad-vanced standing, 58 percent of those in theGreat Lakes and Plains region gave collegecredit for courses skipped; 53 percent, in theNorth Atlantic region; 49 percent, in the Westand Southwest region; and 47 percent, in theSoutheast region.
A large percentage of institutions in theSoutheast region gave college credit for collegealgebra and trigonometry, whereas a verysmall percentage of colleges in the NorthAtlantic region did so. In contrast, an ex-tremely high percentage (72 percent) of institu-tions in the North Atlantic region gave creditfor calculus, compared with only 27 percent inthe Southeast region.
There was some regional variation in theemphasis put on particular measures of ad-vanced standing. Whereas a national proficiencyexamination was by far the most commonmeans of determining advanced standing inthe North Atlantic region (57 percent), thelocally constructed examination was by far themost common in each of the other three regions.
Comparisons by Enrollment Size
The enrollment sizes of instutions seemedto have some bearing on their advanced stand-ing policies. For example, a much largerpercentage of institutions with enrollments ofmore than 5,000 had programs of advanced
38r-
standing and also gave credit for coursesskipped than did institutions with smallerenrollments. Institutions with fewer than 700students had the smallest proportion of pro-grams of advanced standing.
Institutions with fewer than 700 studentsgave credit for college algebra and trigo-nometry more commonly than did institutionsof any other size. On the other hand, the per-centage of institutions giving credit in analyticgeometry and calculus followed the order ofenrollment size from high to low.
The largest proportion of institutions, re-gardless of size of enrollment, used a locallyconstructed proficiency examination, the sec-ond most popular measure being an examina-tion made up by a national agency. In addition,institutions with more than 5,000 studentsbased advanced standing on high school recom-mendation less frequently than did institutionsof any other size category.
UNDERGRADUATE HONORSPROGRAMS IN MATHEMATICS
(ITEM 7)
More and more emphasis has been placedby colleges and universities in recent yearson programs specially designed for under-graduates of superior ability. This increasedemphasis has resulted from several factors:(1) the complaint during the 1950's that thefailure of many colleges to challenge the giftedwas wasteful, both to the individuals concernedand to the Nation; (2) a greater interest,especially since the launching of Sputnik in1957, in nurturing to the full the talents ofsuperior students; and (3) the expanding en-rollments in most colleges and universities,making it more feasible economically to pro-vide special sections.
Statistical Findings
A total of 266 (30 percent) of the 877respondents in the survey indicated that theyhad an honors program. A breakdown of the266 by type of institution shows that 60 per-cent of the universities, 27 percent of theliberal arts colleges, 15 percent of the teacherscolleges, and 16 percent of the technologicalinstitutes offered a special program. An analy-
39
51
sis by public versus private control showsalmost no difference: 31 to 30 percent, re-spectively. Regional differences do not seemgreat, either. In both the North Atlantic regionand the Great Lakes and Plains region, about34 percent of the reporting institutions of-fered such a program; in the Southeast, 26percent; and in the West and Southwest, 25percent. Size of institution seemed a veryimportant factor, since 57 percent of thelargest institutions (more than 5,000 students)offered an honors program, whereas only 17percent of the smallest institutions (fewerthan 700 students) did so. Among institutionswith enrollments between 1,500 and 5,000, 30percent offered special programs; among thosewith enrollments between 700 and 1,499, 29percent offered them.
Types of Program
The most popular program consisted ofindependent study culminating usually in anhonors thesis. The offering of special coursesopen only to honors students and not part oftheir regular mathematics program was nextin popularity. Many institutions offered ac-celerated courses in which the gifted wouldgo faster and do more work than the others.These types of programs were offered, re-spectively, by 43 percent, 12 percent, and 11percent of those institutions with special pro-grams.
In addition, there were programs in whichthe student was given directed reading, pro-grams consisting of seminars with specialresearch projects and reports, and programswhich permitted and encouraged the giftedundergraduate to take graduate courses. Manyprograms which do not require a thesis re-quire an oral examination, occasionally byoutside examiners.
Independent study.--There were enough in-stitutions with programs of independent studyto make a breakdown by categories. While thistype of program was very popular among
beral arts institutions (89 schools, or 57percent of those offering honors programs,offered this kind), it was less popular amongother types of institutions. Only 38 percent ofthe teacher's colleges with honors programs
offered independent study programs, 21 per-cent of the universities, and no technologicalinstitutes.
The independent study method was practicedat 50 percent of the private institutions withspecial programs for the superior under-graduate student, but at only 30 percent of thepublic institutions. Independent study seemedto be the predominant form of program forthe superior student at the smaller colleges,being offered by 60 percent of the schools withenrollments between 700 and 1,500 and 62 per-cent of those with enrollments of fewer than700, On the other hand, the corresponding per-.centages were only 22 percent for schoolswith enrollments of more than 5,000 and 36percent for schools with enrollments between1,500 and 5,000.
There were few regional differences: NorthAtlantic, 49 percent; Great Lakes and Plains,43 percent; Southeast, 49 percent. Only theWest and Southwest region showed great varia-tion, with only 21 percent of its schools of-fering this particular form of honors program.
The data on the other programs are in-sufficient for detailed statistical analysis. Theavailable data suggest that the largest schools- -those with enrollments of more than 5,000- -usually universities, make the most use both ofspecial courses and special sections. Beyondthis it is impossible to generalize.
Admission Criteria
The usual criteria for entry into an honorsprogram in the freshman year were the highschool record and scores on placement exami-nations and on various ability tests. For thoseentering honors programs later in the collegecareer, class standing and records in collegemathematics were the usual criteria.
General Observations
Honors programs in mathematics wereusually part of a college-wide honors program.Although only 30 percent of the colleges indi-cated having such programs, many others re-ported that they were considering or were aboutto establish one.
At present, special or honors programsseem to be concentrated in the large public
A
universities, where the wide spread of abilitiesand background makes a diversity of pro-grams necessary and where the large number ofstudents makes an extensive honors programpossible. That the typical honors program atthese institutions consists of special sectionsor classes seems to reflect the large numberof students eligible for the program and pos-sibly a student-teacher ratio which precludesa program of independent study at reasonablecost. Similarly, the prevalence of independentstudy programs at liberal arts colleges mightbe indicative of the small number of eligiblestudents and of a more favorable student-teacher ratio,
A number of colleges and universities havedevoted considerable attention to developingspecial programs in mathematics for under-graduate students, such as the following ex-amples:
The Program at Carleton College
Carleton College, a coeducational college inNorthfield, Minn., with fewer than 1,300 stu-dents, has been experimenting with programsfor superior undergraduate mathematics stu-dents for a number of years. A program in effectduring the period 1955-59, and another beingconducted during the period 1961-65, will bedescribed here. Both programs have receivedsupport from the National Science Foundation.
Program during 1955-59.2 --The programfor gifted students centered around honors sec-tions in the freshman and sophomore yearsand a "colloquium" for advanced students.Students with unusual promise in mathematics(as shown chiefly by scores in both the verbaland mathematical aptitude tests of the CollegeEntrance Examination Board) were invited toenroll in a 2-year honors section.
The usual freshman-sophomore sequence inmathematics starts with an introduction tologic, set theory, and other notions funda-mental to modern mathematics, and proceedsto a course in the calculus through manipula-tive differential equations and the calculus of
2 See also Kenneth 0, May, "Undergraduate Researchin Mathematics," The American Mathematical Monthly,Vol, LXV, No, 4, April 1958, P. 241-46.
several variables. Using the same textbooks,the honors section covered this material withconsiderable enrichment in three semestersinstead of four. The second semester of thesophomore year was devoted to projects chosenby the class.
Because the honors students could quicklymaster definitions and techniques, it was foundundesirable to spend' much class time onroutine matters or on drill. Rather, the em-phasis was on creativity, even through grading.Merely learning definitions, theorems, andskills did not earn a high grade. The grade Bdepended to some extent, and the A primarily,on evidence of originality and initiative.Memory and recall earned C's, whereas Awas the scholar's grade. This is consistentwith the practice in the English departments,where a student gets A for a theme only if,in addition to being free of grammaticaland spelling errors, it shows evidence ofindependent thinking. The average grade in anhonors section was expected to be between anA and a B, usually with more A's than B'sbeing assigned. Students who did not maintainthis standard were asked to transfer to a regu-lar section.
The honors sections were conducted on aninformal basis. Some time was taken forlectures introducing supplementary subjectmatter, but most of the class time was de-voted to students exposition of their best workand to discussion of difficult problems. Studentswere told that they would be permitted to handin one problem a week of their own choice,which might be from the part of the bookcurrently being discussed, from previous orfuture problem sets, or from any other source.In any case the student was to select theproblem which, in his opinion, represented hisbest work for the week. It was pointed out tothe class that this manner of judging peopleis similar to the way in which scientists arejudged by their colleagues, namely in terms oftheir best work.
Honors students were expected to engage inresearch activities. These varied from solvingdifficult problems, such as those given in thePutnam Competition (a national annual, com-petitive examination for undergraduate mathe-matics students) to carrying on a long-termproject. There was no concern for whetherresults were publishable, because, it was felt,
the student who obtains previously publishedresults by doing work original for him, gainsas valuable an experience as if the work hadnever been done before.
Research assistants were chosen informallyby the entire staff on the basis of demon-strated interest and ability. Assistantshipswere awarded to nonmajors with the neces-sary interest and qualifications. Assistantswere paid stipends, the amounts dependings onfinancial need and amount of service rendered.
Approximately once a week, the mathe-matics staff and research assistants met in-formally in a room equipped with comfortablechairs and a blackboard. The programs at thecolloquia were varied: an introduction to someresearch problem, a report on research ac-tivities, an expository talk by a visiting mathe-matician, a joint discussion of a paper or bookthat had been read by the group, or a co-operative attack on a problem. Participation inthe colloquium was open to all interestedstudents and faculty at Carleton College andat neighboring St. Olaf College.
This entire program was Costly in time,since staff members needed time to preparefor individual students, to confer with them,and to help them undertake original work. Inworking with honors students, it was con-sidered important for faculty members to workwith smaller sections. The grant from theNational Science Foundation permitted the ad-dition of one full-time person for this purpose.This allowed two extra sections of freshmanand sophomore mathematics and a reductionof teaching load equal to half a full-time load,which was distributed among the entire staffsince all staff members were expected toparticipate in the program.
Program for 1961-65.--In 1961 the programwas revised to provide greater economic ef-ficiency. Although the program of 1955-59 wasin general quite successful, it could not besustained without continued outside financialsupport. The honors sections were somewhatinefficient because of errors in selection andthe necessity of spending a large proportion ofthe time in duplicating activities of the regularsections. The program of 1961-65, also receiv-ing support by a grant from the NationalScience Foundation, was developed to test thehypothesis that the desired results could be
achieved without honors sections by utilizingcolloquia and a local journal at all levels.The program is designed for able studentstaking many credits in mathematics, usuallyas many as are consistent with a liberal artsdegree.
In 1961-62, colloquia were held separatelyfor freshmen, for sophomores, and for juniorsand seniors. As a result of the experiencegained during that year, the colloquia forfreshmen and for sophomores were combinedinto one colloquium for both freshmen andsophomores.
An informal journal, called Delta-Epsilon,commenced publication in 1961-62. It has noregular dates of publication, but whenever afew pages of student work are produced, theyare typed awl duplicated. The journal containshonors problems, problems of the month,interesting student papers from classes at alllevels, reports on research projects, news ofgraduates, and anything else that deservescirculation. It is sent free to majors and otherswho request it. It has been very helpful as astimulus and means of recognition. 3
The Program at Wesleyan UniversityWesleyan University, at Middletown, Conn.,
has embarked on a series of experiments tostrengthen the impact of liberal education onundergraduates. If the experiments provesound, the institution is to be divided intogroups of "colleges." The colleges are onlyincidentally and marginally social units; thestudents enter a college as sophomores andare united principally in their intellectualgoals. Most important, the colleges are de-signed to promote unity of students and facultyin a common enterprise. Thus, the studentsin a college are under the jurisdiction of atutorial committee, which maps out a meaning-ful program of study for each student, anddetermines when he is to be recommended fora degree. Much of the traditional apparatus ofthe American university is abandoned--specific
3 For further information on undergraduate researchin mathematics, see Undergraduate Research in Mathe-matics (Report of a conference held at Carleton College,June 19 to 23, 1961, with support from the NationalScience Foundation, edited by Kenneth 0. May and Sey-mour Schuster, Carleton Duplicating Service, Northfield,Minn., 1962.)
requirements (in terms of courses passed),the accumulation of "credits" in a recorder'sbooks, and frequent quizzes, tests, and exami-nations.
'Two examinations, a Junior Qualifying Ex-amination and a Senior Comprehensive Ex-amination, are prepared by outside examiners;.the college faculty are not inquisitors, butrather preceptors, instructors, and older col-leagues. The examinations cover all threeaspects of the student's experience--his coreprogram, the central part of his major study;his supplementary program, study related tothe core; and the generalizations, subjects ofinterest to the student, outside the range ofhis specialization.
Two college-plan experiments began in 1959:a College of Letters and a College of PublicAffairs. A College of Quantitative Studies, in-volving mathematics, began in 1960. It is beingrun according to the following three guide-lines:
(a) Students are introduced to "real" as con-trasted with "text-book" problems earlyin their careers, and their study is keyedto the solution of such problems. Prob-lems are taken from many academicdisciplines--from economics, govern-ment, psychology, sociology, and biology,as well as from disciplines with a longerhistory of 'use of mathematical tech-niques--and from business, industry, andgovernment.
(b) Summers are used in (small or large)part to continue study, to prepare forthe next year, and to work on projects.A change of pace from the academicyear is considered essential. Throughacceleration, a student can earn an M.S.degree with 4 years beyond high school.
(c) The students usually participate in theteaching of others through freshmanproblem sessions, machine programing,the symposium, and similar activities.
The College of Quantitative Studies is super-vised by directors of studies, representingeconomics, administration, astronomy, geologyand mathematics. Among their other duties,the directors recommend students to theWesleyan faculty for a B.A. degree. Thedirectors are assisted by faculty membersfrom various departments as needed. In ad-dition, six distinguished men from business,
434
industry, the arts, and scientific research areassociated with the college as fellows. Theyoccasionally participate in the discussions,seminars, and social affairs of the college.
Students are selected on the basis of strengthof interest rather than high native ability. In1960, there were a few juniors and seniors,along with 20 sophomores. in each of the next2 years, 20 sophomores were added; a 5-yearexperiment will thus have been completed whenthe last group has graduated.
The core program consists of 5 one-semestercourses in mathematics. Usually these coursesare:
(a) Third-semester calculus(b) Finite mathematics--logic and sets,
probability, vectors and matrices, withapplications
(c) Differential equations and related topics(d) Numerical analysis I(e) Numerical analysis II
Other courses in mathematics may replacesome of these courses if the ability and interestof a particular student warrant a substitu-tion.
The supplementary program consists of ap-proximately four semesters of related course-work (e.g., economics, psychology, or moremathematics), four semesters of "problemwork," and two semesters of a "project."
Thus, the core and supplementary pro-grams together amount roughly to the equivalentof 15 semester-courses during the 3-yearperiod, out of a total of about 25 courses.Hence, 60 percent of the student's time isdevoted to these two programs, and about 40percent is left for generalization.
As part of the generalization work, studentsare expected to participate in a symposiumduring their sophomore and senior years: aninterdivisional reading course, with studentsand faculty from other colleges representingdifferent disciplines. There are common read-ings on a central theme designed to preparethe student to continue to read comparablematerials after graduation.
Although students are expected to followgenerally the program outlined here, thedirectors of studies have great freedom inmaking allowances for individual differences.
43
The Program at Dartmouth College
At Dartmouth College, Hanover, N.H., thebasic sequence in mathematics for the first 2years consists of two semesters of calculus,followed by a specially designed introductionto modern mathematics, which leads to a coursein multivariate calculus. The student is ex-posed in the freshman year to differentiation,series, and differential equations, and in thesecond year to an introduction to logic, prob-ability theory, linear algebra, and a moderntreatment of vector calculus. Students with aspecial interest and aptitude for mathematics,who do not need to be drilled in routinematters, are placed in honors sections ofthese four courses, where a much deeper the-oretical understanding of the subject matter ispossible. The emphasis in the first 2 years ofthe honors program is on depth of understand-ing, not acceleration. Students entering withadvanced training may be placed in honorssections, a sophomore course, or a specialadvanced-placement course. A special two-semester sequence enables students in thebiological and social sciences to absorb thebasic ideas of the,2-year program, and to seethem illustrated in their own area of interest.
There are two mathematics major programsat Dartmouth. The honors major is designedfor students contemplating graduate work inmathematics. Such students complete severalgraduate-level courses in their junior andsenior years. Advanced courses are offeredin algebra, algebraic geometry, analysis,geometry, logic, numerical analysis, prob-ability theory, statistics, and topology, aswell as applications to the physical and socialsciences. The major is enriched by a de-partmental reading program, aiming forbreadth in the junior year and for depth inthe senior year. Honors seniors write a thesisin an area of special interest to them, workingclosely with a member of the faculty.
The Program at the University ofMaryland
The mathematics honors program at theUniversity of Maryland began in 1959-60. Its
purpose is to discover the mathematicallygifted undergraduates and to develop theirability in mathematics as fully as possible.Starting in the winter of each year, a con-certed drive is made in the high schools ofthe State to recruit outstanding mathematicsstudents. Although most students who com-plete the entire program are mathematicsmajors, the program is not restricted to them.As an aid to recruitment, four $500 scholar-ships are awarded by the Business Associatesof the University of Maryland for academicexcellence to freshmen or sophomores fromthe State of Maryland having exceptional abilityand interest in mathematics. Following is abrief description of the program:
(a) Discovery of candidates: Candidatesamong the University of Maryland fresh-men are located by recommendationsfrom high school teachers and/or byscores on the placement examinations.Non-freshman candidates are recom-mended by the faculty.
(b) Selection of participants: Participantsare chosen by the departmental honorscommittee from among students who showexceptional ability and interest in mathe-matics. A student may be invited toenter the honors program at any time,on or before the beginning of his senioryear.
(c) Participants: Participants are candidatesfor honors programs of the College ofArts and Sciences. All regulations andprivileges of the honors program of thecollege apply to participants in the mathe-matics honors program. The participantsremain under the continual observationof the departmental honors committee.Those who do not progress satisfactorilyare returned to the regular program.
(d) Honors program (Phase I): Studentsentering the program in their firstsemester take a special three-semestercourse (5 hours per week) with a seniormember of the faculty. This coursecovers the material of the regular fresh-man and sophomore course, but its mainaim is to develop the mathematicalmaturity of the students as quickly aspossible. Emphasis is placed on modernconcepts and rigor. Independent work isencouraged.
(e) Honors program (Phase II): During thefourth, fifth, and sixth semesters thestudents normally take 14 hours of ad-vanced undergraduate courses in mathe-matics. Wherever possible, the honorsstudents are placed in special sections.Independent work is encouraged duringboth the summer and the school year.This may be done in place of formalcourses (under the approval of the honorscommittee). A weekly seminar is heldduring the summer and the school year.
(f) Honors program (Phase III): The senioryear is devoted to advanced under-graduate courses, graduate-level courses(courses which, except for students inthis program, are not open to under-graduates), seminars, independent study,and preparation for written and oralfinal honors comprehensive examina-tions in mathematics. This work nor-mally carries 12 hours of credit. Recom-mendation for graduation with honors,no honors, or high honors in mathe-matics is made by the departmentalhonors committee after review of thestudent's record and the results of thefinal honors comprehensive examina-tions.
UNDERGRADUATE THESISREQUIREMENTS (ITEM 11)
Table 21 gives data on the requirement ofmathematics theses by undergraduates. A totalof 142, or 16 percent of all the institutions inthe survey, required an undergraduate thesisin mathematics for some or all mathematicsmajors. Fifty-five percent of the 142 requiredit for honors students only; 40 percent, for allmathematics students; and 5 percent, for othertypes of students.
Comparisons by Category ofInstitution
The type of institution seemed to have somebearing on thesis requirements. Liberal artscolleges as a type required an undergraduatethesis more frequently and teachers collegesless frequently than other types of institutions.
44
5U
Table 21.--Number and percent of institutions which require undergraduate theses of atleast some mathematics majors, and percent requiring them of specified categories ofstudents; by type, control, region, and enrollment size: Aggregate United States,1960-61
Category ofinstitution
Number ofinstitutionsrequiring
undergraduatetheses
Percent requiring
(number in column2 + number of
institutionsin category)
Percent of institutions incolumn 2 which require
undergraduate theses of:
Allmathematics
majors
Honors
Studentsonly
Othertypes ofstudents
(1) (2) (3) (4) (5) (6)
All institutions 142 16 40 55 5
TypeUniversities 21 15 19 71 10Liberal arts college 112 20 43 54 3
Teachers colleges 3 2 50 50 0Technological schools 6 19 33 50 17
ControlPublic 20 7 26 63 11Private 122 21 42 54 4
RegionNorth Atlantic 61 24 41 56 3
Great Lakes and Plains 45 17 40 53 7Southeast 26 13 27 69 4West and Southwest 10 7 22 67 11
Enrollment sizeOver 5,000 16 11 27 67 61,500-5,000 32 14 25 72 3
700-1,499 52 21 39 57 4Under 700 42 16 56 37 7
Both universities and liberal arts collegesrequired the thesis more of honors studentsonly than they did of all mathematics majors.However, the difference in the percent wasmuch greater in the case of the universities,varying between 71 percent and 19 percent,respectively. The number of teachers colleges(3) and -die- number of technological institu-tions (6) requiring undergraduate theses weretoo small to provide meaningful percentagebreakdowns on types of students of whomtheses were required.
Private institutions (21 percent) requiredtheses much more often than did public insti-tutions (7 percent). In the public institutionsthe requirement applicable to honors studentsonly (63 percent) far exceeded that for allmathematics majors (26 percent). The com-
45
parable difference amounted to only 12 percentamong the liberal arts colleges.
The North Atlantic region was way aheadin the requirement of undergraduate thesesin mathematics, 24 percent of all institutionsin this region having this requirement. At theother extreme, only 7 percent of the institu-tions in the West and Southwest region hadthis requirement. In all four regions, the per-centage of schooT.s maintaining this require-ment only for honors students exceeded thepercentage maintaining it for all mathematicsmajors, the difference between the two per-centages being greatest in the West andSouthwest region.
Institutions in the size category of 700 to1,499 students were more likely (21 percent)to have undergraduate thesis requirements
than other size categories of institutions. Ofinstitutions of all types, control, region, andenrollment size, only those with enrollmentsof fewer than 700 students required the thesismore of all mathematics majors (56 percent)than they did of honors students only (37percent). The institutions with largest en-rollments more frequently limited thesis re-quirements to honors students only, perhapsbecause reading theses for all students wouldbe an impossible staff task.
A COLLEGE-LEVELMATHEMATICS COURSE AS A.GRADUATION REQUIREMENT
(ITEM 10)
Many academic institutions, as part of theirprograms of general education, require allstudents to take at least one mathematicscourse of college level. The survey revealedthat 292 of the 877 participating institutions,or 33 percent, had such a requirement!' Alarger percentage of public institutions (44percent) than of private institutions (28 percent)had such a requirement.
Further analysis revealed that the incidenceof such a requirement was much lower atuniversities (22 percent) and liberal artscolleges (29 percent) than at teachers colleges(52 percent) and technological institutions(78 percent). Similarly, striking categoricaldifferences appeared in the regional break-down; in the North Atlantic and Southeasternregions, relatively high percentages of in-stitutions had such prerequisites (59 per-cent and 43 percent, respectively and inthe Great Lakes and Plains and the West andSouthwest regions, relatively small percent-ages (only 29 percent and 24 percent, re-spectively).
Size of institution, by contrast, had rela-tively little bearing on the presence or absenceof this requirement. Percentages for institu-tions of different sizes, from largest tosmallest enrollment-size categories, were 37
4 A sizable number of institutions reported thatalthough they had no express requirement for a coursein mathematics, they had had a requirement that couldbe filled by two or more alternatives one of which wasmathematics. A rather common requirement was achoice between mathematics or philosophy and logic.
percent, 30 percent, 39 percent, and 26 per-cent, respectively.
Most likely, the high percentage of teacherscolleges having such a requirement is due tothe necessity for many graduates of theseschools to teach a course in mathematics atsome point in their career; the reason for thehigh percentage among technological schools,of course, is that mathematics is an integralpart of any technical background.
The regional breakdown is somewhat moredifficult to explain. Perhaps the greater con-centration of industry in the East and thus agreater emphasis on technology accounts forthe predominance of required mathematicsthere. This very tentative hypothesis, how-ever, is perhaps more than the data justify.
INNOVATIONS IN MATHEMATICSPROGRAMS FROM 1950 to 1961
(ITEM 17)Among the innovations cited on the ques-
tionnaire, the most commonly adopted was thesubstantial expansion of course offerings, astep taken at 517 of the 877 responding insti-tutions, or 59 percent. (See table 22.) Nextmost frequent was the introduction of moremodern freshman courses, an innovationcarried out by 409 schools, or 47 percent.The change in, or introduction of, a programfor the undergraduate preparation of mathe-matics teachers was adopted by 317 schools,or 36 percent, over this 10-year period.
The other innovations were somewhat lessprevalent. Some were infrequent simply be-cause the practices had already been in exist-ence. For example, only 30 percent of allinstitutions reported having introduced aprogram of advanced standing since 1950. Yet67 percent reported the existence of suchprograms, indicating that 37 percent of theinstitutions had already had these prior to1950.
Least commonplace was the provision ofcourses in data processing and computing,which were offered by only 149 institutions,or 17 percent of the participating schools. Itmust be realized, however, that the respond-ents in this survey were mathematics depart-ment heads and that, in some institutionswhere computing departments have been es-tablished, data on these departments may nothave been reported.
Table 22.--Percent of institutions making specified innovations in undergraduate mathe-
matics programs between 1950 and 1961; by type, control, region, and enrollment size:
Aggregate United States
Code:A. New degree programsB. Substantially expanded course offeringsC. New freshman courses emphasizing suchconcepts as structure, logic, set theory,etc.D. New courses for biological and socialscience majors`
E. New programs, or substantially alteredprograms, for the undergraduate preparationof mathematics teachersF. New courses and instruction leading tocareers in data processing and computingG. New honors programH. New advanced standing program
Percent of institutions introducing innovations
institution A B C D E F G H
All institutions 22 59 47 24 36 17 18 30
TypeUniversities 30 71 32 40 39 42 42 45
Liberal arts colleges 18 55 53 21 33 12 14 28
Teachers colleges 26 65 43 18 53 7 13 19
Technological schools 31 53 13 13 6 44 16 22
ControlPublic 30 67 46 25 47 23 23 28
Private 17 55 47 23 31 14 16 31
RegionNorth Atlantic 23 59 52 26 34 16 20 32
Great Lakes and Plains 17 57 48 23 39 15 21 31
Southeast 19 55 23 23 32 14 14 25
West and Southwest 32 67 20 21 41 26 16 29
Enrollment sizeOver 5,000 27 69 52 34 36 41 41 45
1,500-5,000 29 68 50 26 41 21 20 31
700-1,499 17 57 47 22 37 12 14 30Under 700 17 47 40 17 31 6 8 20
Comparisons by Type of Institution
Universities made innovations in theirmathematics programs more than did any othertype of institution. They were highest per-centagewise in the substantial expansion ofcourse offerings (71 percent); in the provisionof new mathematics courses for biology andsocial science majors (40 percent); in theintroduction of honors programs (42 percent);and in the introduction of programs of advancedstanding (45 percent). The universities alsojust barely trailed the technological schoolsin introduction of new degree programs andintroduction of courses and instruction leadingto careers in data processing and computing.
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The liberal arts colleges ranked first in theintroduction of freshman courses emphasizingstructure, logic, set theory, etc. (53 percent),and teachers colleges were first in new orrevised programs for mathematics teaching(53 percent).
Comparisons by Control
Public institutions introduced the innovationslisted on the questionnaire relatively morefrequently than did the private institutions,with two exceptions; The introduction of fresh-man courses emphasizing basic concepts, andthe introduction of programs of advanced
s tanding--both of which the private insti-tutions had a slight edge.
Comparisons by Region
The regional breakdown shows a spread ofinnovative tendencies. The West and Far Westregion led in new degree programs, courseexpansion, new or revised programs for thepreparation of mathematics teachers, anddata-processing and computer courses; theseinnovations were adopted, respectively, by32 percent, 67 percent, 41 percent, and 26percent of the participating schools there.Their lead over the region with the secondhighest percentage in each of these types ofinnovation generally was considerable. In threeof these four types of innovation, the closestcompetitor was the North Atlantic region,which led, in its own right, in freshman courserevision, mathematics courses for the biologi-cal and social scientists, and programs ofadvanced standing; these innovations wereadopted, respectively, by 52 percent, 26percent, and 32 percent of t' ie participatingschools there. Second to the North Atlanticregion in these types of innovation was theGreat Lakes and Plains region. Least innova-tive of all was the Southeast region.
Comparisons by Enrollment Size
With only two minor exceptions, there wasa direct correlation between size of institutionand the tendency to adopt innovations. Theseexceptions were the slightly higher per-centages among institutions with enrollmentsbetween 1,500 and 5,000 than among those withenrollments of more than 5,000 in new degreeprograms and in new or revised programs forthe preparation of teachers. Institutions withenrollments of fewer than 700 tended generallyto make relatively few of the innovations listedon the questionnaire.
Frequency of Innovations perInstitution
The kinds of institutions that adopted a num-ber of these new programs may be a more
meaningful index of innovational tendencies.Fifty-three percent of the universities thatinstituted any of these reforms had institutedfour or more during the past decade. Com-parable figures for other types of institutionare 30 percent for liberal arts schools, 41percent for teachers colleges, and 40 percentfor technological institution s. Similarly,whereas only 30 percent of the private institu-tions in the survey had made four or moreinnovations, 49 percent of the public institutionshad done so.
Using this scale, few regional differencesappeared. In the North Atlantic region, 37percent of the innovating institutions hadadopted four or more reforms; for each of theother three regions--the Great Lakes andPlains, the Southeast, and the West and FarWest--the corresponding figure was 35percent.
COMMENTS AND OBSERVATIONSON UNDERGRADUATE PROGRAMS
(ITEMS 17 AND 18)
Number of Comments
The questionnaire's invitations to commentelicited some sort of response from 420 ofthe 877 participating institutions, or 48 percent.In considering these responses, the readershould realize that, unlike the rest of thequestionnarie, these items were expresslyintended to elicit subjective data.
Most pronounced of the problems citedwere that of the mathematics department'sbeing made a service department for otherdepartments of the college, and that of up-grading or modernizing the mathematicscurriculum. Of the 420 respondents, 99, or24 percent, mentioned the former, and 103,or 25 percent, the latter.
The Mathematics Department as aService Department
Service requirements involved many ac-tivities. Various schools recognized the neces-sity of supplying adequate mathematics coursesfor the physicists and chemists, statistics
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and probability theory for the social scientists,and at those schools which had a general edu-cation requirement; a course that was simul-taneously an adequate introductory and anadequate terminal course in mathematics.The most pronounced awareness of the prob-lem of service courses seemed to exist in theteachers colleges, where the major academictask is to train teachers of secondary andelementary education. The problem, however,appeared to be a universal one: All sizes andtypes of school, both public and private, allover the country, indicated their concern, asshown in some of the following comments:
A private liberal arts college, Great Lakesand Plains region, enrollment between 700and 1,499: "Next year there will be approxi-mately thirteen courses servicing other de-partments in the school and about nine coursesfor mathematics majors and minors. Some ofthe advanced courses are still alternatedduring two years to permit a greater variety."
A private technological college, North At-lantic region, enrollment between 1,500 and5,000: "The Department of Mathematics...is a part of the School of Engineering. Coursesof instruction in mathematics are offered forstudents in the various engineering curricula,architecture majors, chemistry majors, andmathematics majors."
An institution, similar to the preceding one,except that its enrollment is more than 5,000:"Undergraduate work in this department istailored to the needs of engineering studentsin electricity, chemistry, and mechanics."A small private liberal arts school in theMidwest: "A serious remaining problem con-cerns intermediate algebra. Students in areasnot requiring the calculus, but requiring suchcourses as elementary physics, chemistry,statistics, and mathematics of finance, haveelected to take intermediate algebra evenwhen they have credit for two years of highschool algebra."
A small, private, liberal arts college in theEast, enrollment below 700: "The one ques-tion we have still not resolved is whether themathematics major for those going intosecondary teaching should be any differentthan for those planning to continue graduatework in mathematics with other goals in mind."
A small private liberal arts college in theWest: "The major innovation at present is
the beginning of a mathematics program forelementary school teachers."
A private liberal arts institution in theEast: "There is no program specificallydesigned for the preparation of mathematicsteachers. There is a pseudo program toproduce physics-mathematics teachers."
A small private Southeastern liberal artsschool that provides inservice training fa-cilities for secondary school teachers:"During the fall of 1958 some of the highschool teachers of mathematics held severalmeetings [here] to cLscuss some of the con-cepts such as logic, set theory, etc. In thespring and summer of 1959 some of theseteachers attended our mathematics seminar,for our juniors and seniors, in which westudied recommended curricular revisions ofthe mathematics program for high schoolsand CUPM recommendations for beginningcollege courses."
A State university in the West, enrollmentbetween 1,500 and 5,000: "The major unsolvedproblem of the undergraduate mathematicsprogram is not how to present mathematicsto the students who are to become mathe-matics teachers and/or mathematicians, butrather how to do this and provide the trainingwhich is essential to the other sciences andengineering."
Among the solutions most often suggestedwere special courses for the non-major toprovide him with the mathematics requisitefor his task. A less frequently mentionedalternative was to establish special programs,or tracks, for the non-major and the major.
Updating in the MathematicsCurriculum
Updating the mathematics curriculum camein for much attention, for several reasonsapparently. One was that entering studentsat many institutions seemed better able tohandle advanced mathematics, and another,the need to introduce changes that would pre-pare students better for present-day mathe-matics requirements. Here are some samplecomments:
A small Eastern private liberal arts college:"The content of all our courses has been
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modernized. Such traditional courses as col-lege geometry and theory of equations havebeen dropped, and courses in projective ge-ometry, number theory and modern algebrahave been added."
A small private technological school inthe East: "In general, what were first-yeargraduate programs in 1950 have been madesenior-year courses in 1960."
A small private liberal arts school in theEast: "Our program provides for a juniorand senior seminar. This permits the mathe-matics department to keep up with the moderntrends in mathematics."
A large private Eastern university: "Mod-ern mathematics emphasized in all coursesis the objective toward which we are working.With a knowledge of the concepts and founda-tions, students will be better equipped tothink in the field instead of performing opera-tions mechanically. The 'How' and 'Why'should go hand in hand."
In different parts of the country moderniza-tion meant different things. Although anotherquestion in this survey dealt objectively withthe courses these schools now teach, andthose which they had introduced during thepast 10 years, it is interesting to note whatvarious respondents considered as moderniza-tion.
A small private liberal arts school in theWest: "The most serious deficiency in theundergraduate mathematics program at thepresent time is that there is no course in thefoundations of mathematics."
A moderately large, public liberal artsinstitution in the West: "We still need coursesin geometry, numerical analysis, moderncomputation, and history of mathematics toround out our bachelor's degree curriculum."
A small public technological institution inthe Southwest: "[We] now require for a mathe-matics major both advanced calculus anddifferential equations as well as recommend-ing vector analysis. Courses in college algebraand geometry have been updated to includecontemporary algebra and geometry."
A moderately large, private liberal artscollege in the Great Lakes region: "Threeyears ago the requirements for a major inmathematics were increased from 14 hoursbeyond calculus to 26 hours beyond calculus.We found that giving matrices and modern
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algebra to juniors increased their interest inmathematics and also prepared them to profitfrom point set topology in the fourth year."
As mentioned above, it was the improve-ment in the secondary schools that had fa-cilitated this upgrading. In part, these changespermitted the dropping of a trigonometry-algebra course as the introductory course forfreshmen, and its replacement by an analyticgeometry-calculus course. Another commonresponse was the integration of trigonometryand algebra and also of analytic geometry andcalculus. There were some indications that"depressed areas" existed, in which improve-ment in secondary education had been minimalor nonexistent, but the improvement did seemto be nationwide. Responses to such improve-ment and the upgrading that it made possibleincluded placement examinations with tracksfor freshman year, advanced-placement credit,and honors programs.
The Quality of Entering Freshmen
Unlike awareness of the mathematics de-partment's functioning mainly as a servicedepartment and of the necessity of upgradingcourses to meet professional standards, theimpression of an improving quality of enteringfreshmen was not uniformly distributed overinstitutions of all types, sizes, regions, andkinds of control. Of the 420 institutions thatresponded to the invitation to comment, 55mentioned problems caused by improved highschool preparation. Of the 288 private institu-tions which offered comments, 43, or 15percent, were so concerned, compared to 12,or 9 percent, of 132 public institutions. Al-though these percentages are hardly con-clusive, they do suggest that relatively moreof the better-prepared students were enteringprivate institutions.
Similarly, there were suggestive regionaldifferences on the improving quality of enteringfreshmen. Sixteen percent of those institutionsin the Great Lakes and Plains region thatoffered comments expressed an awareness ofthis problem, compared to 16 percent in theNorth Atlantic region, 12 percent in theSoutheast region, and only 3 percent in theWest and Southwest region. These figuresindicate a fairly high consciousness of change
in the Great Lakes and Plains, in contrastto an almost non-existent one in the West andSouthwest. Here are some of the commentson the improving quality of entering freshmen:
A small private liberal arts college in theEast: "By advanced standing we have meantcalculus. However, in 1961 we will offercalculus with analytic geometry as a freshmancourse for students. with adequate high schoolpreparation."
A small Eastern private liberal arts college:"Incoming students have 3 or '4 years ofhigh school mathematics, some of which is ofcollege level."
A small private technological school in theEast: "The incoming freshman seems betterprepared."
A small private liberal arts school in theEast: "We used to offer college algebra andtrigometry to freshmen and did not startcalculus and analytics until sophomore year(except for students given advanced standings).We now start calculus and analytic geometryin the freshman year and as a result we haveadded advanced calculus to the program."
A small Midwestern private liberal artscollege: "I am hoping that the freshman pro-gram may be expanded more to allow wellprepared students to start in taking analyticgeometry and calculus courses.
"Better entrance tests and placement ofstudents from advanced placement tests givenin high school more adequately and efficientlyare desirable objectives hoped for in thenear future."
A small private liberal arts school in theSouthwest: '1We are planning to make trigo-nometry and college algegra non-creditcourses. We are creating a separate coursein analytic geometry so that suitable enteringfreshmen may go directly into the calculus.Analytic geometry and calculus will nct begiven as an integrated subject."
A small liberal arts college in the Sout:h-west: "This year, for the first time, someentering freshmen were placed in analytir.:geometry. This was done on the basis of highschool records and scores on the entranceexaminations. No special placement examina-tion was given."
A moderate..V large, private liberal artscollege in the West: "A problem facing us atpresent is to know what is the best content
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for the freshman year of college mathematics.Most students who have had four years ofhigh school mathematics seem unpreparedto start a rigorous course in calculus intheir freshman year. Many students come tocollege with a superficial knowledge of muchof the mathematics taken in high school.They know a little algebra, a little trigo-nometry, some modern concepts, some analyticgeometry and have a thorough knowledge ofnone of these. They are weak in necessaryalgebraic techniques."
A moderately large State university in theSoutheast: "A large percentage of enteringfreshmen have had only one unit of high schoolmathematics; even those who wish to majorin mathematics have had (only) algebra andperhaps, geometry and trigonometry."
Even within States, improvement in highschool training in mathematics was not uni-form. For some schools the variation inbackground of the incoming freshmen presentssome of their most pressing problems. Thisproblem appeared most frequently among thesmall, private liberal arts colleges. Followingare some comments on this topic:
A small private liberal arts college in theWest: "Entering freshmen are coming withmore and more varied high school preparation;a small college finds it difficult to provide acurriculum which will meet their needs."
A small private liberal arts college in theGreat Lakes area: "Mathematics is an electiveat (our) college. Freshmen who elect mathe-matics are divided into two groups: thosewho have had only two years of mathematicsand those who have had three or four yearsin high school. The first group takes collegealgebra and trigonometry. It is the secondgroup which presents a problem. For the pastfour years I have given a four-hour course inanalytic geometry to this group. Last year13 students came from 13 different high schoolsoutside the city while five were from the city.Hence their preparation was so varied that itpresented a great problem. I am not satisfiedwith the present program and am contemplat-ing a change."
A small private liberal arts school in theGreat Lakes area: "Unsolved problem--artic-ulation of our first two years with highschool mathematics. A small school with onlytwo mathematics teachers finds it difficult
to provide just the right course for all thewidely different degrees of preparation weencounter."
A moderately large, State teachers collegein the North Atlantic region: "As we attractmore of the better students, we will have toprovide for more extreme variations in back-grounds and abilities. We expect to do thisthrough the initiation, September 1, 1961, ofHonors and Advanced Standing Program."
Providing Suitable MathematicsCourses for General Education
The offqring of suitable mathematics coursesfor students who take mathematics to meet ageneral education requirement appeared to bea problem at a number of institutions. Beloware some of the comments on this topic:
A small private liberal arts school in theWest: "The most serious deficiency in theundergraduate mathematics program at thepresent time is that there is no course in thefoundations of mathematics. This is partly dueto the fact that there are no mathematicscourses included in the general educationrequirements. The 'department feels that atleast one year of appropriate mathematicscourses should be required of all candidatesfor the B.A. degree."
A small private liberal arts school in theEast: "Would like to require a college-levelcourse of all liberal arts students--at presenttheir curriculum is already too full."
A small public liberal arts school in theSoutheast: "All students are now required tocomplete the equivalent of 6 semester hoursof mathematical analysis before graduation.This will eventually be largely a freshmancourse, but it is now taken by students fromall four classes."
A small private liberal arts school in theSoutheast: "Problems: a) should some mathe-matics be required of all students? b) shouldthere be only one or several different coursesdesigned to fulfill this requirement? and c) ofwhat nature should such required courses be?"
A small private liberal arts college in theEast: "All entering freshmen take CEEB,SCAT, STEP test. The ratings on these testsin mathematical ability, together with a knowl-edge of the student's record in high school
mathematics and grades in Regents examina-tions, serve as a guide to separate studentsinto homogeneous groupings. The two groupswith the highest scores start mathematics inthe freshman year. Other students with lowergrades and no indication of further interest inmathematics or science wait until the sopho-more year to begin mathematics. The firstyear of college helps them to adjust to thecollegiate curriculum and methods. They seema bit more mature in the sophomore year."
The Mathematics Faculty
There were several matters brought up inthis section which were of only peripheralrelevance to problems of curriculum. Oneof the more striking was the concern of therespondents that their faculties were inade-quate to the various tasks now being imposedon mathematics departments. Although mostof the complaints were about size of staff,several were about faculty hostility to the"new" or "modern" mathematics, and a fewwere about faculty overeagerness to abandonthe "old" or "solid" mathematics. This prob-lem (mentioned by 45, or 11 percent of the420 institutions) was felt most strongly bycolleges in the 700 to 1,499 enrollment range.Whereas schools of this category make uponly 137, or 33 percent of the 420 respondentsto this item, their concern with this particularproblem is indicated by 20 of 45, or 44 percent,of these responses. Some of the commentswere as follows:
A large private university in the middleWest: "Because of the tremendous shortageof mathematically trained people it will benecessary for many years to use graduatestudent assistants in the teaching of under-graduate courses. We feel that if we couldwork with our incoming graduate studentsduring the sumnier preceding their entranceinto our graduate school, we could significantlyimprove their performance as teachers. Wewould like to have the funds for such a pro-gram."
A small private liberal arts college in theEast: "We do not offer many mathematicscourses in our college. We could not teachsome of them, because we do not have enough
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mathematics teachers. The teaching load formathematics teachers is heavy and theirsalaries are low."
A small private liberal arts college in theWest: "We try to make good use of the visitinglecture programs available. Our very smallstaff is a real handicap both to students andto the staff!"
A small, State teachers college in the West:"Our mathematics offerings were carried ona 'one-nan' basis until 1958. We are nowoffering two advanced courses each quarterwhere we had previously offered only one."
A small, State teachers college in theGreat Plains area: "These plans [for expand-ing and updating the mathematics programs]depend on two things ... obtaining and keepingan adequately prepared staff. (This is thegreatest problem)."
A small private liberal arts college in theGreat Plains area: "We get hurt by non-availability of competent staff. We released(in June 60) two master's degree teachers andreplaced them with two outstanding graduating(B.S.) students. I now handle all advancedcourses (except one) in physics and mathe-matics and try to help my new instructors."
A small private liberal arts school in theSoutheast: "Our college is a small collegefor women. Its mathematics department issmall both student-wise and staff-wise. 1 heburden of instruction falls on me. My prepara-tion has been strictly theoretical and hence
the course offerings lean away from appliedm athem atics. "
This situation has been aggravated by atrend, revealed in the responses, toward theformation of new departments and majors andalso of new schools. Forty-five institutionsreferred to the creation of either a majorin mathematics for the first time, or theformation of a mathematics department.Twelve institutions stated that they had comeinto existence within the 10 years coveredby the question. Moderately large schools(enrollments of 1,500 to 5,000) show a dis-proportionately large increase in the numberof new departments and majors, with 42percent of the increase being due to suchschools though they represent only 27 percentof the total number of institutions.
Also adding to the need for more staff wasthe tendency to increase the course loadrequired of undergraduate mathematicsmajors. Twenty-six institutions indicated thatduring the past 10 years they had raised thenumber of credit-hours required of mathe-matics majors.
Appearing in the comments and observationswere also expansions on questions alreadydealt with in the main body of the question-naire. Many schools discussed their placementexaminations, honors programs, and particu-lar courses. Since these topics are treatedelsewhere in this book, the comments willnot be amplified on here.
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CHAPTER III. GRADUATE PROGRAMS(Part II of the Questionnaire)
As explained in Chapter 1, data wereobtained from more than 95 percent of theuniverse of programs at the master's leveland from 100 percent at the doctoral level.The lists of institutions having these programs,and specific characteristics of the programsas reported by the institutions, appear inAppendixes A and B. Appendix A lists the 36institutions that were known to confer master'sdegrees in statistics. This list was compiledchiefly from the 1956-57,1957-58, and 1958-59reports on Earned Degrees Conferred of theU.S. Office of Education. Too few institutionsprovided detailed data about master's pro-grams in statistics to make possible anyreliable statistical analysis of them.
Two institutions--DePaul University inChicago and Kansas State Teachers Collegeat Emporia--reported that, in addition to amaster's degree, they award a specialist'sdegree, which is intermediate between a mas-ter's and a doctor's degree. At DePaul thedegree is Degree of Mathematics Specialist;the requirement for it is 48 semester-hoursbeyond the bachelor's degree. At Kansas StateTeachers College, the degree is Specialistin Education, and the general requirementsfor it, beyond those for the master's degree,are 9 semester-hours of professional educa-tion, 15 semester-hours in courses open onlyto graduate students, and a field study (thesis)of not more than 6 semester-hours.
MASTER'S PROGRAMS INMATHEMATICS (SECTION A)
Data were obtained on 220 master's pro-grams in mathematics. (See Appendix A forthe list of institutions having these programsand specific data on them.) With only a fewexceptions (for example, the separate mas-ter's programs in the College of Letters,Science, and Arts and in the Institute ofTechnology at the University of Minnesota),
these programs represent different institutionsor distinct campuses of institutions, such asthe University of California campuses. In thediscussion which follows, these separatecampuses, as well as departments that havedistinct mathematics programs of their own,will be considered as "institutions."
Kinds of Degrees Awarded
Of 214 institutions which gave the names ofthe specific master's degrees that they awardin mathematics, 64, or 30 percent, conferredthe Master of Science (M. S.) degree alone. Twoof these 64 titled the degree S.M., probablyto duplicate the word order on a diploma inLatin. A Master of Science in Applied Mathe-matics was awarded by four, or 2 percent, ofthe institutions. Eighty-seven, or 41 percent,granted the Master of Arts (M.A.) degreealone, with two of these calling it A.M. Inaddition, one institution gave a Master of Artsin Natural Science and another, a Master ofNatural Science. Fifty-nine, or 28 percent, ofthe institutions conferred both the M.A. andM.S., and set slightly different requirementsfor each.
In summary, a student might, upon com-pletion of a master's degree program inmathematics, receive an M.S. at 123, orapproximately 57 percent, of the reportinginstitutions; an M.A. at 146, or approximately68 percent; a Master of Science in AppliedMathematics at 4 institutions; a Master ofArts in Natural Science at 1 institution; or aMaster of Natural Science at 1 institution.
Credit Requirements in Mathematics
Two hundred seven institutions reportedtheir requirements in terms of credit-hoursin mathematics. The number of requiredsemester-hours ranged from 12 to 36, both the
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median and the mode being 24 semester-hours.Because of variations allowed within a pro-gram, some institutions represented requiredcredit-hours in mathematics in terms of arange. The ranges in semester-hours extendedfrom 15-20 to 30-36.
The number of required quarter-hours inmathematics ranged from 18 to 46, the medianbeing 33 and the mode 30.
Total Credit Requirements for theDegree
Two hundred four institutions reported aspecific number or range of credit-hours re-quired. The total number of required creditsin semester-hours ranged from 18 to 38, themedian and the mode being 30 semester-hours. Again, some requirements were ex-pressed as ranges, extending from 18-24 to30-38 semester-hours.
The total number of required credits inquarter-hours ranged from 30 to 48, with themedian and mode 45 quarter-hours.
In 58 institutions the credit-hour require-ment was all in mathematics. In the remaininginstitutions it was divided between a certainnumber of credit-hours required in mathe-matics and a certain number that could beearned either in mathematics or in othersubjects.
Thesis Requirements
Of the 220 institutions reporting master'sprograms in mathematics, 114, or 52 percent,required a thesis. Of these 114, some requireda thesis for one degree only where more thanone degree was offered; some permitted analternative of two papers, and one permittedthe alternative of an expository paper andnine extra credit-hours. At 77, or 35 percent,of the institutions the thesis was optional.Twenty-eight, or 13 percent, of the institutionsmade no provision at all for a thesis.
Foreign Language Requirements
A modern foreign language was a require-ment of 97, or 45 percent, of the 218 institu-
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tions responding to this question. Of the 97institutions, 15 required a foreign languageonly for a specified degree, for a particularplan within a program, or in one departmentof the institution. Two institutions requiredknowledge of two modern languages: Frenchand German at one, and any two from amongFrench, German, or Russian at the other. Atone institution a test in basic statistics couldbe substituted for a foreign language.
Special Methods of Obtaining Degree s
It was possible to earn the master's degree inmathematics by evening and/or Saturday studyat 59, or 27 pei cent, of the 220 reporting in-stitutions and through summer study alone at82, or 37 percent.
Final Comprehensive ExaminationRequirements
Of 217 institutions responding to this item,192, or 88 percent., required some kind offinal comprehensive examination; 1 left suchan examination optional; and 24, or 11 percent,had no provisions for it.
Of the 192 institutions requiring a finalcomprehensive examination, 114, or 59 per-.cent, required only an oral examination--to betaken at one institution before the studentstarted his thesis work. Twenty-four, or 13percent, of the institutions required a writtenexamination, which in one case might besupplemented by an oral examination if deemednecessary.
A combination of both an oral and writtenexamination was part of 52, or 27 percent, ofthe programs. At one institution both examina-tions were required only when a student'sgrade point average was under 1.5. At oneinstitution an oral examination was requiredfor M.A. candidates and a written one for M.S.candidates. At another institution an oral ex-amination was part of the thesis plan and awritten one, part of a non-thesis option. Inthree other programs either an oral or awritten examination was required. One depart-ment head said that the choice was made bythe staff according to the number of candidates:if the number was large enough to make an
adequate reading of written examinations im-possible, then an oral examination was sub-stituted.
"Minor" Requirements
Fifty-five schools, or 25 percent of the 216which responded to this item, reported that aminor was required; 76, or 35 percent, that aminor was optional, with one program limitingthe minor to physics only; and 95, or 44 per-cent, that no provision was made for a minor.1In the last group, one respondent said that noprovision for a minor was made for M.S.candidates, implying that for candidates ofanother degree, some provison might be made.
Provisions for a Minor inMathematics
At 144 institutions, or 68 percent of the 213respondents to this item, a mathematics minor,acceptable in conjunction with a master's pro-gram in another department, was available.In one school a mathematics minor wasacceptable only for majors in chemistry andlife science. In 33 schools where mathematicsminors were acceptable in conjunction with amaste.,:'s program in another department, themathematics department itself made no com-parable provision for its own degree candi-dares.
Variations in Programs
Of the 220 institutions reporting master'sprograms with a major in mathematics, 45responded that they had several master'sprograms with slightly varying. requirements.Actually this figure is rather high because ofdifferent interpretations of the question.Whereas the respondents were asked to pointout the differences among their several mas-ter's programs in mathematics some respond-ents pointed out unique features of their pro-grams as compared with typical master's
1Percents do not add to 100 percent since some insti-tutions may have various requirements within the sameProgram.
programs in mathematics and some elaboratedon a particular program.
Among those interpreting the item in thelatter sense, one institution pointed out thatalthough it granted the master's degree, itdid not intend to admit students seeking aterminal master's degree. Two other institu-tions reported that their master's programswere basically 2-year programs, with the totalnumber of hours not of primary consideration.One institution said that its requirementswere not stated in terms of a specific numberof credit hours, but rather in terms of acertain amount of knowledge, as shown by anexamination; usually students acquired thisknowledge by taking courses but were notrequired to do so. Still another institutionclaimed that its master's program was de-finitely tailored to meet the needs and futurecareer plans of the individual student.
In elaborating on their particular programs,some department heads reported basic corerequirements. In some instances specificcourses were required: one institution re-quired one year of complex variables, oneyear of algebra, and one year of geometry- -some or all of which might be taken before thebachelor's degree; another called for sixsemester-hours each in modern algebra, prob-ability and statistics, and introductory realvariables. In other cases, candidates had totake a certain number of advanced, completelygraduate courses; for example, in one programa student was required to take two strictlygraduate courses, whereas the rest could besenior college courses.
Some institutions did report actual differ-ences among their master's programs in math-ematics. A common cause for a diversity ofprograms was the granting of both Master ofArts and Master of Science degrees. In oneinstitution candidates for the M.A. were per-mitted to take courses in other graduate fields,while candidates for the M.S. were requiredto take more graduate units in mathematicsand had more specific courses prescribed. Inone institution a minor was optional for theM. A.; in another a thesis, worth 5 to 9 quarter-hours, was required for the M.A., and aspecial research paper worth 3 quarter-hours,for the M.S. The course work and thesis for theM.S. in one institution emphasized applicationto industry; whereas the M.A. degree program
56
stressed pure mathematics. At another institu-tion, where candidates for an M.A. had to writean expository thesis, M. S. candidates eitherhad to write a research thesis or else pass thegeneral examination for the Ph.D.
In some institutions specialized degreesother than the M.A. or M.S. were granted aseither the regular degree in mathematicsor as alternative degrees. At one institution,students completing a master's program withmathematics as the major field of interestwere granted the degree Master of Sciencein Engineering Science, and in two otherinstitutions, the Master of Arts in NaturalScience. An alternative degree, Master inLetters, was offered in one program, with re-quirements of 16 to 20 credits in mathematicsand 10 to 14 in related fields and with no thesis.Some institutions also offered specialized de-grees in applied mathematics and in statistics.
Frequently, there were variations at oneinstitution in thesis requirements for master'sdegrees. A common pattern was to offer twoalternative plans, one with a thesis and onewithout. In programs requiring a thesis, therewere usually a foreign language requirementand a smaller required number of credit-hours than in non-thesis programs. To com-pensate for the waiving of a thesis require-ment, non-thesis programs usually called formore credit-hours in the major field and alsoin the minor, where one existed, and some-times additional papers. For example, Plan Ain one program called for a thesis, 18 creditsin the major, and 9 credits in the minor;Plan B required 27 credits in the major field,18 credits in a combination of two minors,and three papers. At some institutions, highlyindividualized arrangements or substitutionswere occasionally made, such as allowinga student to write a thesis in an applied areaoutside mathematics or to substitute a finalcomprehensive examination for a thesis.
Other variations occurred in major/minorcombinations and in related study areas. Oneinstitution allowed four different alternatives:
(1) A major of not less than 30 semester-hours;
(2) A major of not less than 20 hours, plusa minor of 10 hours;
(3) A major of not less than 20 semester-hours, plus 10 hours of related courses;or
57
G3
(4) A split major arranged by the adviserand approved by the Graduate Dean.
At some institutions students could choose todo as much as half their course work inphysics; one institution permitted students totake 6 hours of work in areas with no im-mediate connection with mathematics. Atanother institution candidates could take all30 hours in one department or a maximum of12 in a "related area."
Finally, program variations also existed atinstitutions where no program was specificallydesigned. for preparing teachers, but wherespecial provision was made for teachers whowished to enroll in regular master's degreeprograms in mathematics. In one program,high school teachers could combine mathemat-ics and physics. In another they could writea thesis on some phase of mathematics re-lated to their teaching positions.
MASTER'S PROGRAMS SPECIALLYDESIGNED FOR THE TEACHING OF
MATHEMATICS (SECTION B)
Data were obtained from 183 institutions onmaster's programs specially designed to pre-pare mathematics teachers. (See Appendix Afor the list of institutions with these programsand specific data on them.) These programsare primarily directed at upgradyng thequalifications of secondary school teachersof mathematics. Many of them have been newlyestablished as a result of the emphasis inrecent years on improved teacher preparation,stemming in turn from the introduction ofnewer mathematical concepts into many cur-riculums. The National Science Foundationinstitutes, have lent great impetus to thesetrends. Even a new degree, Master of Artsin Teaching, was finding favor among anincreasing number of institutions.
Kinds of Degrees Awarded
Of 181 institutions which gave the names ofthe sperific master's degrees awarded formathematics-teaching programs, 81, or 45percent, conferred a Master of Arts degreein some form (see below); 73, or 40 percent,a Master of Science degree; and 48, or 27
percent, an Education degree. One institutiongave a Master of Mathematics degree. Someinstitutions provided for variations within agiven program and as a result offered morethan one type of degree for the same program.
Of the 81 institutions awarding a Master ofArts degree, 39 conferred a straight M.A.;28, a Master of Arts in Teaching (M.A.T. orA.M.T.); and 9, a Master of Arts in Education.The remaining institution in the group grantedmore specialized degrees, such as a Masterof Arts for Science Teachers, a Master ofArts in Secondary Ed',cation, a Master of Artsin Natural Science; and a Master of Arts inTeaching in Science and Mathematics.
Of the 73 institutions bestowing a Master ofScience degree, 29 gave an M.S.; 23, a Masterof Science in Education; and 10, a Master ofScience in Teaching (M. S. T. ). Other institutionsgranted such degrees as Master of Sciencein Basic Science, Master of Science in GeneralScience, Master of Science in Natural Science,and Master of Science in Mathematics Educa-tion.
The most common Education degree wasthe Master of Education (M.Ed.), conferredby 38 institutions. Four awarded a Master ofTeaching; and the rest, such degrees asMaster of Teaching Science (M.T.S.), Masterof Education in Natural Science, and Masterof Secondary School Science.
Credit Requirements in MathematicsOne hundred seventy-six institutions re-
ported their mathematics requirements interms of credit-hours. The required numberof semester-hours ranged from 6 to 36, boththe median and the mode being 18 semester-hours. Since some institutions allowed forvariations in a student's program, credit-hourswere sometimes presented as a range. Theranges in semester-hours ran from 6-9 to24-30 semester-hours.
The total number of credits required inquarter-hours ranged from 6 to 45, with amedian of 27 quarter-hours and equal modesof 18 and 30 quarter-hours., Quarter-hoursexpressed in ranges extended from 9-27 to33-36.
One institution reported that there were nocredit requirements in mathematics in itsprogram.
58
70
Credit Requirements in EducationCourses
Specific credit requirements in educationcourses were reported by 153 institutions. Inthose institutions on the semester plan, therequired semester-hours ranged from 2 to26, with the median being 10 semester-hoursand the mode 6 semester-hours. Those re-quirements expressed as ranges ran from0-6 to 18-24.
Quarter-hour requirements in educationcourses ranged from 3 to 36, with the medianbeing 15 and the mode 12. The ranges inquarter hours extended from 8-16 to 24-30.
Twenty-six institutions reported that theyhad no specific credit requirements for educa-tion courses.
Total Credit Requirements for theDegree
The total credit requirements for the mas-ter's degree were reported by 175 institutions.The range in semester-hours was 24 to 36,the median and mode both being 30. Again,some requirements were expressed as ranges;these extended from 30-35 to 30-38 semester-.hours.
The range of total quarter-hour require-ments was 36 to 60, with the median and modeboth being 45. Two institutions recorded therequirements in terms of ranges, 39-54 and45-60.
Thesis Requirements
Of the 183 institutions reporting master'sprograms expressly designed for the teachingof mathematics, 38, or 21 percent, requireda thesis; some of these required it for onedegree only where more than one degree wasoffered, and others allowed the alternativesof an expository paper, two papers, or anessay. Seventy-four, or 40 percent, of theinstitutions made the thesis requirementoptional, in two instances for one degreeonly. Seventy, or 38 percent, of the institutionsmade no provision at all for a thesis.
Foreign Language Requirements
A modern foreign language was a require-ment in only 17, or 9percent of the 182 institu-tions responding to this item. In 3 of these 17, thelanguage requirement applied only to candi-dates for the M.A. degree; and at 2 otherinstitutions of the 17, a test of basic statisticscould be substituted for the language require-ment.
Special Methods of Obtaining Degrees
It was possible to earn the master's degreeby evening and/or Saturday study in 55, or30 percent of the 183 reporting institutions,and through summer study alone in 135, or74 percent of them. At one of the latter in-stitutions, only the M.Ed. could be obtainedby summer study, not the M.S.T. degree. Thatalmost three-fourths of the colleges and uni-versities made it possible to earn a degreethrough summer study alone is evidence ofthe special effort to accommodate teachers.
Final Comprehensive ExaminationRequirements
Of the 183 institutions reporting mathe-matics-teaching programs on the master'slevel, 180 responded to the item on final com-prehensive examination. Of these respondents,135, or 75 percent, required some kind offinal comprehensive examination; 44, or 24percent, had no provision for such an examina-tion; and 1 reported that no decision had yetbeen made.
Of the 135 institutions requiring a final com-prehensive, 51, or 38 percent, required only anoral examination (although at 1 institution, awritten report on independent study had to besubmitted as well). Thirty-nine, or 29 percent,required a written examination (to be supple-mented, at 1 institution, by an oral examinationif deemed necessary, and required, at anotherschool, for non-thesis students only).
A combination of both an oral and writtenexamination was a part of 42, or 31 percent,of all programs reported. In three otherprograms either an oral or a written examina-tion was required.
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"Minor" Requirements
A minor was required in 40, or 24 percent,of the 167 institutions responding to this item.At one institution the minor was a require-ment for the "credential" which must accom-pany the degree in this type of program ratherthan for the degree itself; at another institutionminors had to be taken in two of the followingfields: astronomy, physics, biology, geology,and chemistry. A minor was optional at 45,or 27 perCent, of the institutions, with thecondition at one institution that an under-graduate requirement of 32 hours of sciencebe made up if not already completed. At 82,or 49 percent, of the responding institutions,,a minor was not required.
Provisions for a Minor inMathematics
Of the 166 institutions reporting on thisitem, 105, or 63 percent, said that a minor,acceptable in conjunction with a degree pro- -gram in another department, was available;one specified that such a minor was acceptableonly in conjunction with the physical sciences.Sixty-one, or 37 percent, reported having nosuch provision.
Variations in Programs
Of the 183 institutions and branches of in-stitutions with mathematics-teaching pro-grams at the master's level, 46, or 25 percent,provided pertinent and interesting informationon variations among their programs. As inregular master's programs in mathematics,there were different interpretations of thequestionnaire item.
Some institutions that offer more than onespecial degree-program for those who planto teach mathematics used this item to de-scribe how other, similar programs of theirsvaried frGin the one described in Items 1-5.An examination of these responses led to thefollowing generalizations. Programs leading toan M.A. or M.S. degree frequently requireda large proportion of credit-hours in mathe-matics and, more often than in other degreeprograms, had a thesis and foreign language
requirement. Master of Education degree can-didates, in contrast, were usually required toearn only half or even fewer of their credit-hours in mathematics, with a thesis optionalin many instances and with no foreign languagerequirement. One institution reported thatcandidates for the M.Ed. degree could take12 hours of course work in extension courses.In programs leading to the Master of Arts inTeaching degree, the candidates usually tookslightly more than half their course work inmathematics, frequently had to take specifi-cally "graduate" education courses, and, moreoften than M.Ed. candidates, had to write athesis and meet a foreign language require-ment. (These generalizations were made onlyfrom responses in this section on variationsand not from all data on all programs in thisgroup).
Some institutions used this item to recordvariations allowed within one degree-program.Frequently a specific number of credit-hoursin mathematics were required and a particularnumber of credit-hours specified for electiveseither in mathematics and/or related areas.For example, as a variation to one programwhere 20-24 semester hours in mathematicswere required, a student could take as few as10 hours in mathematics and 10 hours in arelated field such as physics. In another pro-gram, rather than taking all 40 quarter-hoursin mathematics, a student could take up to 15quarter-hours in a related subject.
One institution reported a thesis option inthe program. A minimum of 30-35 semester-hours, plus a research project, were requiredfor the degree, but if a thesis were written,only 30 semester-hours were required and noresearch project.
In some programs the education courserequirements varied greatly according to thestudent's undergraduate course of study. Forexample, one program required a studentwithout any undergraduate credits in educationto take 16 hours of education in graduateschool; if a student had had the equivalent asan undergraduate, no education courses wererequired.
At some institutions, candidates could choosewhether to major in mathematics and minor ineducation or vice versa. At one institution,when a student chose to major in education, hewas required to take 18-24 semester-hours of
7
professional education courses and 6-12semester-hours in mathematics. With no prac-tice teaching experience, he had to earn 6additional credits in serving his apprentice-ship. The same institution also offered anextended 12-month program for Retired ArmedServices Officers, who had to take 21-27semester Mars in mathematics and 12-18semester hours in education, including practiceteaching, for a total of 39 semester-hours.
Another large group of respondents to theitem on variations elaborated on specific,sometimes unique, characteristics of theirprograms. Some said that programs wereavailable only to experienced teachers orto those who already possessed a SecondarySchoQl Teaching Certificate. One institutionhad a program designed especially for teachersin small high schools where mathematics andscience were taught by the same person.Another had a program designed to preparejunior high school mathematics teachers only.At one institution a 6-hour course called"Elementary Mathematics from an AdvancedPoint of View" had been set up especially forhigh school teachers; and at another, a specialcourse, "Elementary Mathematics from anAdvanced Standpoint," which could be countedas either an education or a mathematicscourse, was offered. One program was acoordinated 5-year program leading to aB.A. in mathematics and an A.M.T. in teach-ing. As part of still another program, anexpository paper in mathematics was re-quired in cooperation with the College ofEducation, though not a part of the regulargraduate degree requirement. Finally, oneinstitution reported that although no formalprofessional education courses were required,special courses of interest to teachers wereprovided according to their previous back-grounds and preparation.
DOCTORAL PROGRAMS INMATHEMATICS (SECTION C)
During the decade of the 1950's, 76 institu-tions (counting as separate institutions theUniversity of California at Berkeley, the Univ-versity of California at Los Angeles, the Univ-versity of North Carolina at Chapel Hill, and
the University of North Carolina, State Collegeat Raleigh) awarded at least one doctoraldegree each in mathematics. By 1961, 94institutions were offering doctoral programs inmathematics, including applied mathematicsand statistics, which are taught in separatedepartments at some universities. (See Ap-pendix B for data on programs at each ofthese institutions.) Several of the respondentsin this survey indicated that plans wereunderway to inaugurate doctoral programs attheir institutions.
Kinds of Degrees Awarded
Of the 94 institutions awarding doctoraldegrees in mathematics in 1961, 91 awardedthe Doctor of Philosophy (Ph.D.) degree; 2,the Ph.D. in Applied Mathematics; and 1, thePh.D. or the Doctor of Science, Sc.D.
Credit Requirements inMathematics
The minimum credit requirements in mathe-matics at the 54 institutions which specifiedthem varied considerably from institution toinstitution. For institutions on a semester-hour basis the minimum number of requiredsemester-hours ranged from 36 to 96, with themode being 60 semester-hours. Because ofvariations permitted within doctoral programs,four of these institutions reported the mini-mum semester-hour requirements in terms ofranges, extending from 45-60 to 74-90.
At the 10 responding institutions that were onthe quarter plan, the minimum quarter-hourrequirements in mathematics ranged from 45to 145, with the median being 80. One institu-tion expressed its minimum requirements as arange, 120-145 quarter-hours.
Total Credit Requirements forthe Degree
The total number of credit-hours requiredfor the doctor's degree was reported by 57institutions, 47 of which were on the semesterplan and 10, on the quarter plan. The remain-ing 37 institutions did not have a specified
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73
minimum number of credits. Of the 47 institu-tions on the semester plan, 26 included thecredits earned for the thesis in the reportedtotal credit requirements for the degree. Atthese institutions the total required number ofsemester-hours ranged from 36 to 96, themode being 90 semester-hours. Twenty-oneinstitutions on the semester plan reported totalcredit-hour requirements in courses only, athesis also being required. These require-ments ranged from 48 to 90 semester-hoursplus a thesis, the mode being 60 semester-hours.
Of the 10 institutions on the quarter plan, 6included credits earned for a thesis in the re-ported total credit-hour requirements, whichranged from 100 to 135 quarter-hours. At thefour institutions not including thesis creditsin total credit-hour requirements, the rangeextended from 671 quarter-hours to 90 quarter-hours, plus a thesis.
In most of the institutions reporting specificcredit requirements, the required credits wereentirely in mathematics. Two institutions spec-ified the number of required courses insteadof the number of credits.
Several respondents emphasized that theirfigures represented absolute minimum re-quirements and that generally the totals forindividual students were higher. Others saidthat, despite the specified requirements, thedoctor's degree depended less on the accumu-lation of credits than on demonstration ofqualifications considered requisite by thefaculty and on writing a thesis involvingoriginal results. Some respondents statedsimply that their minimum specified require-ment was 3 years of study beyond the bac-calaureate.
Examination Requirements
Ninety-two institutions made usable re-sponses to this item. All but two requiredmore than one type of examination. Seventy,or 76 percent of the 92 institutions, requiredan oral preliminary or qualifying examination;58, or 63 percent, a written preliminary orqualifying examination; 41, or 45 percent, afinal comprehensive oral examination; 20, or22 percent, a final comprehensive written
examination; 89, or 97 percent, an oral exami-nation on the thesis; and 1, an examination ona minor thesis in mathematics.
Of the 90 institutions requiring more than oneexamirn.tion, 24, or 26 percent, required two.The most frequent combinations (at 14 institu-tions were an oral preliminary examination andan oral examination on the thesis, and (at 9 in-stitutions) a written preliminary examinationand an oral examination on the thesis.
Forty-five, or 49 percent, of the institutionsrequired three examinations, the most commoncombination being an oral preliminary, awritten preliminary, and an oral examinationon the thesis.
Thirteen, or 14 percent, of the institutionsrequired four examinations, the most commoncombination being an oral preliminary, awritten preliminary, a final comprehensiveoral, and an oral examination on the thesis.
Eight, or 9 percent, of the institutionsrequired five examinations: an oral and awritten preliminary, oral and written finalcomprehensive, and an oral examination onthe thesis.
Foreign Language Requirements
Ninety-three schools required doctoral can-didates to show competence in one or moreforeign languages; the 94th responding in-stitution failed to provide information on thisitem. Two languages were required in allprograms with the exception of two programsat Harvard University (statistics and appliedmathematics, which required only one lan-guage).
German, French, and Russian were thelanguages acceptable for the language require-ment at 73, or 79 percent, of the institutions.Of this number, 10 specified German andFrench as the preferred languages; 5, Germanand Russian; 2, German; 1, French; and 1,French and Russian. Nine of the 73 institutionssaid that occasionally other languages vitalfor research in a particular field of interestmight be substituted.
Thirteen, or 14 percent, of the respondinginstitutions named Italian as a fourth, ac-ceptable language; of these, specified German,French, and Russian as preferred languages;4, German and French; and 2, German and
A
Russian. One of the 13 institutions said thatone language could be French or Italian, butthat both would not be accepted. Another in-stitution in this group required a strongreading knowledge in one language and a lesserproficiency in a second one.
At three institutions, German and Frenchwere the only acceptable languages. Two otherinstitutions accepted German, French, Russian,and Japanese, with German, French, andRussian preferred at one and German andRussian at the other. One institution acceptedGerman, French, Russian, Italian, and Japa-nese, with German preferred; and one acceptedGerman, French, Russian, Italian, and Spanish,with German and French preferred.
In summary, all 93 institutions acceptedGerman and French toward meeting the lan-guage requirements; 90, Russian; 13, Italian;3, Japanese; and 1, Spanish. As indicated,some substitutions were permissible. In ad-dition, 2 institutions indicated that the require-ment for a. second language was often waivedfor students whose native language was notEnglish.
In specifying the level of foreign languagecompetence required, 88, or 97 percent, of theinstitutions reported that reading comprehen-sion only was required; 2, reading comprehen-sion and the ability to write; and 1, the abilityto speak and write.
"Minor" Requirements
Thirty-three institutions, or 35 percent, saidthat a minor was required; 29, or 31 percent,that a minor was optional; and 31, or 33 per-cent, that they had no provisions for a minor.One specified that the minor was usually in asecond field of mathematics; and another, thatthe minor could be taken within the mathe-matics department.
Special Methods of ObtainingDegrees
At nine institutions a student could earn aPh.D. in mathematics through evening and/orSaturday study, and at four, through summerstudy (see Appendix A for the names of theseinstitutions).
Areas of Specialization andNumbers of Degrees
Many institutions which offered certain spe-cializations did not award degrees in thembetween January 1958 and January 1961, thetime period specified on the questionnaire. Inmany cases this was because the program wastoo new. For the statistical findings on thisitem, see table 23.
Table 23.--Number of institutions offering particular doctoral specializationsin mathematics, and number of doctoral degrees awarded in each: January
1958 to January 1961, inclusive
Area ofspecialization
Number of institutionsNumber of
degrees awardedwithin this time
intervalOffering thisspecialisation
Which gave oneor more degreeswithin this time
interval
Algebra 76 46 110
Analysis 85 61 304
Applied mathematics 48 27 114
GeometryLQg ie
3924
1711
2818
Statistics 49 32 164
Topology 67 39 94
Number theory 9 5 9
Probability 3 3 4
Other 13 10 19
The 94 institutions with doctoral prdgramsawarded a total of 864 doctor's degrees.Analysis was the most popular specialization,being offered at 85 of the institutions and ac-counting for 304 doctor's degrees, or morethan a third of the total number. Algebra wasnext most popular from the standpoint ofnumber of institutions (76) offering it forspecialization, but it accounted for only 110degrees, whereas statistics, offered by 49institutions, claimed 164 degrees over the 3-year period. Applied mathematics (114degrees) and topology (94 degrees) also ac-counted for sizable portions of the 864 degreesconferred.
DOCTORAL PROGRAMS SPECIALLYDESIGNED FOR THE TEACHINGOF MATHEMATICS (SECTION D)
In 1961, 25 institutions offered a doctoralprogram specially designed for the teaching ofmathematics. (See Appendix B for data o:iprograms at each of these institutions.) Fourof these programs had only recently beenintroduced.
7c.13
The objectives of these programs varied.The objective at Yeshiva University was toprepare college teachers of mathematics. Anexpository or analytical thesis and 9 creditsin education and psychology were the only es-sential differences from the traditional doctor-ate in mathematics. In most other programsthe objective was to prepare an individualwith dual competencies in mathematics and inprofessional education. Such degree holdersfrequently become mathematics teachers injunior or senior colleges, professors of mathe-matics education in universities, and special-ists in mathematics education at local, State,and national levels.
Kinds of Degrees Awarded
The Doctor of Philosophy (Ph.D.) degreewas the only degree offered at 8, or 32 percent,of the 25 institutions; the Doctor of Education(Ed.D.), the only degree in 6 others, or 24percent; and either the Ph.D. or Ed.D. in theremaining 11, or 44 percent.
Credit Requirements inMathematics
The credit-hour requirements in mathe-matics at the 13 reporting institutions thatwere on the semester plan ranged from 24 to60 semester-hours, with the median being 34and the mode 30. At two of these institutions,where both the Ph.D. and the Ed.D. weregranted, credit-hour requirements differedfor the two degrees. One institution requiredonly 28 semester-hours in mathematics for
Ed.D. and 50 semester-hours in mathe-matics for the Ph.D.; similarly, the otherrequired 30 semester-hours for the Ed.D. and40 for the Ph.D. Because of variations per-mitted within the program, one institution re-ported its requirements as a range, 27-42semester-hours.
The credit-hour requirements in mathe-matics for the three institutions on the quarterplan were 20, 36, and 72 quarter-hours. Eightinstitutions did not respond to this item.
Credit Requirements in EducationCourses
Semester-hour requirements in educationcourses ranged from 9 to 48 semester-hours,with a median of 30. Again, credit-hour re-quirements in education courses differed forthe Ed.D. and Ph.D. where both were offeredby the same institution. One institution re-quired 48 semester-hours in education coursesfor the Ed.D. and 36 for the Ph.D.; the other,37 semester-hours for the Ed.D. and 12 forthe Ph.D. Semester-hour requirements wereexpressed as a range at one school: 27-42semester-hours.
Quarter-hour requirements in educationcourses were 16, 54, and 60 at the three in-stitutions on the quarter plan. Eight institutionsdid not provide usable information.
Total Credit Requirements for theDegree
The total number of semester-hours re-quired for the degree ranged from 60 to 96,with a mode of 90. Three institutions grantingboth the Ed.D. and Ph.D. reported a differenttotal number of semester-hours required foreach degree--at all three, the credit re-quirements were greater for the Ed.D. thanfor the Ph.D.
Two institutions on the quarter plan re-quired a total of 108 quarter-hours for thedegree; and one, 135 quarter-hours. Seveninstitutions did not report the specific numberof credits required for the doctorate.
Examination Requirements
Of the 22 institutions reporting on this item,15, or 68 percent, required an oral prelimi-nary or qualifying examination; 16, or 73 per-cent, a written preliminary; 14, or 64 percent,a final comprehensive oral examination; 11,or 50 percent, a final comprehensive writtenexamination; and 22, or 100 percent, an oralcomprehensive on the thesis. One institutionspecified that the Graduate Record Examina-tion and the Millers Analogy Test were re-quired for admission to graduate study.
Three, or 14 percent, required 2 examina-tions; 6, or 27 percent, 3; 9, or 41 percent,
64.
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4; and 4, or 18 percent, 5 examinations. Themost frequent combination at the nine in-stitutions requiring four examinations was anoral and a written preliminary, a final oralcomprehensive, and an oral comprehensiveexamination on the thesis.
Foreign Language Requirements
Respondents were asked if competence inone or more foreign languages was requiredin their doctoral programs. Two failed toprovide the requested information. Of the 18responding institutions that conferred the Ph.D.for this type of program, 16 required com-petence in two languages, and 2 required it inonly one language. Of the 15 responding in-stitutions that offered the Ed.D. degree, nonerequired two languages, and only 2 required'one language. One institution reported thatknowledge of one or more foreign languagesmight be required if they were needed for athesis.
When asked to name the languages acceptedfor meeting the language requirement, 10, or59 percent, of the 17 institutions respondingtothis item checked German, French, and Rus-sian, with 4 stating the substitutions that mightbe made upon petition. At two of these fourinstitutions, a course on the use of com-puters or statistics might replace the foreignlanguage requirement. At one, statistics mightreplace one language.
Two of the responding institutions namedGerman, French, Russian, and Italian as ac-ceptable languages, with German, French, andRussian being preferred at one of the in-stitutions. Two additional institutions reportedthat German and French were the languagesgenerally accepted, although the graduate coun-cil at one of the institutions sometimes ac-cepted Russian as a substitute.
One institution accepted French, German,and a general knowledge of the Romance lan-guages; two others accepted German, French,Russian, and Spanish, with the first threepreferred.
In summary, all 17 responding institutionsaccepted German and French; 14, Russian; 4,Italian; 2, Spanish; and 1, Romance languages.
All 17 institutions also insisted upon readingcomprehension as the necessary level of foreign
language competency, with one institutionspecifying reading comprehension in the litera-ture of mathematics.
"Minor" Requirements
At 12, or 50 percent, of the 20 institutionsresponding to this item, a minor was requiredfor at least one of the doctoral degrees inmathematics-teaching programs; at 4, or 20percent, a minor was optional; and at 4, or 20percent, there were no provisions for a minor.
At two institutions where a minor was re-quired, it was customarily in an area of mathe-matics other than the particular field ofspecialization. At another school, a minor inprofessional education was common, though notmandatory. One institution required twominors.
Special Methods of Obtaining Degrees
At only one institution could a student earnhis doctoral degree through Saturday and/orevening study, and at only three, throughsummer study (see Appendix B for the namesof these institutions).
Number of Degrees
Between January 1958 and January 1961 in-clusive, 14 institutions awarded 63 doctoratesspecially designed for the teaching of mathe-matics. The largest numbers of these degreesawarded by single institutions were 18 and 15.Two institutions awarded 5. Another institutionconferred 4 degrees; 2, 3 degrees each; 3, 2degrees each; and 4, 1 degree each.
Special Programs for PreparingCollege Teachers of Mathematics
Although many mathematics-teaching pro-grams at the doctor's level are intended forprospective secondary school teachers, atleast two programs--one in operation at thetime of the survey and one then in prepara-tion--have as their special aim the training ofcollege teachers.
The first of these two, at Yeshiva Univer-sity, requires candidates to earn the samenumber of credits in graduate mathematicsas are required in its regular Ph.D. program.The student is encouraged, however, not tospecialize intensively, but rather, to selectcourses for breadth of coverage. A sequenceof courses especially pertinent to collegeteaching, plus some experience in collegeteaching, are required. One significant varia-tion from the traditional Ph.D. mathematicsprogram is that the student may fulfill hisdissertation requirement by submitting aserious study of some phase of mathematicalthought without creating new mathematicaltheory or thought.
The Ph.D. mathematics-teaching programat Dartmouth College, established in 1962, alsohas as its principal aim the training of collegeteachers. This special program differs fromthe traditional Ph.D. program in requiringgreater mathematical breadth. Teachingduties, which normally consist of conductingdiscussion sections in freshman courses for 4or 5 hours each week, are part of the program.
To qualify for the Ph.D. in this program,the student must obtain a grade of Honors inat least five graduate courses at Dartmouthand in a general examination. In addition, hemust pass eight advanced courses at Dart-mouth, and show a capacity to read mathe-matical literature in two of the languagesFrench, German, or Russian. He must alsocomplete a thesis, which may either containnew mathematical theory or may be criticalor expository in nature.
Additional Preparation for TeachingMathematics in College(Section E)
Over the years a complaint frequently heardis that many professors are poor teacherseven though they know their subject well.Another common charge is that faculty mem-bers entering the profession lack an under-standing of basic principles of learning and ofhigher education in general. There is no un-animity on the need to correct these allegedinadequacies. Some colleges favor programsfor this purpose; others seem indifferent; andstill others oppose such programs as too
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general or as wasteful, since these inadequaciesare overcome, they claim, after the first yearor two of full-time teaching.
Nevertheless, an increasing number of in-stitutions are providing programs designed toimprove the preparation of college teachers.A total of 64 departments in 63 different in-stitutions reported some arrangements forpreparing college teachers. In all probability,there were many more programs than theresponses indicated, since the heads of mathe-matics departments in larger universitiesmight not be aware of all such programs intheir institutions. Indeed, some heads made itclear that they could speak only for their owndepartments.
Statistical FindingsOf the colleges and universities offering
these programs, about 70 percent were insti-tutions with an enrollment of 5,000 or more,and approximately 75 percent of them werelocated in the Mideast, Great Lakes andPlains, and Southeast regions.
Of the departments responding onrequire-ments for professional education for collegeteaching careers, 13 said that such coursesor seminars were required; 21, that they werenot required, but were encouraged; and 25, thatthey were neither required nor particularlyencouraged.
Variations in ProgramsThere was wide variation in the kinds of
preservice professional education availablefor college teachers in training. A few in-stitutions had a separate Department of HigherEducation. Other colleges offered a graduateminor in higher education. One State university,for example, offered a graduate minor incollege teaching, which consisted of 15-24quarter-hours of course work or seminars,including an independent teaching project underthe direction of a faculty member in thestudent's major department.
Teachers for Junior Colleges
Several regular courses in the differentphases of higher education were offered for
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future college mathematics teachers by theresponding institutions, and in a few cases suchcourses were compulsory. With the rapid ex-pansion in the number of junior colleges inthis country, it was not surprising to see manycourses devoted to that particular type ofinstitution. One mideastern State universityrequired those planning to teach in juniorcolleges to take "The Community College" andencouraged them to elect "Junior CollegeTeaching." Other course offerings in this areaincluded "Teaching in the Community College,""Junior and Technical Colleges," "Problemsand Methods in Teaching on the Junior-CollegeLevel," and "Seminar in the CommunityCollege." Looking to the future, the depart-ment of education at one State college ex-pected to add three courses, "The PublicJunior College," "Junior College Curriculum,"and "Internship in Junior College Education,"to form the core of a new program for thepreparation of junior college teachers.
Kinds of Courses and Programs
Frequently, courses of this type were re-quired only for particular types of studentsand for specific degrees. One university re-quired all graduate assistants to take thequarter-hour course, "Orientation to CollegeTeaching," given in the Department of HigherEducation; another required all new teachingfellows to attend each week a 1-hour semineron preparing college teachers of mathematics,for which 2 semester -hours of credit weregiven. One Eastern university required allcandidates for the Ph.D. in science- ormathematics-teaching to take the regular 3-hour course "The Philosophy of Higher Educa-tion," given at the school of education, and aseminar on teaching mathematics in college.In many instances, candidates for an M.Ed. orEd.D. with a specialty in mathematics educa-tion were required to take specific courses inhigher education.
Some heads of mathematics departmentswho did not know the exact titles of coursesin higher education offered by other depart-ments of the institution simply reported thatsuch courses were given by the college ofeducation, the psychology department, theschool of vocational education and psychology,
the department of general studies or, in oneinstance, by the dean of the graduate division.
A wide variety of specific courses was re-ported. One Southeastern university offered atwo-semester course "History of Education inthe United States" and a seminar "The LiberalArts College and Its Philosophy." A RockyMountain university awarded one semester-hour of credit for each of two semesters forthe course "Practicum in College or UniversityTeaching;" this consisted of a series of lecturesby individuals from all campus areas duringthe first semester and work with the majorprofessor in the field of specialization duringthe second semester. Some of the othercourses reported were "Origin and Develop-ment of Higher Education in the United States,""Comparative Higher Education," "Organiza-tion, Government, and Administration ofAmerican Higher Education," "InternationalOrganization in Higher Education," "Topics inHigher Education," "Methods of College Teach-ing," and "Internship in College and JuniorCollege Teaching."
As indicated in the last-named course, pro-visions were made for student teaching in a
few instances. Many of the graduate studentswere teaching-assistants as well and workedunder the careful supervision of the depart-ment head, meeting with him and fellowgraduate assistants for at least I hour a weekto discuss problems and philosophy of teach-ing. One department head said that studentspresented, in their regular mathematicscourse, half-hour talks on specific topics inmathematics to gain practice in teaching ideas.One university offered courses preparing stu-dents' to teach at the junior college level andat the 4-year college level, and two others re-ported having internship provisions.
Informal seminars or meetings, usuallywithout credit, were commonly used to pre-pare college teachers. One mideastern Stateuniversity had weekly lectures on collegeteaching, and attendance at these lectures wasnoted on students' transcripts. In other in-stitutions it was the practice to have mathe-matics majors and graduate students meetoccasionally to discuss teaching methods,curriculums, and job opportunities or to de-vote portions of subject-matter courses tothese topics.
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CHAPTER IV. SOME RELATED FACTORS(Part I of the Questionnaire)
This chapter discusses factors that are notpart of specific mathematics programs assuch, but that are important to their overallsuccess--clubs, mathematics contests, andvisiting lecturers; instructional techniquesthat accommodate unusually large numbers ofstudents; inservice education for mathematicsteachers; libraries; and computing facilities.
ACTIVITIES DESIGNED TOSTIMULATE INTEREST IN
MATHEMATICS
Apart from formal courses, one of the mosteffective ways of promoting study and researchin mathematics is the undergraduate club.Other ways include mathematics contests andvisiting lecturers. Newsletters or bulletinsprepared by the mathematics department andsent to high schools are an effective way ofpromoting interest in mathematics at thatacademic level and of attracting potentialstudents.
The Undergraduate MathematicsClub (Item 12)
Almost half (49 percent) of the 877 institu-tions participating in this survey reportedthat they had an undergraduate mathematicsclub on campus. (See table 24.) Thirty-onepercent of the 877 had local clubs with noaffiliation; 7 percent had clubs affiliated withPi Mu Epsilon; 6 percent, clubs affiliated withKappa Mu Epsilon; and 5 percent had clubswith other affiliations.
Comparisons by category of institution.- -Universities (73 percent) had clubs more thanany other type of institution, and teacherscolleges ranked second, with 51 percent. PiMu Epsilo;i clubs were popular at the uni-versities, 32 percent of the universities having
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them. Kappa Mu Epsilon clubs were mostcommon at the teachers colleges (10 percent).
Public institutions tended to have under-graduate clubs more than did private institu-tions (63 percent versus 41 percent). Publicinstitutions also tended more to have affiliatedclubs: 22 percent of them had clubs affiliatedwith Pi Mu Epsilon or Kappa Mu Epsilon,whereas only 9 percent of the private institu-tions had clubs so affiliated.
Regionally, there were no great differences,except that Kappa Mu Epsilon clubs wererelatively popular (10 percent) in the GreatLakes and Plains region and relatively un-popular (2 percent) in the North Atlanticregion, and that local clubs were especiallypopular in the North Atlantic region (37percent).
There was a direct correspondence betweenenrollment size and undergraduate clubs oncampus, which were found in frequenciesranging froin 78 percent among institutionswith enrollments of more than 5,000, down to30 percent among institutions with enrollmentsof fewer than 700. The Pi Mu Epsilon clubwas particularly popular among very largeinstitutions (more than 5,000 students), 31percent of which had clubs with this affiliation.The predominant affiliation at institutions inthe 1,500-5,000 enrollment-size category waswith Kappa Mu Epsilon (12 percent).
Characteristics of club programs.--Thereseemed to be no significant categorical dif-ferences in the type of programs offered.Between one-third and one-quarter of all 877institutions devoted time to each of three ac-tivities: the presentation of papers by membersof the clubs, talks by faculty members, andtalks by speakers from outside the institution.There was no uniformity in frequency of clubmeetings. Nineteen percent held only 1 to 4meetings per academic year, while 32 percentheld 5 to 7 meetings, 31 percent 7 to 10, and18 percent, more than 10 meetings yearly.
Table 24.--Number and percent of institutions having undergraduate mathematics clubs on campus, andpercent of these institutions having specified clubs; by type, control, region, and enrollment size:Aggregate United States, 1960-61
Number of Percent havingPPercents of institutions
Category of institution
institutionshaving amath clubon campus
clubs (number incolumn 2+ numberof institutions
in category)
having clubs which are--
Affiliatedwith l'i MuEpsilon
Affiliatedwith KappaMu Epsilon
Local clubswith no
affiliationOther
(1) (2) (3) (4) (5) (6) (7)
All institutions 426 49 7 6 31 5
TypeUniversities 102 73 32 4 38 4Liberal arts colleges 241 42 3 5 29 6
Teachers colleges 69 51 0 10 36 4Technological schools 14 44 6 6 28 3
ControlPublic 183 63 13 9 38 6Private 243 41 4 5 28 5
RegionNorth Atlantic 124 48 7 2 37 3
Great Lakes and Plains 125 46 7 10 26 4Southeast 104 53 7 6 32 8West and Southwest 73 48 8 6 30 3
Enrollment sizeOver 5,000 111 78 31 6 43 6
1,500-5,000 123 56 6 12 35 4700-1,499 114 46 1 3 35 6
Under 700 78 30 1 3 19 6
1 Percents in columns 4 through 7, which are based on the total number of institutions in each cate-gory, may not add up to the number in column 3; this is because of rounding and because, in the case oflarger institutions, there were instances of more than one mathematics club on campus.
Activities Other Than Clubs
A total of 473, or 54 percent of the institu-tions participating in the survey, reportedthe sponsorship of extracurricular activitiesother than clubs. Most popular by far amongsuch activities was the visiting lecturer pro-gram, with 38 percent of all institutions havingthis program. Mathematics contests werenext, with 21 percent. Only 4 percent of theinstitutions mailed out a newsletter or bulletinto high schools.
Comparisons by category of institution,- -More than three-fourths (77 percent) of theuniversities sponsored one or more activitiesother than mathematics clubs, to stimulate
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undergraduate student interest in mathematics(see table 25.) Only about one-half of each ofthe other types of institution did so. Universi-ties ranked high in the use of both visitinglecturers (60 percent) and mathematics con-tests (39 percent). Teachers colleges ratedlowest in visiting lecturers (27 percent) andin mathematics contests (15 percent). Uni-versities (9 percent) and teachers colleges(8 percent) issued newsletters and bulletinsdr high schools proportionately more fre-quently than did liberal arts colleges andtechnological schools. About two-thirds of thepublic institutions utilized one or more ofthese activities, whereas only about one-halfof the private ones did so. Regionally, theNorth Atlantic institutions utilized the specifiedactivities less than did those in other regions.
Table 25.--Number and percent of institutions sponsoring one or more activities other than mathematicsclubs, to stimulate interest in mathematics at the undergraduate level and the percent of theseinstitutions sponsoring specified activities; by type, control, region, and enrollment size:Aggregate United States, 1960-61
Category ofinstitution
Number ofinstitutionssponsoring
suchactivities
Percent sponsor-ing such activi-ties (number in
column 2 fnumber of institu-tions in category)
1iPercent of institutions sponsoring--
Mathematicscontests
Visitinglecturers
Newsletters orbulletins tohigh schools
Other
(1) (2) (3) (4) (5) (6) (7)
All institutions 473 54 21 38 4 14
TypeUniversities 107 77 39 60 9 15
Liberal arts colleges 280 49 18 36 2 12
Teachers colleges 70 51 15 27 8 21
Technological schools 16 50 28 38 3 19
ControlPublic 192 66 26 42 9 19
Private 281 48 18 36 2 11
RegionNorth Atlantic 116 45 16 29 1 14
Great Lakes and Plains 155 57 24 44 6 13
Southeast 111 56 18 39 5 13
West and Southwest 91 59 27 42 6 15
Enrollment sizeOver 5,000 110 77 41 56 6 15
1,500-5,000 145 66 26 46 8 14
700-1,499 123 49 16 35 2 15
Under 700 95 36 11 25 2 11
1 Percents in columns 4 through ?, which are based on the total number of institutions in eachcategory, do not add up to the percents in column 3; this is because many institutions reported spon-soring more than one of these activities.
There was a direct relationship between size-category of institution and use of these ac-tivities; the range was from 77 percent forinstitutions with enrollments of more than5,000, down to 36 percent for institutions withenrollments of fewer than 700. The use ofmathematics contests and visiting lecturerswas also in direct relationship to size ofinstitution. The larger institutions, with largerstudent bodies and larger staffs, are probablymore able to conduct the various activities.
INSTRUCTIONAL TECHNIQUESOTHER THAN THE STANDARD
LECTURE (Item 13)The traditional teaching technique in mathe-
matics has been the lecture, usually before aclass of 20 to 40 students, but expanding
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enrollments in recent years, the advent of tele-vision, and other factors have heightenedinterest in newer instructional techniques.There are a number of alternatives to ex-clusive dependence on the standard lecturer.Of the 877 participating institutions, 428, or49 percent, indicated that they used one ormore of the techniques listed on the question-.naire (see table 26). "Continental Classroom"was the technique most frequently used (22percent of the institutions). Large lectureclasses with help sessions were utilized by 15percent and an organized program of inde-pendent study, by 13 percent.
Comparisons by Type of InstitutionThese other techniques were especially
prevalent at universities; 63 percent of the
Table 26.--Number and percent of institutions using one or more instructional techniques other than the standard lecture, andpercents using specified techniques; by type, control, region, and enrollment size: Aggregate United States, 1960-61
Category ofinstitution
Number ofinstitutionsusing one or
more techniquesother than
standard Lecture
Percent usingone or more
such techniques(number in column2 t number ofinstitutions in
category)
Pereent2 of institutions using--
Large lectureclasses withsmall quiz
section
Large lectureclasses withhelp sessions
Organizedprogram ofindependent
study
"ContinentalClassroom"television
course
Other3
(1) (2) (3) (4) (5) (6) (7) (8)
All institutions 428 49 6 15 13 22 13
TypeUniversities 87 63 18 31 12 23 17Liberal arts colleges 267 47 4 13 15 22 12Teachers colleges 63 46 2 12 8 30 21Technological schools 11 34 12 7 9 3 16
ControlPublic 148 51 6 17 8 28 15Private 280 48 6 14 15 19 12
RegionNorth Atlantic 109 43 6 10 13 15 12Great Lakes and Plains 153 57 11 21 16 29 12Southeast 94 47 4 16 13 21 14West and Southwest 72 47 1 14 8 24 14
Enrollment sizeOver 5,000 90 63 18 29 11 24 251,500-5,000 103 47 5 12 11 25 11700-1,499 118 47 4 12 18 20 12Under 700 117 44 1 14 11 20 10
1 Percent in this column does not equal sum of percents in columns 4 through 7 because many institutions used more than oneof these techniques.
2 Based on total number of institutions in each category.3 Includes broadcast television courses other than "Continental Classroom," courses by closed-eirLat television, and
courses by film. These categories were also listed on the questionnaire form, but they were so sparsely used that statisticalbreakdowns by categories are not given here for them. They are discussed in the text, however.
universities--contrasted to 47 percent of theliberal arts colleges, 46 percent of the teacherscolleges, and 34 percent of the technologicalschools--used at least one of them. As wouldbe expected, universities led in the use oflarge lecture classes with help sessions (31percent) and large lecture classes with smallquiz sections (18 percent). Liberal arts col-leges ranked highest in organized programs ofindependent study (15 percent) and teacherscolleges, in "Continental Classroom" (30percent).
Comparisons by ControlOverall, there was little difference between
public and private institutions in the use ofinstructional techniques other than the standardlecture, with about half of the institutions ineach category doing so. In comparing specifictechniques, however, private institutions pre-dominated in the use of organized programsof independent study and public institutions,in the utilization of "Continental Classroom."
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Comparisons by Region
The use of other techniques was mostcharacteristic of the Great Lakes and Plainsregion (57 percent) and least characteristicof the North Atlantic region (43 percent). Theother regions hovered around 47 percent. TheGreat Lakes region led all other regions inthe use of large lecture classes with smallquiz sections (11 percent), large lectureclasses with help sessions (21 percent),organized programs of independent study (16percent), and "Continental Classroom" (29percent).
Comparisons by Enrollment Size
The largest institutions (those with enroll-ments of more than 5,000) were most likelyto employ techniques other than the standardlecture. Almost two-thirds (63 percent) ofthese institutions employed one or more ofthese techniques, whereas the corresponding
percentages for the other size categorieswere all around 45 percent. The largestinstitutions were far ahead in the use of largelecture classes with help sessions (29 percent)and in the use of large lecture classes withsmall quiz sections (18 percent), The only otherdifference worth noting was between institu-tions in the 700-1,499 enrollment-size category(18 percent) and those in all other size-categories (11 percent each) in the use oforganized programs of independent study.
Less /Frequently Used Techniques
Only 14 colleges reported that they gavemathematics courses by broadcast televisionother than "Continental Classroom," only 13gave them by closed-circuit television, andonly 14 gave courses by film. A total of 72institutions reported that they used instruc-tional techniques other than those which havebeen specifically mentioned.
INSERVICE EDUCATION OFMATHEMATICS TEACHERS
National Science FoundationIt.istitutes
Data obtained directly from the NationalScience Foundation (NSF) showed that duringthe academic year 1959-60 and the summer of1960, a total of 365 NSF institutes and con-ferences, wholly or partly on mathematics,were attended by 11,875 mathematics teachers.A breakdown of the institutes by types showsthat there were 32 academic-year institutes,attended by 600 teachers of mathematics;6 inservice institutes, attended by 200 ele-mentary school teachers and 120 inserviceinstitutes, by 4,400 secondary school teachersof mathematics; 6 summer institutes attendedby 225 elementary school teachers, 176 by5,500 secondary school teachers, 13 by 500secondary school and college mathematicsteachers, and 9 by 350 college professors;and 3 summer conferences (short institutes)attended by 100 college mathematics pro-fessors.
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Other Institutes (Item 16)
Inservice training programs for mathe-matics teachers reported in this survey in-cluded summer institutes; late-afternoon,evening, or Saturday sessions; academic-yearfull-time institutes; and other types, such assingle courses. Of the 877 institutions par-ticipating in the study, 178, or 20 percent,offered such non-NSF programs, and a num-ber of institutions offered more than onetype.
Of the institutions with inservice programs,46, or 26 percent, provided inservice trainingfor elementary school teachers only; 23, or13 percent, for junior high teachers only; 26,or 15 percent, for senior high teachers only;24, or 13 percent, for senior high teachersonly; 24, or 13 percent, for elementary schooland junior high teachers; 53, or 30 percent,for junior and senior high teachers; 38, or 21percent, for elementary, junior high, andsenior high teachers; and 7, or 4 percent, forhigh school and college teachers. No inserviceprogram for college teachers only was offeredthat was not sponsored by the National ScienceFoundation. The most common practice wasto have inservice training programs for ele-mentary school teachers alone and for juniorand senior high teachers together.
Kinds of institutes and sponsorship.--Of the201 institutes held at the 178 institutions, 75institutes, or 37 percent, were summer insti-tutes; 93, or 46 percent, late-afternoon,evening, or Saturday sessions; 4, or 2percent,academic-year full-time institutes; and 29, or14 percent, some other type of program.
Information on the sponsorship of the insti-tures was reported for 186 institutes. Onehundred thirty-two, or 71 percent, were sup-ported by the host institution itself; 22, or12 percent, by a private corporation or foun-dation; 32, or 17 percent, by some otherorganization, such as a local school board,a religious order, or a State department ofeducation.
Comparisons by category of institution.- -Teachers colleges stood out as offering moreinservice programs proportionately than anyother type of institution. Forty-three, or 32percent, of the 136 teachers colleges offered
inservice programs, as compared with 31, or22 percent, of 139 universities; 103, or 18percent, of 570 liberal arts colleges; and 1,or 3 percent, of 32 technological schools.
A larger proportion of liberal arts collegesand teachers colleges, 48 percent and 44percent, respectively, held summer institutesthan did universities (only 23 percent). Late -afternoon, evening, and Saturday sessions werethe most common types of inservice trainingprograms in all institutions, with 63 percentof the teachers colleges, 55 percent of theuniversities, and 48 percent of the liberalarts colleges having these forms.
A very large proportion of liberal artscolleges (80 percent) and teachers colleges(79 percent) financed their own inserviceprograms largely or exclusively by them-selves, as did 48 percent of the universitiesand the one technological school that hadsuch a program. A much larger proportionof universities received aid for their in-service programs from private corporationsor foundations than did any other type ofinstitution, and a larger proportion of teacherscolleges received aid from "other" sources,frequently from State departments of educa-tion, than did other types of institutions.
A larger percentage of publicly controlledinstitutions offered non-NSF inservice pro-grams for mathematics teachers than didprivate ones. Of 291 public institutions, 73,or 25 percent, had these programs, as com-pared with 105, or 18 percent of 586 privateinstitutions.
A larger percentage of private than of publicinstitutions financed their own inservice pro-grams, although the percentage was well overhalf for each type. A larger percentage ofpublic than of private schools received fi-nancial assistance from "other sources" fortheir inservice programs.
A smaller proportion of institutions in theNorth Atlantic region held summer institutesthan in the other regions, and a much largerproportion of institutions in this same regionheld late-afternoon, evening, or Saturdaysessions than in the other regions. Accessi-bility of teachers to institutions of highereducation probably influenced the type ofinservice training programs offered; that is,teachers near large cities and towns withcolleges would be more able to attend late-
afternoon, evening, and Saturday classes thanwould teachers in more remote areas, forwhom summer institutes would be moresuitable.
LIBRARY ORGANIZATION FORMATHEMATICS (Item 14)
Fundamental to the effectiveness of anycollegiate program of instruction is a goodlibrary with a high ratio of books to students,and high percentages of recent volumes and"quality" volumes. This survey did not attemptto measure these factors, but rather, to in-vestigate how mathematics libraries in col-leges and universities were organized. Of the877 schools in the survey, 711, or 81 percent,had no separate mathematics library. Onehundred fifty-three schools, or 17 percent,indicated that they had either a separatemathematics or a combined mathematicsand science library. There were 13 non-respondents, or 1 percent, to this question.Of the institutions having separate libraries,62, or 41 percent, had a departmental library,while 91, or 59 percent, had the combinedform.
Extent of Separate Libraries, byCategories
Universities had a far larger percentage of,loth types of separate library than any othertype of institution. Eighteen percent of theuniversities had mathematics department li-braries; technological institutions were theclosest competitor, with 9 percent (a per-centage that only represented 3 institutions,however). Twenty-five percent of the universi-ties responding to this question had a combinedlibrary, and the next largest contingent wasthe liberal arts colleges, with only 9 percent.Combining the two categories shows that 43percent of the universities had separatelibrary facilities, but only 13 percent of theliberal arts colleges, 12 percent of the teacherscolleges, and 16 percent of the technologicalschools.
The mathematics library was slightly moreprevalent at public institutions, 9 percent ofwhich had such a library, compared to 6
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percent of the private institutions. There wereslight regional differences; in the North At-lantic region 12 percent of the schools hadseparate mathematics libraries and another13 percent, a combined mathematics-sciencelibrary; in greatest contrast to this region wasthe Southeast, in which 4 percent of the insti-tutions had separate mathematics libraries and7 percent, the combined libraries.
Enrollment size was perhaps the mostrelevant of the categories; separate mathe-matics libraries or separate combined li-braries were most prevalent by far at thelargest institutions.
Attitudes Toward Separate Librariesby Those Who Do Not Have Them
Of the 711 respondents that had no separatelibraries, 486, or 68 percent, did not feel aneed for them. Another 212 expressed dis-satisfaction and their preferences (13 did notrespond). Interestingly enough, the same cate-gories in which a relatively high percentagealready had such facilities also had a relativelyhigh percentage desiring them. Of those univer-sities without separate facilities, 52 percentdesired them. Only 27 percent of the liberalarts colleges and 33 percent of the teacherscolleges which did not have separate librarieswere unhappy about not having them. The samerelationship existed in the control categories;40 percent of the public institutions and 26 per-cent of the private institutions that did not haveseparate facilities wanted them. Regional dif-ferences were quite small, but enrollment-sizedifferences were significant; a desire forseparate libraries was far more commonamong the larger schools.
General Comments
To be fully effective, a library must be con-veniently located for its potential users. Ref-erence books will be used much more oftenif they are readily obtainable. Thus, on largecampuses especially, separate libraries arequite desirable. Of course, a separate librarystaff is required, but in a large enough insti-tution the size of the separate library justifiesthis manner of operation.
On smaller campuses the general library isadequate, being close enough to all departmentsto serve them all efficiently; thus, the addi-tional cost of operating a separate librarycannot be justified. Nevertheless, at manysmall and middle-sized institutions, depart-ment heads have an arrangement with thehead librarian whereby a number of essentialbooks are informally assigned to the depart-ment for departmental use. Frequently astaff member or a student assistant will haveresponsibility for operation of this informallibrary.
DIGITAL COMPUTERS ONCOLLEGE CAMPUSES (Item 15)
Since World War II the field of computinghas been the most rapidly growing branch ofmathematics. More and more persons, withvarying levels of mathematical background,have been attracted to it, and indications arethat greater numbers will be needed in thefuture.
Colleges and universities have been pro-viding training in high-speed computing inincreasing numbers. Many departments offercourses in computer programing, data proces-sing, and numerical analysis. Many largeruniversities have established separate com-putation centers, and at these institutions,training in computing is not specifically afunction of the mathematics department, al-though the instruction provided by the mathe-matics department is fundamental to a careerin computing.
Because of the complexity of some institu-tions, complete information on the make andmodel number of each high-speed computerand the year of installation of each could notbe furnished by department heads, and it wasnecessary to make direct contact with thedirectors of the computation centers to useother sources of information.
A list of the 158 institutions and theirdigital computers on campus during the Springof 1961 is given in Appendix C. In many of theinstitutions which had been in the computingfield for some time, newer models had re-placed older ones. Many institutions had
acquired their first high-speed computer withina few years of the time of the survey. Thedepartment heads of a number of institutions,principally smaller ones in metropolitan areas,mentioned that although they had no computerfacilities of their own, they had use of in-dustrial facilities nearby and that they pro-vided courses for those interested in careersin high-speed computing. Many mathematics
departments that did not have high-speed com-puters reported a desire for them.
A total of 27 institutions also providedinformation about their analog computers.A ilk of institutions having analog computersis not given in this publication, as it wouldundoubtedly be incomplete--many institutionsdid not mention analog computers that theymay have had.
CHAPTER VSUMMARY
This is the final, comprehensive report ofa study in depth of mathematics programs ininstitutions of higher education that was con-ducted in the Winter and Spring of 1961. Atotal of seven preliminary publications, high-lighting certain aspects of the survey, havepreceded this final report. A total of 877colleges and universities granting bachelor'sor higher degrees, or about 82 percent of the1,069 to which questionnaires were sent,participated. Both undergraduate and graduateprograms were surveyed; data were solicitedon types of curriculums, degrees, course of-ferings, credit requirements, examinationrequirements, special features, and innova-tions and trends. In addition to analysis ofthe data for all institutions in the survey,analysis was also made according to type,control, region, and enrollment size of in-stitution. Unless indicated otherwise, however,the data in the following summary of high-lights are to be understood as applying to allinstitutions reporting programs.
UNDERGRADUATE PROGRAM
Slightly over half (52 percent) of the enter-ing freshmen enrolled in mathematics coursesin Fall 1960 were in college algebra, trigo-nometry, or courses of an equivalent level.One-fourth were enrolled in courses of a lowerlevel and slightly less than one-fourth incourses of a higher level. Technological schoolsas a type had the highest percentage ofstudents at the higher-level courses. Privatecolleges as a group had proportionately morestudents at the more advanced level than didthe public institutions. The North Atlanticregion also exceeded the other regions in thisrespect.
The liberal arts, or general, curriculum wasby far the most common kind, being offered by87 percent of the 877 institutions participatingin the survey. Fifty-nine percent of them re-
ported having a mathematics-teaching curricu-lum. At most of the other institutions, however,students could generally prepare to be mathe-matics teacher by taking the regular mathe-matics curriculum and the appropriate num-ber of courses in professional education(education courses) in order to meet teachercertification requirements. Of the types ofinstitutions in the survey, the only type atwhich a student generally could not study tobecome a secondary school mathematicsteacher was the college devoted exclusively toengineering. Only 27 institutions reportedhaving specifically an undergraduate statisticalcurriculum; 7, an actuarial science curricu-lum; and 36, an applied mathematics curricu-lum.
The most common mathematics require-ment in semester credit-hour requirementsfor a liberal arts or general curriculum is 29to 31, with 30 being the most usual require-ment. Private institutions tended to have lowercredit requirements than did public institutions.In the mathematics-teaching curriculum therewas a bimodal distribution in semester credit-hour requirements, with 28 percent of the in-stitutions having a requirement in the 29-31credit range and 26 percent in the 23-25 creditrange.
Almost four-fifths (79 percent) of all in-stitutions having a mathematic-teaching cur-riculum had a requirement in professionaleducation (education courses) in the range of17 to 25 credits. Almost one-third (32 per-cent) had a requirement in the 17 to 19 range(usually 18 semester credit-hours). The medianrequirement for all institutions was in the 20to 22 credit range.
In a liberal arts or general curriculum,more than half (55 percent) of the institutionsawarded a Bachelor of Arts (B.A.) degreeonly; 21 percent, a Bachelor of Science (B.S.)degree only; and 24 percent, either a B. A. orB. S. In a mathematics-teaching curriculum,about one-third offered a B. A. only; about
76
8
one-third, a B. S. only; about one-seventh, aB. A. or B. S.; and one-fifth, a bachelorsdegree with the designation of education in it.
The liberal arts or general curriculum wasthe most popular curriculum, accounting for58 percent of the bachelor's degrees awardedby all institutions. The mathematics-teachingcurriculum accounted for 36 percent of thedegrees; applied mathematics, for 4 percent;and statistics, for 1 percent. The fact that 36percent of all mathematics degrees awardedwere in mathematics-teaching curriculums,however, does not mean that only 36 percent ofall mathematics degree-holders were qualifiedto teach. Actually, many of the graduates ofliberal arts or general curriculums had quali-fied for teaching by taking appropriate pro-fessional education (education courses) at theircolleges. It is estimated that between 40 and50 percent of all recipients of bachelor'sdegrees in mathematics are fully qualified toteach mathematics in secondary schools.
Of the 570,954 students reported by the 877colleges in this survey as enrolled in under-graduate mathematics courses during Fall1960, almost two-thirds (65.6 percent) wereat the freshman level; 16.6 percent at thesophomore level; and 17.7 percent at thejunior and senior level. Enrollment figuresshowed that college algebra, with an enroll-ment of 82,125 students, or 21.9 percent of thefreshman mathematics enrollment, was themost popular freshman course, and that analyticgeometry and calculus (offered by 41 percentof the institutions) was second with 50,874, or13.6 percent of the total. Mathematical analysiswas next with 46,151 students, or 12.3 percentof the total freshman enrollment. The inter-grated course, analytic geOmetry and calculus,was the most popular sophomore course, ac-counting for 39.0 percent of the totalsophomore-year enrollment. At the junior andsenior level the course offered by the mostinstitutions (74 percent of them) was advancedcalculus, but the greatest enrollment was inordinary differential equations, which ac-counted for 15.0 percent of the total mathe-matics enrollment at this level. A greatvariety of courses were offered at thejunior and senior level; 43 different courseswere cited with sufficient frequency to belisted in the table on enrollments in the variouscourses.
Fifty-eight percent of all institutions of-fered at least one course in what they con-sidered remedial mathematics. About onestudent in seven taking freshman-year mathe-matics was enrolled in such a course. Almostthree-fourths of the public institutions offeredsuch instruction whereas only one-half of theprivate institutions did so. Intermediate alge-bra was the subject most frequently given asprerequisite instruction. Only a small per-centage of institutions offered college algebraor trigonometry as 'remedial instruction. Atotal of 84, or 23 percent, of the 369 institu-tions which were not at the time of the surveyoffering prerequisite instruction as part oftheir program had offered it some time durLigthe preceding 10 years. The reasons mostcommonly given for discontinuing this in-struction were better high school preparationof students, the belief that such instructionmore properly belongs in the high school orshould be an extension activity, and the short-age of faculty.
Seventy-five percent of the institutions par-ticipating in the survey reported that theyrequired an admissions examination that in-cluded mathematics. The College EntranceExamination Board (C.E.E.B.) test was themost commonly used. Private institutions re-quired admissions examinations involvingmathematics more than did public institutions,and institutions in the North Atlantic regionrequired such examinations more than did otherregions.
Fifty-nine percent of the institutions re-ported that they administered a mathematicsplacement examination. More than half (54percent) of those which gave such examina-tions required them of all entering freshmen.Twenty-nine percent restricted the exami-nation to students taking mathematics in collegefor the first time and 14 percent only tostudents in special curriculums, such asengineering. Algebra (88 percent) is the subjectmost commonly tested for; half of the institu-tions test for geometry and half for trigo-nometry. The most common objective of theplacement examination (70 percent of theresponses) was to determine the specificcourse in which to enroll the student. Publicinstitutions (71 percent) required placementexaminations more than did private institutions(53 percent).
77
Of the 877 institutions in the survey, 589, or67 percent, had programs of advanced stand-ing. Of these, 310, or 53 percent, gave collegecredit toward graduation for courses for whichstudents had met the requirements throughprevious study. Fifty-five percent of the 310institutions gave credit for college algebra;54 percent, for trigonometry; 52 percent, foranalytic geometry; 51 percent, for calculus;and 14 percent, for some other subject. In-stitutions frequently used more than one methodof determining advanced standing. Twenty per-cent of the institutions having programs ofadvanced standing admitted students to theseprograms on the basis of recommendationby the high school; 48 percent, on the basis of alocally constructed proficiency examination;37 percent, in accordance with scores made ona nationally distributed proficiency examina-tion; and 17 percent, by some other measures.Universities offered programs of advancedstanding more than did other types and alsotook the lead in the percentage giving collegecredit for courses skipped.
A total of 266 (30 percent) of the 877respondents in the survey had an honors pro-gram. A breakdown of the 266 by categoriesshoWs that 60 percent of the universities, 27percent of the liberal arts colleges, 15 per-cent of the teachers colleges, and 16 percentof the technological instituties in the study of-ferred a special program. The size of the in-stitution seemed a very important factor, since57 percent of the largest institutions (morethan 5,000 students) offered a program, whileonly 17 percent of the smallest institutions(fewer than 700 students) did so. The mostprevalent kind of honors program was in-dependent study.
A total of 142, or 16 percent, of all institu-tions in the survey required an undergraduatethesis in mathematics of some or all mathe-matics majors. Fifty-five percent of theseinstitutions required it of honors students only;40 percent, of all mathematics students; and 5percent, of other types of students. Privateinstitutions (21 percent) required theses of atleast some students more often than did publicinstitutions (7 percent). The North Atlanticregion was way ahead of other regions inrequiring undergraduate theses in mathe-matics, almost one in four (24 percent) of the
institutions in this region having this require-ment.
One-third of the institutions in the surveyrequired each student to take at least onemathematics course of college level prior tograduation. Public institutions (44 percent) hadsuch a requirement more than did privateinstitutions (28 percent). This requirement wasmuch more common among institutions in theNorth Atlantic region (59 percent) than in in-stitutions in the other regions.
There were many changes in mathematicscurriculums in colleges and universities from1950 to 1961. The most commonly adopted in-novation of the eight listed on the question-naire was the substantial expansion in courseofferings (by 59 percent of the institutions).Next most frequent was the introduction offreshman courses emphasizing such conceptsas mathematical structure, logic, and settheory (47 percent). Changes in, or introduc-tion of, a program for the undergraduatepreparation of mathematics teachers weremade by 36 percent of the responding in-stitutions.
A little less than half of the respondents(48 percent) accepted the invitation to makecomments about their mathematics programs.Of these, 24 percent discussed the problem ofthe mathematics department's being a servicedepartment for other departments, and 25 per-cent discussed the problem of upgrading ormodernizing the mathematics curriculum.Eleven percent made comments on problemsrelating to faculty. Many of these felt that theirfaculties were inadequate to the various tasksthat were being imposed on their departments.
GRADUATE PROGRAMS
Master's Programs in Mathematics
Data were obtained on 220 master's pro-grams, or more than 95 percent of the universeof master's programs in mathematics. A stu-dent could receive a Master of Arts (M.A.)degree at approximately 68 percent, and aMaster of Science (M.S.) degree at approxi-mately 57 percent, of the reporting institutions.(Either the M.A. or the M.S. could be obtainedat a number of the institutions.)
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The number of required credit-hours inmathematics for institutions on a semester-hour basis ranged from 12 to 36, both themedian and the mode being 24 semester-hours.The total number of required credits for thedegree ranged from 18 to 38 semester-hours,the median and the mode both being 30 semesterhours. In 26 percent of the programs, theentire credit requirement for the degree was inmathematics. In 52 percent of the programs athesis was required; in 35 percent, it wasoptional; and in 13 percent, no provision at allwas made for a thesis. A modern foreignlanguage was required in 45 percent of theprograms.
It was possible to earn the master's degreein mathematics by evening and/or Saturdaystudy at 59, or 27 percent, of the 220 reportinginstitutions and through summer study aloneat 82, or 37 percent, of them.
A final comprehensive examination was re-quired at 88 percent of the institutions, wasoptional at 1 percent, and was not provided forat 11 percent. Of the institutions requiringcomprehensive examinations, 59 perceht in-sisted upon only an oral examination; 13 per-cent, only a written examination; and 27 per-cent, both oral and written examinations.
Twenty-five percent of the respondents re-ported that a minor was required; 35 percent,that a minor was optional; and 44 percent,that no provision was made for a minor.(Percentages do not add to 100 percent, sincesome institutions may have various require-ments among programs teaching to the samedegree.)
Sixty-eight percent of the respondents re-ported that a minor in mathematics was avail-able to those majoring in other departments.In 33 mathematics departments minors wereoffered in conjunction with a master's degreein another department even though the mathe-matics department made no provision for aminor for its own degree candidates.
Master's Programs SpeciallyDesigned for Teaching
Data were obtained on 183 master's pro-grams specially designed for the teaching ofmathematics. In 45 percent of the programs,a student could earn an M.A. degree in some
form; in 40 percent, an M.S. degree; and in27 percent, an Education degree. (Some in-stitutions provided for variations within a givenprogram and as a result offered more thanone type of degree for the same program.)Of the 81 institutions awarding a Master ofArts degree, 39 conferred a straight M.A.; 28,a Master df Arts in Teaching (M.A.T.); and9, a Master of Arts in Education. The mostcommon Education degree was the Master ofEducation (M. Ed.), conferred by 38 institu-tions.
The required number of credit-hours inmathematics among institutions on a semester -hour basis ranged from 6 to 36, both themedian and the mode being 18 semester-hours. Twenty-six institutions reported thatthey had no specific credit requirements foreducation courses. Among institutions on asemester-hour basis that had a requirementin education courses, the requirement rangedfrom 2 to 26, with a median of 10 semester-hours and a mode of 6 semester-hours. Therange in total credit requirements for thedegree was 24 to 36 semester-hours, themedian and the mode both being 30. In 21 per-cent of the programs a thesis was required;in 40 percent, it was optional; and in 38 per-cent, no provision was made for a thesis. Amodern foreign language was a requirement inonly 9 percent of the programs.
It was possible to earn the master's degreeby evening and/or Saturday study in 55, or 30percent, of the 183 reporting institutions andthrough summer study alone in 135, or 74percent of them.
At 75 percent of the responding institutionsa final comprehensive examination was re-quired. Of these institutions, 38 percent in-sisted upon only an oral examination; 29 per-cent, a written examination; and 31 percent,both oral and written examinations.
A minor was required in 24 percent of theprograms and was optional in 27 percent ofthem.
Doctoral Programs in Mathematics
Data were obtained from 94 institutionsoffering doctoral programs in mathematicsin 1961, or 100 percent of the universe ofdoctoral programs. Several of the respondents
79
indicated that plans were underway to in-augurate doctoral programs at their institu-tions.
The total number of credit-hours requiredfor the degree was reported by 57 institutions,47 on the semester plan and 10 on the quarterplan. The remaining 37 institutions had nospecified minimum number of credits. Of the47 institutions on the semester plan, 26 in-cluded the credits earned for the thesis inthe reported total degree-credit requirements.At these institutions the total required num-ber of semester-hours ranged from 36 to 96,the mode being 90 semester-hours. Twenty-one institutions on a semester plan reportedtotal credit-hour requirements without includ-ing thesis credits. These requirements rangedfrom 48 to 90 semester-hours plus a thesis,the mode being 60 semester-hours. The mini-mum credit-hour requirements in mathematicsvaried considerably from institution to institu-tion. For institutions on a semester-hour basis,the minimum number of semester-hours inmathematics ranged from 36 to 96, with themode of 60 semester-hours.
All but two institutions had more than onekind of examination in partial fulfillment ofthe doctoral degree. Twenty-six percent re-quired two kinds of examinations; 49 percent,three kinds; 14 percent, four kinds; and 9 per-cent, five kinds. Seventy-six percent of theinstitutions required candidates to take an oralpreliminary or qualifying examination; 63percent, a written preliminary or qualifyingexamination; 45 percent, a final comprehen-sive oral examination; 22 percent, a finalcomprehensive written examination; 97 per-cent, an oral examination on thesis; and 1 per-cent, an examination on a minor thesis inmathematics.
Competence in two modern languages wasrequired in all programs with the exceptionof two programs at Harvard University(statistics and applied mathematics, which re-quired only one foreign language). All 93institutions which reported on their foreignlanguage requirements accepted German andFrench; 90, Russian; 13, Italian; 3, Japanese;and 1, Spanish.
Thirty-five percent of the institutions re-ported that a minor was required; 31 percent,that a minor was optional; and 33 percent,that no provisions were made for a minor.
At nine institutions it was possible for astudent to earn a doctor's degree in mathe-matics entirely through evening and/or Satur-day study. At four institutions the degree couldbe earned entirely through summer study.
The 94 institutions awarded a total of 864doctor's degrees in mathematics from January1958 to January 1961, inclusive. Analysis wasthe most popular specialization, being offeredat 85 of the institutions and accounting for 304doctor's degrees, or more than a third of thetotal number. Algebra was the next mostpopular in terms of the point of number of in-stitutions offering it (76), but accounted foronly 110 degrees whereas statistics, offeredby 49 institutions, claimed 164 degrees overthe 3-year period. Applied mathematics (114degrees) and topology (94 degrees) also ac-counted for sizable portions of the 864 degreesconferred.
Doctoral Programs SpeciallyDesigned for Teaching
In 1961 twenty-five institutions offered adoctoral program specially designed for theteaching of mathematics. Four of these pro-grams had only recently been introduced.
The Doctor of Philosophy (Ph.D.) degreewas the only degree offered for this programat 8 of the 25 institutions; the Doctor of Edu-cation (Ed.D.), the only degree in 6 others;and either the Ph.D. or Ed.D in the remain-ing 11.
The credit-hour requirements in mathe-matics at the 13 reporting institutions on thesemester plan ranged from 24 to 60 semester-hours, with a median of 34 and a mode of 30.Semester-hour requirements in educationcourses ranged from 9 to 48 semester-hours,with a median of 30. The total number ofsemester-hours required for the degreeranged from 60 to 96, with a mode of 90.
Of the 22 institutions reporting examinationsrequired in partial fullfillment of the doctoraldegree, 15 required an oral preliminary orqualifying examination; 16, a written pre-liminary; 14, a final comprehensive oralexamination; 11, a final comprehensive writtenexamination; and 22, an oral examination onthe thesis. Three of the 22 institutions in-sisted upon 2 of these examinations; 6, upon 3;9, upon 4; and 4, upon 5.
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Of 18 responding institutions with Ph.D.teaching programs, 16 required competencein two modern foreign languages, and tworequired only one. Of the 15 responding in-stitutions offering the Ed.D. degree, none re-quired two languages for the degree, and onlytwo institutions required one language. Of the17 institutions indicating which languages wereacceptable in meeting the requirement, all 17accepted German and French; 14 Russian; 4,Italian; 2, Spanish; and 1, Romance languages.
Of 20 institutions which answered the ques-tion on minors, 12 reported that a minor wasrequired for at least one of the doctoraldegrees in programs specially designed for theteaching of mathematics; 4, that a minor wasoptional; and 4, that no provision for a minorwas made.
At only one institution could a student earnhis doctoral degree through Saturday and/orevening study and at three, through summerstudy.
A total of 63 doctor's degrees speciallydesigned for the teaching of mathematics wereawarded during the period from January 1958to January 1961, inclusive.
Additional Preparation for CollegeTeaching
A total of 64 departments in 63 differentinstitutions reported some arrangements forpreparing college teachers, such as profes-sional courses in education, seminars, andsupervise.': teaching experience. However,there were actually more programs in Ameri-can colleges and universities than the re-sponses indicated because the respondents insome of the larger universities were not awareof all the programs at their institutions.
Of the 59 respondents who commented ontheir programs, 13 said that education coursesand/or teaching seminars were required ofprospective teachers; 21, that they were notrequired but encouraged; and 25, that theywere neither required nor particularly en-couraged.
SOME RELATED FACTORSAlmost half (49 percent) of the 877 institu-
tions participating in this survey had anundergraduate mathematics club on campus.
Thirty-one percent of the 877 institutions hadlocal clubs with no affiliation. Seven percenthad clubs affiliated with Pi Mu Epsilon and 6percent, with Kappa Mu Epsilon. There was adirect correspondence between enrollment sizeand undergraduate clubs on campus, rangingfrom 78 percent of the institutions with morethan 5,000 students down to 30 percent of theinstitutions with fewer than 700 students.
Better than three-quarters (77 percent) ofthe universities sponsored one or more ac-tivities, other than mathematics clubs, tostimulate undergraduate student interest inmathematics. Only about half of each of theother types of institutions did so. These otheractivities consisted primarily of mathematicscontests and visiting lecturers.
Forty-nine percent of the institutions usedone or more instructional techniques otherthan the standard lecture before a classtypically consisting of 20 to 40 students. "Con-tinental Classroom" was the technique mostfrequently used (22 percent of the institutions).Large lecture classes with help sessions wereutilized by 15 percent of the institutions and anorganized program of independent study, by 13percent. These other techniques were espe-cially prevalent at the universities, as 63 per-cent of the universities, contrasted to 47 per-cent of the liberal arts colleges, 46 percent ofthe teachers colleges, and 34 percent of thetechnological institutes, used at least one ofthem.
Of the 877 institutions participating in thesurvey, 178, or 20 percent, offered inserviceinstitutes for mathematics teachers other thanthose sponsored by the National ScienceFoundation. Of the 201 institutes at the 178institutions, 37 percent were summer in-stitutes; 46 percent, late-afternoon, evening,or Saturday session institutes; 2 percent,academic year full-time institutes; and 29, or14 percent, some other type of program.Seventy-one percent of the institutes werefinancially supported by the host institutionsthemselves; 12 percent, by private corporationsor foundations; and 17 percent, by some othergroup or organization, such as a local schoolboard, a religious order, or a State departmentof education. Teachers colleges stood out asoffering more of these inservice programsproportionately than any other type of institu-tion.
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Seventeen percent of the institutions in thesurvey had a separate library, separate fromthe main library, for mathematics alone or formathematics and one or more sciences alone.Of the institutions possessing separate li-braries, 41 percent had the library for mathe-matics alone and 59 percent had a library formathematics combined with one or more ofthe sciences. Of institutions without suchseparate facilities, only 30 percent desiredthem, with universities (52 percent) leading inthis respect.
In Spring 1961, a total of 158 institutionshad high-speed digital computers on their
campuses. In many of the institutions whichhad been in the computing field for some time,newer models had replaced olders models.Many institutions reported that they had ac-quired their high-speed computer only re-.cently. The department heads of a number ofinstitutions, principally smaller ones in metro-politan areas, mentioned that although they hadre computer of their own, they had use ofindustrial facilities nearby and that they pro-vided courses for those interested in careersin high-speed computing. Many departmentswere feeling the need and desire for high-speedcomputers.
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APPENDIXES
95
APPENDIX A. MASTER'S PROGRAMS
In Mathematics: Institutions, program requirements, program characteristics, 1961
Explanation and abbreviations:
M.-Master; A.-Arts; S.-Science; Appl.-Applied; Not spec.-Not specified; req.-required; opt.-optional.
Absence of an entry in column (6) means that no provision is made for the writing of a thesis.
An "x" in column 7 means that a modern foreign language is required for the degree.
An "x" in column 8 means that it is possible to earn the degree through evening and/or Saturday studyalone.
An "x" in column 9 means that it is possible to earn the degree through summer study alone.
An asterisk * means that information relative to that item was not supplied by the respondent.
StateInstitution and
CityDegree(s)awarded
Credit requirement(inc. credit for thesis)s. semester; q. quarter
Thesis
For-eignlan-
gungereq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
InMath.
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Ala. Auburn University, Auburn M.S. 30q 45q req. xUniversity of Alabama, University M.A. 24s 30s opt. x
Alaska University of Alaska, College M.S. 25-30s 30s req. xAriz. Arizona State University, Tempe M.A. 30s 30s opt. x x x
University of Arizona, Tucson M.S., M.A. 30s, M.S. 30s x, M.S.Ark. University of Arkansas, Fayette- 18s
ville M.A., M.S. 18s 30s opt. xCalif. California Institute of Tech- 15 quarter
nology, Pasadena (*) courses (*) opt.Fresno State College, Fresno M.A., M.S. 21s 30s xGeorge Pepperdine College,
Los Angeles M.A. 30s (*) req. xLong Beach State College,
Long Beach M.A. 18s 30s opt. xLos Angeles State College,
Los Angeles M.A. 24s 30s opt. xPomona College and Claremont
Grad. Sch., Claremont M.A. 24s 30s req.Sacramento State College,
Sacramento M.S., M.A.30s, M.S.20s, M.A.
36s, M.S.30s, M.A. opt.
San Diego State College,San Diego
San Francisco State College,San Francisco
M.A., M.S.
M.A.
24s,
24s
30s
30s
opt. x,M.A. x
San Jose State College, San Jose M.A., M.S. 24s 30s opt.Stanford University, Stanford,
Palo AltoUniversity of California at
M.S.M.A.
30-36q24s, Math.
45q opt.req.
Berkeley Math.,Stat. 18s, Stat. 24s StatisticsUniversity of California at
DavisM.A.
in Math. 24s 24sUniversity of California at
Los Angeles M.A. 24s 24s opt. xUniversity of California at
Santa Barbara M.A. 24s 24sUniversity of Southern California,
Los Angeles M.A., M.S. 18s 30s x,M.A. xColo. Colorado State College, Greeley M.A. 35q 45q opt. x
Colorado State University,Fort Collins M.S. 35q 45q req. x
University of Colorado, Boulder M.A. 20s 24s req. x xUniversity of Colorado, (Appl. M.S. inMath.), Boulder Appl. Math. 22 -28s 26 -32s opt. x'
University of Denver, Denver M.A. 45q 45q opt.Conn. Trinity College, Hartford M.S. 24s 30s x
University of Connecticut, Storrs M.A., M.S. 24s 24s opt.Yale University, New Haven M.A. approx. 26s approx. 26s opt. x
Del. University of Delaware, Newark M.A., M.S. 30s 30s req. xD.C. American University M.A. 30s 30s req. x
Catholic University of America M.A., M.S. 24s 30s req. x xGeorge Washington University M.A., M.S. 30s, Math. 30s req. x xGeorgetown University 18s, Stat.Georgetown University M.A. 24s 24s req. x xHoward University M.S. 30s 30s req. x
Fla. Florida State University,Tallahassee M.A., M.S. 21s 30s opt.
University of Florida, Gaines-ville M.A., M.S. 24s 30s req. x xl
May be obtained by resident extension class work in Denver.
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96
4
APPENDIX A. IVIASTER'S PROGRAMS
In Mathematics: Institutions, program requirements, program characteristics, 1961 -- Continued
State Institution and
Cit y
Degree(s)awarded
Credit requirement(inc. credit for thesis)s. semester; q. quarter
Thesis
For-eignlan-gugreq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
InMath.
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Fla. University of Miami, CoralGables M.S. 18-30s 30s
Ga. Atlanta University, Atlanta (*) 24s 24s req. x x
Emory University, Atlanta M.A., M.S. 45q 45q req. xGeorgia Institute of M.S. in 18s plus 33s plus
Technology, Atlanta Appl. Math. thesis thesis req.University of Georgia, Athdns M.A. 45q 45q req. x
Hawaii University of Hawaii, Honolulu M.A. 18s 30s req.Ida. University of Idaho, Moscow M.S. 24s 30s req. xIll. DePaul University, Chicago M.S. (*) 36s opt. x x
Illinois Institute of Technology M.S. 32s 32s req. xIllinois State Normal Univer- M.S.
sity, Normal in Educ. 20s 32s req.2 x
Loyola University, Chicago M.A., M.S. 30s 30s opt. x xNorthern Illinois University
De Kalb M.S. 23s 32s req. x xNorthwestern University,
EvanstonSouthern Illinois University,
Carbondale
M.A., M.S.
M.A., M.S.
36q
30q
36q
48qreq. ofM.A. x
x x
University of Chigago, Chicago S.M. 30q (*) xUniversity of Illinois, Urbana M.A., M.S. 18s 24s opt. xWestern Illinois University,
Macomb M.S. 36q 48q xInd. Ball State Teachers College,
MuncieM.A.M.S. 32q 45q opt. x, M.A. x x
Earlham College, Richmond M.A. 18q 30qIndiana State Teachers College,Terre Haute. M.A., M.S. 20-30s 32s opt. x x
Indiana University, Bloomington M.A. 30s 30s xPurdue University, Lafayette M.S. 21s 33s opt.Rose Polytechnic Institute,
Terie Haute M.S. 18s 30s req. xUniversity of Notre Dame,
Notre Dame M.S. 30s 30s opt. xIowa Iowa State University, Ames M.S. 30q approx. 45q req. x
State University of Iowa,Iowa City M.S. (*) 30-38s opt x
Kans. Fort Hays Kansas State College,Hays M.A. 20s 30-32s req. x
Kansas State College of M.A., 30sPittsburg, Pittsburg M.A., M.S. 20s M.S., 32s (4) x, M.A. x
Kansas State Teachers College,Emporia M.A. 20s 30s req. x
Kansas State University,Manhattan M.S. 20-26s 32d req. x
University of Kansas, Lawrence M.A. 30s 30s req.University of Wichita, Wichita M.A. 15s 30s req.
Ky. University of Kentucky,Lexington M.A., M.S. 24s 24s req. x x
University of Louisville,Louisville M.A. 18s 30s req. x
La. Louisiana Polytechnic institute,Ruston M.A. 21s 30s req. x x
Louisiana State University,Baton Rouge M.S. 30s 30s req.
Northwestern State College,Natchitoches M.S. 30s 30s opt. x
Tulane University, New Orleans M.S. 36s 36s xMe. University of Maine, Orono M.A. 30s 30s req. xMd. Johns Hopkins University,
Baltimore M.A. Not spec. Not spec. x5University of Maryland,
College Park M.A. 18s 30s req.6 x
2 Or two papers.3 Also an M.A. in Ed. and an M.S. in Ed.4 A thesis is required for the M.A. degree, optional for the M.S. degree.5 A reading knowledge of both French and German is required.6 Also available is an option allowing substitution of an expository paper instead of a thesis. This requires 9 extra
credit hours of course work, 33 hours in all.
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APPENDIX A. MASTER'S PROGRAMS
In Mathematics: Institutions, program requirements, program charactezistics, 1961--Continued
State Institution andCityCity
Degree(s)
Credit, requirement(inc. credit for thesis)a. semester; q. quarter
Thesis
For-signlan-guagereq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
InMath.
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Mass. Boston College, Chestnut Hill M.A.? 30s 30s req xBoston University, Boston M.A. 20s 30s req. xBrandeis University, Waltham M.S. 18s 18s xClark University, Worcester M.A. 30s (*) req. xHarvard University, Cambridge A.M. 12s (*) xLowell Technological Institute,
Lowell M.S. 18s 30s req. xMassachusetts Institute of
Technology, Cambridge S.M. 18s 24s req.
Northeastern University, Boston M.S. 20s 30s x
Smith College, Northampton M.A. 24s 24s req. x
University of Massachusetts,..mherst M.A. 24-30s 30s opt.
Mich. Andrews University, BerrienSprings M.A. 18s 18s opt. x
Central Michigan University,Mount Pleasant M.A. 20-24s 30s opt. x x
Michigan State University, EastLansing M.A., M.S. 33q 45q opt. x
University of Detroit, Detroit M.A. 30s 30s opt. x x xUniversity of Michigan, Ann Arbor M.A., M.S. 18s 24s opt. xWayne State University, Detroit M.A. 26s 32s (*) (*) x x
Minn. Mankato State College, Mankato M.S. 27q 45q req. x
University of Minnesota, Col. ofISA, Minneapolis
M.A.,M.S. 27q 36-45q opt. x x
University of Minnesota, Inst.of Technology, Minneapolis M.S. 18-21q 27-45q opt. x
Miss. Mississippi Southern College,Hattiesburg M.A., M.S. 46q 46q (8) x x
Mississippi State University,State College M.A., M.S. 24s 30s req. x
University of Mississippi,University M.A., M.S. 30s 30s req.
MO. Central Missouri State College,Warrensburg M.A. 26s 32s x
St. Louis University, St. Louis M.A., M.S. (*) 24s req. xUniversity of Kansas City,
Kansas City M.A., M.S. 18s 30s opt. xUniversity of Missouri, Columbia. M.A. 26-32s 32s opt.Washington, University, St. Louis M.A. 24s 24s req.
Mont. Montana State College, Bozeman M.S. 30q 30-45q opt. (9) xMbntana State University,
Missoula M.A., M.S. 30q 45q req. x xNebr. University of Nebraska, Lincoln M.A., M.S. 24s 30-36s opt.Nev. University of Nevada, Reno M.A., M.S. 18s 30s req. xN.H. Darmouth College, Hanover M.A. 30s 30s x
University of New Hampshire,Durham M.S. 30s 30s
N.J Fairleigh Dickinson University,Rutherford M.S. 32s 32s opt. x
Rutgers The State University,New Brunswick M.S. 24s 30s opt. x
Stevens Institute of Technology,Hoboken M.S. 20s 30s opt. x
Trenton State College, Trenton M.A. 26s 32s opt.
N.M. Eastern New Mexico University,Portales M.A. 27s 30s req. x x
New Mexico Highlands University,Las Vegas M.S. 36q 48q req.
New Mexico Institute of Miningand Technology, Socorro M.S. 24s 30s req. x
New Mexico State University,University Park M.S. 30s 30a opt.
University of New Mexico,Albuquerque M.S. 21s 32s opt x x x
7 A nonresearch M.A., in which no theets or language is required, is offered primarily for students in National ScienceFoundation Institutes.
8 A thesis is required for the M. A. degree, optional for the M. S. degree.9 One language is required for Plan A, which is the thesis plan with 30 credits. No language is required for Plan B,
which requires 45 credits and no thesis.
86
98
APPENDIX A. MASTER'S PROGRAMS
In Mathematics: Institutions, program requirements, program characteristics, 1961--Continued
StateInstitution and
City
Degree(s)awarded
Credit requirement(inc. credit for thesis)a. semester; q. quarter
Thesis
For-eignlan-gungereq.
Degree can beobtained by
Eve. and/or Sat.study
SummerstudyIn
Math.Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
V.Y. Adelphi College, Garden City M.S. 24s 368 opt. xBrooklyn College, Brooklyn M.A. 21s 30s plus
thesisreq. x
City College, New York M.S. 18s 308 opt. x xColumbia University, Columbia
College, New York M.A. 24s 308 opt. xCornell University, Ithaca M.A. Not spec. Not spec. req. xFordham University, New York M.A. 30s 30a opt. xHofstra College, Hempstead,
Long IslandM.A. inNat. Sci. 218 338 opt. x x
Manhattan College, New York M.A. 18s 24s plusthesis
req. x x x
New York University, New York M.S. 24s 308 req. xPolytechnic Institute of
Brooklyn, Brooklyn M.S. 20s 308 req. x xRensselaer Polytechnic Institute,Tray M.S. 21-30s 308 opt. x
St. John's University, Jamaica M.A. 308 30-338 opt. (10) x xSyracuse University, Syracuse M.A., M.S. 21s 30s opt.Union College and University,Schenectady ,. M.S. 24s 308 req. x
University of Buffalo, Buffalo... M.A. 26s 32s req. x xUniversity of Rochester,Rochester A.M. 32s 32s x
Yeshiva University, New York M.A. 24s 308 xN.C. Appalachian State Teachers
College, Boone M.A. 30-45q 45q opt. xDuke University, Durham M.A. 24s 308 req. x xEast Carolina College, Greenville M.A., M.S. 27q 45q req. x xUniversity of North Carolina,
Chapel Hill M.A. 24s 308 req. x xUniversity of North Carolina,Raleigh
M.S. inAppl. Math. 20s 308 req. x
Wake Forest College, Winston-Salem M.A. 24s 308 req. x x x
N.D. North Dakota State University,Fargo M.S. 30q 45q opt.
University of North Dakota,Grand Forks M.A., M.S. 15-20s 308 req. x,M.A. x
Ohio Bowling Green State University,Bowling Green M.A. 15s 338 opt.
Case Institute of Technology,Cleveland M.S. 24s 308
John Carroll University,Cleveland M.S., M.A. 308 308 opt. xii
Kent State University, Kent M.A. 23q 48q req. xMiami University, Oxford M.A., M.S. 21s 308 req.Ohio State University, Columbus M.A., M.S. 45q 45q req. xOhio Universita, Athens M.S. 23-32s 32s req.University of Cincinnati,
Cincinnati M.A. 30s 308 req. (12)
University of Dayton, Dayton M.S. 24s 308 opt. xUniversity of Toledo, Toledo M.A., M.S. 18s 30s req.Western Reserve University,
Cleveland M.A., M.S. 30s 30s opt.Xavier University, Cincinnati M.S. 308 (*) x,Plan A x x
Okla. Oklahoma State University,Stillwater M.S. 32s 30-328 opt.
University of Oklahoma, Norman M.A., M.S. 20-26s 308 opt.University of Tulsa, Tulsa (*) 308 30s req.
Ore. Oregon State University,Corvallis M.A., M.S. 30q 45q req. x,M.A. x
University of Oregon, Eugene M.A., M.S. (*) 45q opt. x,M.A.
10 A foreign language is required in Plan A along with a thesis and a total of 30 credits:no language in Plan B which requires a total of 33 credits and no thesis.
11 A test in basis statistics (10 problems in 1 1/2 houts) may be substituted for foreign language.12 One modern language is required in the college of Arts and Sciences program; none in the College of Engineering.
APPENDIX A. MASTER'S PROGRAMSIn Mathematics: Institutions, program requirements, program characteristics, 1961--Continued
State Institution and
City
Degree(s)awarded
Credit requirement(inc. credit for thesis)a. semester; q. quarter
Thesis
Fo r-
ei gn
lan-
guagereq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
In
Math.
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Pa. Bryn Mawr College, Bryn Mawr M.A. 2. yr.courses
3 yr.courses
req. x13
Bucknell University, Lewisburg M.A., M.S. 18s 30s opt. x,M.A.
Carnegie Institute ofTechnology, Pittsburgh M.S. 21s 32s opt.
Duquesne University, Pittsburgh M.A. 30s 30s req. x x
Lehigh University, Bethlehem M.S. 18s 30s req.
Pennsylvania State University,University Park (*) 21s 30s req. x
Temple University, Philadelphia M.A. (*) (*) opt. x
University of Pennsylvania,Philadelphia M.A. 24s 24s opt.
University of Pittsburgh,Pittsburgh M.A.,M.S.14 18s 30s req. x x
Villanova University, Villanova M.A. 24s 30s opt. x x
P. R. University of Puerto Rico,Mayaguez M.A. (*) 30s opt. x
R. I. Brown University, Providence M.A. 24s 24s req. x
University of Rhode Island,Kingston (*) 30s 30s req.
S.C. Clemson College, Clemson M.S. 24s 30s opt xUniversity of South Carolina,
Columbia M.A., M.S. 30s 30s req. x xS.D. South Dakota School of Mines and
Technology, Rapid City M.S. 24s 30s req.South Dakota State College,
Brookings M.S. 30q 45q req. xState University of South Dakota,
VermillionM.A.,
M.N.S.19s, M.A.18s, M.N.S.
28s, M.A.35s, M.N.S.
req.,M.A. x
Tenn. East Tennessee State College,Johnson City M.S. 30q 45q req. x
George Peabody College forTeachers, Nashville M.A. 24-36q 48q opt. x
Middle Tennessee State College,Murfreesboro M.A. 15s 32s opt. x x
University of Tennessee,Knoxville M.A. 36q 45q req.
Vanderbilt University, Nashville. M.A., M.S. 18s 24s req. xTexas Abilene Christian College,
Abilene M.A. 18-24s 30s req. xAgricultural and Mechanical
College of Texas, CollegeStation M.Sc. 20s 32s req. x
Baylor University, Waco M.A., M.S. 18-30s 30s req. x x xNorth Texas State College, Denton M.A., M.S. 24s 30s req. x xPrairie View Agricultural and
Mechanical College Prairie View M.S. 21s 30s req. xRice University, Houston M.A 4 adv.
courses4 adv.courses
req. x
St. Mary's University, SanAntonio M.S. 36s 36s opt. x
San Houston State Teachers 18s, M.A. 30s, M.A.College, Huntsville M.A., M.S. 24s, M.S. 36s, M.S. req. x x
Southern Methodist University,Dallas M.A., M.S. 24s 30s opt. x x
Stephen F. Austin State College,Narcogdoches M.A. 18s 30-36s opt. x
Texas Christian University,Forth Worth M.A., M.S. 30-36s 30-36s (15)
x xTexas College of Arts and
Industries, Kingsville M.A. 18s 30s req. xTexas Southern University,Houston M.A. 30s 30s req. x x
Texas Technological College,Lubbock M.A., M.S. 24s 30-36s opt. x x
13 Two languages (French, German, or Russian) are required.14 Also offered is a Master in Letters degree. From 16 to 20 credits are required in mathematics and 10 to 14 credits
in one or two related fields. A thesis is not required for this degree.15 Thesis is required for the M.A. degree, optional for the M.S. degree.
d80
O
APPENDIX A. MASTER'S PROGRAMS
In Mathematics: Institutions program requirements, program characteristics, 1961--Continued
StateInstitution and
City
Degree(s)awarded
Credit requirement(inc. credit for thesis)s. semester; q. quarter
Thesis
For-eignlan-guagereg.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
In
Math.Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
texas University of Houston, Houston M.A., M.S. 18s 30s req. x x
University of Texas, Austin M.A. 18s 30s req. x x
Itah Brigham Young University, Provo M.A. (*) . (*) req.
University of Utah, Salt LakeCity M.A., M.S. 45q 45q req. x,M.A.
Utah State University, Logan M.S. 39q 45q req.
It.
la.
University of Vermont,Burlington
College of William and Mary,Williamsburg
M.A.
M.A.
30s
24s
30s24s plusthesis
req.
req. x
Madison College, Harrisonburg M.A. 24s 30s req. x
University of Richmond, Richmond. M.A., M.S. 15s 27s req. x
University of Virginia,Charlottesville M.A. 24s 24s req. x x
Virginia Polytechnic Institute,Blacksburg M.S.
39q, Math.30q, Stat. 45q req. x
Virginia State College, Peters-burg M.S. 21s 30s req. x x
Wash. Gonzaga University, Spokane M.S. in 24s 30s req. x
Appl.Math.
University of Washington, Seattle M.A., M.S. 36q 36q (16) x x
Washington State University,Pullman M.A. 24s 30s req. x
W. Va. West Virginia University,Morgantown M.A., M.S. 24-30s 30s opt x
Wis. Marquette University,Milwaukee M.S. 24s 30s opt. (17) x x
University of Wisconsin,Madison M.A. 24s 24s
University of Wisconsin,Milwaukee A.M., M.S. 18-24s 18-24s (*) x x
Wyo. University of Wyoming, Laramie M.A., M.S. 20s 3Cs opt. x
1
16 Expository thesis for M.A., research thesis for M.S. M.S. awarded without thesis to students who pass generalexamination for Ph.D.
17 Foreign language requirement accompanies the thesis option.
190 1
APPENDIX A. MASTER'S PROGRAMS
Programs specially designed for teaching: Institutions, program requirements, program characteristics, 1961
Explanation and abbreviations:
M.-Master; A.-Arts; E., Ed., or Educ.-Education; S. or Science; N. or Nat.-Natural; req.-required; opt.-optional.Absence of any entry in column 7 means that no provision is made for the writing of a thesis.An "x" in column 8 means that a modern foreign language is required for the degree.An "x" in column 9 means that it is possible to earn the degree through evening and/or Saturday study alone.An "x" in column 10 means that it is possible to earn the degree through summer study alone.An asterisk (44) means that information relative to that item was not supplied by the respondent.
State Institution andCit y
Degree (s)awarded
Credit requirement (incl.thesis cr. if part of req.)8, semester; q, quarter
The-sis
For-eignlan-
guagereq.
Degree can beobtained by
Eve. and/or Sat,study
SummerstudyIn
Math.In educ-courses
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Ala. University of Alabama,University M.A. 188 0 30s opt. x
Alaska University of Alaska,College
M.S. inGen.Sci. 12s 0 308 opt. x
Ariz. Arizona State College,Flagstaff
M.S.in Educ. 168 6s 34s opt. x
Arizona State University,Tempe M.N.S. 12-218 0 30s opt.
University of Arizona,Tucson M.A. 18s (*) 30s
Ark. Arkansas State TeachersCollege, Conway M.S.E. 15s 158 30s req. x
Calif. California State Polytechnic M.A.College, San Luis Obispo in Educ. 18q 12q 45q x
Dominican College of SanRafael, San Rafael M.T.S. 20-24s 0 30s x x
Fresno State College,Fresno
M.A.with creden. 218 22s 30s
Long Beach State College,Long Beach M.A. 18s
As req.for cred. 30s opt.
Los Angeles State College,Los Angeles M.A. 24s 6s 30s opt. x
Sacramento State College,Sacramento M.A. 20s 108 30s opt.
San Diego State College,San Diego M.A. 18s (*) 30s opt.
San Jose State College,San Jose
M.A.(Teach-ing Obj.) 21s (*) 30s opt.
Stanford University,Stanford, Palo Alto
M.A.(Teach-ing Math.) 30-36q 12-15q 45q x
Colo. Colorado College, ColoradoSprings M.A.T. 228 0 30s req. x
Colorado State College,Greeley M.A. 35q 3081 45q opt. x
Colorado State University,Fort Collins M.A.T. 30q 0 45q x
University of Colorado,Boulder
M.BasicScience 24s 0 30s x
Conn. Central Connecticut StateCollege, New Britain M.S. 9-15s 9s 30s req. x x
University of Connecticut,Storrs M.Ed. 12s 158 27a opt. x x
Wesleyan University,Middletown M.A.T. 15s 9s 30s opt.
Yale University, New Haven M.A.T. 28s 16s 36s xDel. University of Delaware,
NewarkM. Ed. inNat. Sci. (*) 6s 30s opt. x x
D.C. American University M.S.S.T. 6s 6s 30s x xCatholic University ofAmerica M.T.S. 24s (*) 30s x
Fla. Florida State University,Tallahassee M.S. 188 128 36s opt. x
University of Florida,Gainesville M.S. 24s 6s 36s x x
University of Miami,Coral Gables M.A. 18s 0 30s
1 30 quarter hours at the undergraduate and graduate levels combined.
90102
APPENDIX A. MASTER'S PROGRAMS
Programs specially designed for teaching: Institutions, program requirements, program characteristics, 1961--Nntinued
StateInstitution and
CityDegree (s)awarded
Credit requirement (incl.thesis or, if part of req.)s, semester; q, quarter The-
sis
For-
eignlan-
gungereq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
In
Math.In educ.courses
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Ga. Emory University, Atlanta M.A.T. 45q 15q 60q xGeorgia State College forWomen, Milledgeville M.Ed. 25q 20q 60q x
Ida. University of Idaho,Moscow M.N.S. lOs 0 30s x
Ill. Eastern Illinois University M.S.Charleston in Educ. 24-28q 12q 48q opt. x x
Illinois Institute of Tech- M.S. fornology, Chicago Teachers 36s 0 36s req. x x
Illinois State Normal M.S.University, Normal in Educ. 20s 9s 32s req.2 x
Northern Illinois University,De Kalb
M.S.
in Educ. 15s 0 32s req. x xNorthwesternUniversity,Evanston
M.A.,M.Ed.
30q.M.A.18q.M.Ed.
6q.
M.A.18q.M.Ed. 36q x
xx
Southern Illinois University,Carbondale
M.S.in Educ. 30q 8-16q 48q x
University of Chicago,Chicago M.A.T. 20-30q 18q 58q req.
University ofIllinois,Urbana
M.S.,M.Ed.
16s,M.S.
16s,M.Ed.
8s'M.S.
16s,M.Ed. 32s xWestern Illinois University M.S.Macomb in Educ. 36q 12q 48q x
Ind. Ball State Teachers M.A. in Ed.College, Muncie M.S. in Ed. 32q (*) 45q opt. x x
Indiana State TeachersCollege, Terre Haute M.A.,M.S. 20s 12s 32s opt. x x
Indiana University,Bloomington M.S.,M.A.T. 10-20s 20s 35s opt. x
Purdue University,Lafayette M.S. 21s (*) 33s x
University of Notre Dame,Notre Dame M.S. 30s 0 30s opt. x
Iowa Drake University,Des Moines
M.Sci.in Teaching 15s 15s 32s req. x x
Iowa State Teachers M.A.College, Cedar Falls in Educ. 188 7s 30-38s opt. x
State University of Iowa,Iowa City M.S. (*) 68 30-38s opt. x
Kans. Fort Hays Kansas StateCollege, Hays M.S. 20s 108 32s opt. x
Kansas State College ofPittsburg, Pittsburg M.S. 20s. 0 32s opt. x
Kansas State TeachersCollege, Emporia M.S. 20-25s 0 30-35s opt. x
La.
University of Kansas,Lawrence....,
Louisiana PolytechnicM.S. in Ed. 10-15s 15s 30s req. x
Institute, Ruston M.Ed. 12s 188 30s opt. x xLouisiana Etate 21s,M.A. 9s,M.A.
University,Baton Rouge
M.A.,M.Ed.
12s,M.Ed.
188
M.Ed. 30sLoyola University,
New Orleans M.S. 188 (*) 30s opt.McNeese State
College,Lake Charles
M.S.in Ed.M.Ed. 188 12s
36s,M.S.30s,M.Ed.
req.
M.S. xNorthwestern State
College, Natchitoches M.S. in Ed. 248 6s 30s opt. xTulane University,
New Orleans M.A.T. 20s lOs 30s opt. xMd. Johns Hopkins University,
Baltimore M.A.T. 128 21s 30sUniversity of Maryland,
College Park M.A. 18s 18s 36s req.Mass. Boston College, Chestnut
Hill M.A.T. 15s 15s 30s xCollege of Our Lady of the
Elms, Chicopee M.E. 168 10a 30s req. x x x
91
103
APPENDIX A. MASTER'S PROGRAMSPrograms specially designed for teaching: Institutions, program requirements, program characteristics, 1961Continued
StateInstitution and
CityDegree (s)
awarded
Credit requirement (incl.thesis cr. if part of req.)s, semester; q, quarter
The-sis
For-eignlan-gungereq.
Degree can seobtained by
Eve. and/or Sat.study
SummerstudyIn
Math.In edue.courses
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Harvard University,Cambridge A.M.T. 12-15s 9-12s 30s
State College at Boston,Boston M.Ed. 7s 28s 33s req.
Suffolk University,Boston A.M.T. 6s 18s 30s x
Mich. Andrews University,Berrien Springs M.A.T. 18-24s 6-12s 30s
Central Michigan University,Mount Pleasant M.A. 10s 10s 30s opt. x x
Michigan State University,East Lansing M.A.T. 33q (*) 45q x
Northern Michigan College M.A. inMarquette Teaching 18s (*) 30s x
University of Detroit,Detroit M.A.T. 24a 0 30s x x
University of Michigan,Ann Arbor
M.A. forSci. Teach. 20-24a 4s 30s opt.
Wayne State University,Detroit M.A. 20s 6s 328 x x
Western Michigan University,Kalamazoo
M.A. inSci.&Math. 20-24s 6-10s 30s opt. x x
Minn. Macalester College,St. Paul M.Ed. 12s 10-13s
31splusthesis
req. x
Mankato State College,Mankato M.S. 27q 9q 45q req. x
Moorhead State College M.S.Moorhead in Educ. 9-27q 9q 45q req. x x
St. Cloud State College,St. Cloud M.S. 15-21q 9-15q 45q req. x
University of Minnesota,LSA College,Minneapolis M.Ed. 24q 9-12q 45q (3) x x
University of Minnesota,Inst. Tech.Minneapolis M.Ed.4 6q 36q 42q x
Miss. Mississippi College,Clinton M.Ed. 12-15s (*) 24-30s opt.
Mississippi SouthernCollege, Hattiesburg M.S.T. 30q 16q 46q opt. x
Mississippi State University,State College M.Ed. 24a 0 30s x
University of Mississippi,University
M.S. inComb. Sci. 24a 0 36s opt.
Mo. Central Missouri State M.S.College, Warrensburg in Educ. 20s 12s 32s x x
St. Louis University,St. Louis
M.A.(T),M.S.(T) (*)
Notspec. 30s (5) x x
Southwest MissouriStateCollege,Springfield
M.Ed.,M.S.T.
32s,M,S,T.
16s,M.Ed.
0,M,S,T16s,M.Ed.
32s x,M.Ed.University of Missouri,Columbia M.S.T. varies (*) 32s x
Washington University,St. Louis
M.A.in Educ. 12 -24a 9-21s 33s
Mont. Montana State University,Missoula
M.A.T.,M.S.T. 28-35q (*) 45-60q
(s)x
Nebr. State Teachers College,Kearney
M.A.in Educ. 15s 9s 36s opt. x
State Teachers College,Wayne
M.S.in Educ. 18s 4a .(*) opt. x
Nev. University of Nevada,nem
M.A. inSec. Ed. 15s 15s 30s req. x
N.H. University of NewHampshire, Durham M.S.T. 30s 0 30s x x
N.J. Montclair State College,Upper Montclair M.A. 18s 6s 32s opt. x x
Rutgers, The State University,New Brunswick M.A. 24s 6s 30s opt. x
92
104
APPENDIX A. MASTER'S PROGRAMS
Programs specially designed for teaching: Institutions, program requirements, program characteristics, 1961--Continued
StateInstitution and
City
Degree (s)awarded
Credit requirement (incl.thesis cr. if part of req.)s, semester; q, quarter The-
sis
For-eignlan-guagereq.
Degree can beobtained by
Eve. and/or Sat.study
SummerstudyIn
Math.
In educ.
coursesTotal forthe deg,
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
N.M. New Mexico Highlands M.A. in Not
University, Las Vegas Sci. Ed. 12q spec. 48q opt.
University of New Mexico,Albuquerque
M.Ed. inScience 188 lOs 348 x x
N.Y. Adelphi College, Garden City M.S. 24s (*) 36s opt. x
Brooklyn College, Brooklyn M.A. 15e 8-14s 30s req. x
Clarkson College of Technology,Potsdam
M.S. inBasic Sci. 20s 0 30s
Colgate University,Hamilton M.A.T.7 24s 6s 30s req. x
Columbia University,New York
M.A.in Educ. 18s 14e 32s opt. x x
Cornell University,Ithaca M.A.T.
Notspec.
Notspec.
Notspec.
Fordham University,New York M.S. 30s 6s 36s x x
Hobart and William Smith M.S.
Colleges, Geneva in Educ. 15e 15s 30s req. x x x
Hofstra College, Hempstead,Long Island
M.A. inNat. Sci. 21s 9s 33s opt. x x
Hunter College, New York M.A. 21s 6s 30s x
New York University,New York
M.A.in Educ. 0 24s
30splusthesis
req. x x
St. John's University,Jamaica
M.A.in Educ. 12-18s 15-21s 33s x x
State University of NewYork, College ofEducation at Albany M.A.,M.S. 188 6s 308 opt. x
College of Education at M.S.
Brockport in Educ. 9-12s 12s 328 opt. x x
College of Education atCortland M.S. 12s 9s 328 x
College of Education atGeneseo M.S. lOs 9s 32s x
College of Education atOneonta M.S. 128 9-12s 32s opt. x
College of Education atOswego M.S. 128 6s 308 x
College of Education at M.S.
Plattsburgh in Educ. 128 18-24s 33s opt. x
College of Education at M.S.
Potsdam In Educ. 15s 38 32s x x
Syracuse University,Syracuse M.Ed. 18s 12s 30s opt. x
Union College and Univer- M.S.
sity, Schenectady in Teaching 20s (*) 308 x x
N.C. Appalachian State TeachersCollege, Boone M.A. 18q ,21q 39-54q opt. x
Duke University,Durham
M.A.in Teaching 18-24s 6-12s 30s8 opt. x
East Carolina College,Greenville M.A. 27q 3q 45q req. x x
University of NorthCarolina, Chapel Hill M.Ed. 18s 6s 30s opt. x
Western Carolina College,Cullowhee
M.A.
in Educ. 18q 27q 45q opt. x
N.D. North Dakota StateUniversity Fargo M.Ed. 15q (*) 45q opt. x x
Ohio Bowling Green State Uni-sity, Bowling Green M.A. 158 (*) 338 x
John Carroll University,Cleveland M.A. 9s 21s 30s opt. (9) x x
Kent State University,Kent M.Ed. 27q 15q 48q x
Miami University,Oxford
M.A.T.M.Ed. 158
9s,M.Ed.
0-6s,M.A.T. 36s x
Ohio State University,Columbus
M.A.,M.Ed. 15q 15q
45q,M.A.52q,M.Ed.
(10)
x
University of Akron,Akron M.Ed. 12s (*) (*) req. x
APPENDIX A. MASTER'S PROGRAMS
Program:: specially designed for teaching: Institutions, program requirements, program characteristics, 1961 -- Continued
StateInstitution and
City
Degree (s)awarded
Credit requirement (incl.thesis Cr. if part of req.)s, semester; q, quarter The-
sis
For-
?ignian-gungereq.
Degree can beobtained by
Eve. and/or Sat.study
SummerstudyIn
Math.In educ.courses
Total forthe deg.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Ohio University of Dayton,Dayton (*) 12-18s 9s 30s x x
Western Reserve University,Cleveland M.A.,M.S. 9s (*) 30s x
Xavier University, CincinnatiCentral State College,
Edmond
M.Ed.M. of
Teaching
12sup to
30s
12s2s
and up
30s
32s
x
x
x
x
Northwestern State M. of
College, Alva Teaching 8-16s 8-16s 32s x
Southeastern State College M. of
Durant Teaching 8-12s 12s 32s x x
Southwestern State M. of
College, Weatherford Teaching 9s 8s 32s x
Ore. Oregon State University,Corvallis
M.S., M.A.,M.Ed. (*) (*) 45q
Reed College, PortlandSouthern Oregon CollegeAshland
M.A.T.M.S.in Educ.
10-15sup to21q
5-10s
21q
30s
45q
req. x x
University of Oregon,Eugene M.A.,M.S. 30q 9q 45q x,M.A.
Pa. Bucknell University,Lewisburg
M.S.in Educ. 18s 0 30s x
Indiana State College,Indiana
M.S.in Educ. 14-22s 8-10s 30s opt. x x
Pennsylvania State Univer-sity, University Park M.Ed. 18s 6s 30s opt.
Temple University,Philadelphia (*) (*) (*) (*) x
Villanova University,Villanova
M.Sec.Sch. Sci. 12s 12s 30s
West Chester StateCollege, West Chester M.Ed. 18-24s 2s 30s req.
R.I. Brown University,Providence M.A.T.
4 math-courses
4-5 ed.courses 32s req.
S.C. Clemson College, Clemson M.Ed. 6-9s 12s 30s x
South Carolina State 15s,M.S.
College,Orangeburg
M.S.,M.Ed.
21s,
M.Ed 15s
30s,M.S.36s,M.Ed.
(*)
University of South Carolina,Columbia
M. ofMath. 24s 6s 30s x
S.D. Northern State Teachers M.S.
College, Aberdeen in Educ. 12-18q 18q 45q opt. x
State University of SouthDakota, Vermillion M.Ed. 15-17s 18-20s 35s k
Tenn. East Tennessee StateCollege, Johnson City M.A. 15-21q 24-30q 45q req. x x
George Peabody Collegefor Teachers, Nashville M.A. 24-36q 1612 48q opt. x
Middle Tennessee StateCollege, Murfreesboro M.A. 15s lOs 32s opt. x x
Vanderbilt University,Nashville M.A.T. 18s
18smax. 36s opt. x
Texas East Texas State College,Commerce M.Ed. 24s 12s 36s opt.
Hardin-Simmons University,Abilene M.Ed. 12s 18s 30s opt. x
Incarnate Word College,San Antonio M.A.,M.Ed. 12-18s 18s 30-36s (13) x,M.A. x x
North Texas State College,Denton M.Ed. 18s 18s 36s opt. x
Prairie View Agric. andMech. College,Prairie View
M.S. 18s 9s 30s req. x x
St. Mary's University,an Antonio M.A. 36s 0 36s opt. x
Sam Houston StateTeachers College,Huntsville
M.Ed.,M.A. 18s (*)
30s,M.A.36s,M.Ed.
req.M.A.
x,
M.A. x
Stephen F. Austin StateCollege, Nacogdoches M.A. 18s 12s 30-36s opt. x
APPENDIX A. MASTER'S PROGRAMS
Programs specially designed for teaching: Institutions, program requirements, program characteristics, 1961--Continued
StateInstitution and
CityDegree (s)awarded
Credit requirement (incl.thesis cr. if part of req.)s, semester; q, quarter The-
sis
For-
?iguJan -
guagereq.
Degree can beobtained by
Eve. and/or Sat.study
Summerstudy
InMath.
In educ.courses
Total forthe deg,
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Texas Christian University,Fort Worth
M.S. inT. of Math. 18s 12s 30s req. x
Texas Southern University,Houston M.Ed. 18s 18s 36s req. x
Texas Technological M.S.College, Lubbock in Educ. 18-248 12-18s 36s opt. (14) x
West Texas State College,Canyon M.Ed. 248 12s 36s opt. x x x
Vt. University of Vermont,Burlington M.A.T. 24s 6s 30s
Va. Madison College,Harrisonburg M.S. 18-21s 9s 30s opt. x
University of VirginiaCharlottesville
M.A.T.,M.Ed.
12s,M.A.T.15s
M.Ed.
12s,M.A.T.9s,
M.Ed. 308opt.,M.Ed. x
Wash. Gonzaga University, M.S. of Ed.Spokane in Nat. Sci. 18s 6s 30s req. x x x
Seattle University,Seattle
M.S. inNat. Sci. 30q 0 45q opt. x
University of Washington,Seattle M.A. 39q (*) (*) req.
Washington State University,Pullman M.A.T. 26s 0 32s x
Western WashingtonCollege of Education,Bellingham
M.Ed.,M.T. ofMath. 33-36q 12q 45q opt. x
W. Va. West Virginia University,Morgantown M.S. 24-30s 0 30s opt. x
Wis. University of Wisconsin,Madison M.A. 12s 12s 24s opt. x
University of Wisconsin,Milwaukee
M.S. inMath.-Ed. 12s 12s 24s (*) (*) x x
Wyo. University of Wyoming,Laramie
M.S. inNat. Sci. lOs 0 30s x
APPENDIX A. MASTER'S PROGRAMS: Institutions with master's programs in statistics, 1961
State Institution1
State Institution
Alabama University of Alabama, University New Jersey Rutgers, The State University, NewBrunswick
California Stanford University, StanfordUniversity of California at Berkeley New York Columbia University, New YorkUniversity of California at Los Angeles Cornell University, Ithaca
New York University, New York
Colorado University of Denver, Denver University of Rochester, Rochester
Delaware University of Delaware, Newark North Carolina University of North Carolina, Chapel HillUniversity of North Carolina, State
District of American University College, Raleigh
Columbia George Washington UniversityOhio Western Reserve University, Cleveland
Illinois University of Chicago, ChicagoUniversity of Illinois, Urbana Pennsylvania University of Pennsylvania, Philadelphia
Villanova University, Villanova
Iowa Iowa State University, AmesState University of Iowa, Iowa City Tennessee University of Tennessee, Knoxville
Kansas Kansas State University, Manhattan Texas Southern Methodist University, DallasUniversity of Texas, Austin
Louisiana Tulane University, New Orleans
Massachusetts Harvard University, CambridgeVirginia Virginia Polytechnic Institute, Blacksburg
Michigan Michigan State-University, East Lansing Washington University of Washington, Seattle
University of Michigan, Ann Arbor
Minnesota University of Minnesota, MinneapolisWisconsin University of Wisconsin, Madison
Missouri University of Missouri, Columbia Wyoming University of Wyoming, Laramie
95
107
APPENDIX B. DOCTOR'S PROGRAMS
In Mathematics: Institutions, credit requirements, areas of specialization, and number ofdegrees, January 1958 to January 1961, inclusive
Explanation of abbreviations and symbols:
"Not spec." means that there are no specific credit requirements.
New prog." indicates that the program has been recently established and no degrees had yet been conferred.
Credit requirementbeyond bachelor's,in cred. for the-
Totalnumber
No. of deg. in area of speciali-zation, Jan. '58-Jan. 61, incl.
(x denotes specialization offered,no deg. was given)
sis except as noted of deg.
StateInstitution and
City(s-semester; q-quar-ter, Data in paren-
Jan. '58
to
.o
0
theses are approx.) Jan. '61
inclusivec41
xe,
-,-1
0 04-I
o1-1
01In
math.Total forthe degree
N 8u,9
4.0t,1
o
E. 8
Ala. Auburn University, Auburn Not spec. Not spec. 8 2 3 2 x
University of Alabama, University488
54s plusthesis
Newprog. x
Ariz. University of Arizona, Tucson 60s 75s New prog. x x x
Calif. California Institute of Technology,Pasadena Not spec. Not spec. 10 4 6 x
Stanford University, Stanford 75q plus75q thesis 28 1 8 2 x 16 1
University of California at Probe-
Berkeley Not spec. Not spec. 42 3 13 6 3 x 15 1 bility 1University of California at Davis Not spec. Not spec. New prog. x x x x x
University of California at Los Number
Angeles Not spec. Not spec. 30 4 11 5 2 5 1 Theory 2University of Southern California,
Los Angeles 60s60s plusthesis 4 1 3
Colo. Colorado State University, FortCollins 60q
90q plusthesis
Newprog.
University of Colorado, Boulder (a) ( b ) 8 5 3
Conn. Yale University, New Haven (50s) plus
(50s) thesis 20 x 16 2 1 x 1
Del. University of Delaware, Newark Not spec. Not spec. New Prog. A x
D.C. American University (50s) 72s 4 x 1 3
Catholic University 54s plus Numer.36s thesis 9 3 3 1 1 Anal. 1
George Washington UniversityGeorgetown University
Not spec.48s
Not spec.48s
7
New prog.x 1
x
x x
Fla.
Ga.
Florida State University,Tallahassee ,
University of Florida, GainesvilleUniversity of Georgia, Athens
60s(80s)
Not spec.
60s plusthesis
(80s)Not spec.
New prog.11c
2
x
3
x
x
3 2 1
Idaho University of Idaho, Moscow 45s45s
60s plusthesis New prog.
Ill. Illinois Institute of Technology,Chicago
Northwestern University, Evanston96s108q
96s108q
75
2x
25
University of Chicago, Chicago Not spec. Not spec. 22 5 6 1 1 4 5
University of Illinois, Urbana 60s 72s 43 5 29 4 x xInd. Indiana University, Bloomington - Proba-
75-80s 90s 7 1 x 1 1 1 1 bility 2Purdue University, Lafayette 48s plus
36s thesis 27 2 9 1 10 5
University of Notre Dame, NotreDame Not spec. Not spec. 1 x x x
Iowa Iowa State University, Ames Stat.
8 0qdd
100q 22 3 6 3 8
Econ. 1
Ag. EngMath. 1
State University of Iowa, IowaCity Alg.
Not spec. 90s 6 x x x 4 x Geom. 2Kans. University of Kansas, Lawrence Not spec. Not spec. 7 3 3 x 1
Ky. University of Kentucky, Lexington 60-72s 72s 6 x 6 x
La. Louisiana State University, Baton Topologi-Rouge (60s) Not spec. 5 1 1 1 cal A1g.
Tulane University,New Orleans 48s
48s plusthesis 5 3 x 1
NumberTheory 1
a In algebra and analysis, 30 sem. hrs. in courses numbered above 500; in applied math. 33 sem hrs.b In algebra and analysis, 30 sem. hrs. in courses numbered above 500; in applied math. 48 sem hrs.c University of Florida granted 2 degrees in analysis during the period, but is not currently offering this
specialization.d Unofficial requirements.
196 8
a
Tt
APPENDIX B. DOCTOR'S PROGRAMS
In Mathematics: Institutions, credit requirements, areas of specialization, and number ofdegrees, January 1958 to January 1961, inclusive--Continued
StateInstitution and
City
beyond bachelor's,in cred. for the-sis except as noted(s-semester; q-quar-ter, Data in paren-
Totalnumberof deg.Jan. '58
to
No. of deg. in area of speciali-zation, Jan. 58 -Jan. '61, incl.x denotes specialization offered,
no deg. was given)
7.1theses are approx.)Jan. '61
inclusive
ai;-.
w
m
4
a,H
fi.'
4-,
8..-1
N
.mr.1
.1-'
or-1
a.E.
'la
8In
math.Total forthe degree
Md. Johns Hopkins University,Baltimore Not spec. Not spec. 3 1 2 x x x
NumberTheory x
University of Maryland, CollegePark Not spec. Not spec. 12 x 2 10 x x x x
Mass. Boston University, BostonBrandeis University, Waltham
68s36s
78s36s
8
New prog.1
x2x
2 3
Harvard University (incl. RadcliffeCollege) Cambridge Not spec. Not spec. 23 4 10 x 4 2 2 1
Massachusetts Institute of (57s) plus Probe-Technology, Cambridge (36s) thesis 21 2 7 6 2 2 1 bility 1
Mich. Michigan State University, EastLansing 120-145qe
f120-145q 10 1 3 2 x 4 x
NumberTheory x
University of Michigan, Ann Arbor Not spec. Not spec. 26 2 5 4 1 1 3 6 (g)Wayne State University, Detroit 90s 90s 6 x. 4 x 1 1
Minn. University of Minnesota,Minneapolis 45q
67 1/2 q plusthesis 16 2 14
Mo. University of Missouri, Columbia Not spec. Not spec. 4 x 2
(60s) plus NumberSt. Louis University, St. Louis Not spec. thesis 9 x 2 x 4 1 Theory 2
Washington University, St. Louis 72s72s plusthesis 2
72q plusMont. Montana State College, Bozeman 72q thesis New prog. x x x x
Number
Neb. University of Nebraska, Lincoln 74-90s 90s 2 x 1 1 x x Theory xMathe-matical
N.J. Princeton University, Princeton Not spec. Not spec. 31 3 8 3 x 5 3 8 Physics 1Rutgers, The State University, New
hBrunswick 81s 90s 4 2 2 x x
Stevens Institute of Technology,Hoboken 40s 90s 0 x x
N. Mex. New Mexico State University,University Park Not spec. Not spec. New prog. x x
University of New Mexico,Albuquerque 48s
60s plusthesis New prog. x x x x x
N.Y. Adelphi College, Garden CityColumbia University, New York
54s
i
54s60s plus
New prog. x x x
60s thesis 18 3 3 2 x x 7 3
Cornell University, Ithaca Not spec. Not spec. 9 1 5 x 1 1 1
New York University, New York 72s plus42s thesis 54 5 19 23 2 3 2
Polytechnic Institute of Brooklyn,Brooklyn (64s) (79s) New prog. x x x
Rensselaer Polytechnic Institute,Troy 45-60s
60s plusthesis 3 3
Syracuse University, Syracuse Not spec. 90s 4 x 2 x xUniversity of Buffalo, Buffalo
64s90s plusthesis 3
University of Rochester, Rochester.64s
64s plusthesis 3 3
Yeshiva University, New York (90s) 90s New prog. x x xN.C. Duke University, Durham 48s 60s 7 2 1 x x
University of North Carolina(Chapel Hill) Not spec. Not spec. 17 2 1 1 x 11 2
Ohio
University of North Carolina(Raleigh)
Case Institute of Technology,Cleveland
(45s)
42s
55s plusthesisbOs plusthesis
15
5 1 x
x
3 x
15
x
e Ninety quarter hours in mathematics and statistics are required for specialization statistics.f One hundred thirty-five quarter hours are required for statistics.g The University of Michigan also offers the following specializations: Functional analysis, number theory, actuarial
science, and the history of mathematics. Four doctoral degrees in functional analysis were conferred during theperiod covered by this study.
h For specialization in statistics 15 semester hrs. in mathematics and 75 semester hrs. in statistics are required.This specialization was first authorized in 1959.Thirty-five semester hrs. are required for specialization in statistics.
97
10J
APPENDDC B. DOCTOR'S PROGRAMS
In Mathematics: Institutions, credit requirements, areas of specialization, and number ofdegrees, January 1958 to January 1961, inclusive -- Continued
Credit requirementNo. of deg. in area of speciali-zation, Jan. '58-Jan. '61, incl.beyond bachelor's, Total x denotes specialization offered,icl. cred. for the-
sis except as notednumberof deg.
no deg. was given)
StateInstitution and
City(s-semester; q-quar-ter, Data in paren-
Jan. '58
to
.44.
mo
theses are approx.) Jan. '61 as .1 mi 1inclusive
;4 W..W-1
4.W 0 W i I-4 PIn Total for
.0wtaD W
,-t
P.00 .-1
taD4-,
03oPo I'
Math. the degree -q 8 .2 8 E2. 8
Ohio Ohio State University, Columbus Not spec. 135q 10 3 3 1 1 1 1
University of Cincinnati,Cincinnati Not spec. Not spec. 6 1 5 x x
Western Reserve University,Cleveland Not spec. Not spec. New prog. x x x x
Okla. Oklahoma State University,Stillwater 90s 90s 9 3 3
University of Oklahoma, Norman 90s 90s 2 x x 2Ore. Oregon State University,
CorvallisComp.
Sci. &80q (135q) 5 x 3 1 x 1 Tech. x
University of Oregon, Eugene Number126q 135q 6 3 1 x Theory 2
Pa. Bryn Mawr College, Bryn Mawr 6
courses8
courses 0 x xCarnegie Institute of Technology,
Pittsburgh 96s 96s 10 1 4 3 2Lehigh University, Bethlehem (60s) plus
Pennsylvania State University,University Park
University of Pennsylvania,Philadelphia
(60s)
k60s
54s
thesis
90sk
54s
4
1
16
x
4
3
1
6
1 x
x
x
4NumberTheory 2
University of Pittsburgh,Pittsburgh Not spec. Not spec. 15 1 4 3 1 6
R.I. Brown University, Providence Math.Not spec. Not spec. 24 1 2 17 2 Econ. 2
S.C. University of South Carolina,Columbia Not spec. Not spec. New prog. x x x
Tenn. University of Tennessee, Knoxville. Not spec. Not spec. 13 3 4 1 5
Vanderbilt University, Nashville 72s plus Lattice54s thesis 2 x x x 1 Theory 1
Texas Agricultural and Mechanical Collegeof Texas, College Station
Differ-ential
Not spec. 96s 1 Equa. 1Rice University, Houston 8 Advanced
Courses8 advancedCourses 5 1 4 x
University of Texas, Austin Differ-ential
Not spec. Not spec. 14 x 7 1 x 3 Ewa. 3Utah University of Utah, Salt Lake City. Not spec. Not spec. 1 1Va. University of Virginia,
Charlottesville Not spec. Not spec. 7 x 1Virginia Polytechnic Institute,
Blacksburg 10581 135q 16 x x x x 16 xWash. University of Washington, Seattle
Washington State University,Pullman
Not spec.
Not spec.
Not spec,
Not spec.
17
1
4
x
7
1 x
2
x
1
x
3
xWis. University of Wisconsin, Madison Not spec. Not spec. 18 6 6 2 4
' Thirty-nine semester hrs. in mathematics and statistics are required for specialization in statistics.k Pennsylvania State University went into a modified quarter system in June 1961.1 Sixty quarter hrs. of mathematics and statistics are required for specialization in statistics.
98
110
i.
4
APPENDIX B. DOCTOR'S PROGRAMS
Programs specially designed for teaching: Institutions, kinds of degrees awarded, credit and foreign languagerequirements, and numbers of degrees from January 1958 to January 1961, inclusive
Explanation of abbreviations and symbols:
Ph. D.-Doctor of Philosophy; Ed. D.-Doctor of Education
"Not spec." means that there are no specific credit requirements.
"New Prog." indicates that the program has been recently established and no degrees had yet been conferred.
An asterisk "*" means that information relative to that item was not supplied by the respondent.
StateInstitution and
cityDegree (s)awarded
Credit requirement beyondbaccalaureate
(s denotes semester; q quarter)Number offoreign
languagesrequired
No. ofdegreesgrantedJan. '58
toJan. '61
In
math.
In
educationcourses
Totalfor thedegree
Calif. Stanford University, Stanford. Ph. D., Ed. D. (*) (*) (*) (*) New Prog.Fla. rlorida State University,
TallahasseePh. D., Ed.Ph. D., Ed.
D.
D.
30s30s
20s20s
60s60s
2 foraPh. D. 1
University of Florida Approx.Gainesville Ed. D. 27-42s 27-42s 84s None 1
Ill. Northwestern University,Evanston Ed. D., Ph. D. 36q 54q 108q 1 for Ph. D. 0
University of Illinois,Urbana Ph. D., Ed. D. 24s 48s 96s 2 for Ph. D. 3
Ind. Indiana University,Bloomington Ed. D., Ph. D. 30s 30s 90s 2 for Ph. D. 1
Purdue University, LafayettePh. D. 48s 21s
96s plusthesis
b2 0
Iowa State University of Iowa, IowaCity Ph. D. Not spec. Not spec. 90s .2 1
Kans. University of Kansas, Lawrence Ph. D. 35s 35s 90s 2 0La. Louisiana State University,
Baton Rouge Ph. D., Ed. D. 36s36s Ph. D.48s Ei. D. 72s 2 New Prog.
Mass. Harvard University, Cambridge. Ed. D. inMath. Educ. (*) (*) (*) (*) New Prog.
Mich. University of Michigan, Ann Ed. D. in 28s, Ed. D. 37s, Ed. D. 1 Ph. D.Arbor Math., Fn. D. 50s, Ph. D. 12s, Ph. D. 65s 2 1 Ed. D.
Mo. Washington University, St. 76s, Ed. D. 1 for Ed. D. 0Louis Ed. D., Ph. D. Not spec. Not spec. 72s, Ph. D. 2 for Ph. D.
N.Y. Columbia University, New York. 30s, Ed. D. 90s, Ed. D. 4 Ph. D.Ed. D., Ph. D. 40s, Ph. D. 37s 75s, Ph. D. 2 for Ph. D. 14 Ed. D.
New York University, New York. 79s, Ed. D. 12 Ph. D.Ed. D., Ph. D. Not spec. Not spec. 67s, Ph. D. 2 for Ph. D. 3 Ed. D.
Syracuse University, Syracuse. Ph. D. 33s 12s 90s 2 0Yeshiva University,d New York. Ph. D. 54s 9s 90s 2 New Prog.
Ohio Ohio State University,Columbus Ph. D.
M.A. inMath. or 20q 60q 135q le 5
Okla. Oklahoma State University,Stilwater Ed. D. 60s 300 Not spec. None 4
Pa. Pennsylvania State University,University Park D. Ei. 458 15s 90s None New Prog.
Tenn. George Peabody College forTeachers, Nashville Ph. D. 72q
f16q 108q 2 2
Texas North Texas State College,Denton Ed. D. Not spec. 36s 90s (g) 0
University of Texas, Austin Ph. D., Ed. D. Not spec. Not spec. Not spec. 2 5Va. University of Virginia,
Charlottesville Ed. D. 30s42s plusthesis
72s plusthesis 2 2
Wis. University of Wisconsin,Madison Ph. D. Not spec. Not spec. Not spec. 2 3
ab For Ed. D. proficiency in statistics is substituted.
Or one language and statistics.d Use of computer, statistics may be used as substitutions.e This is a doctoral program for college teachers of mathematics.
Substitutions permitted in special cases.Not required if student enters with sufficient background in professional education.
g A foreign language requirement is included only if considered needed for thesis.
Note: University of Maryland reported that a doctoral program specially designed for teaching of mathematics is in theprocess of being established.
APPENDIX B.DOCTOR'S PROGRAMS
Institutions at which doctor' s degreesin mathematics may be earned throughevening and/or Saturday study, orthrough summer study.
EVENING AND/OR SATURDAY
Adelphi College, Garden City, N.Y.American University, Washington, D.C.University of Buffalo, Buffalo, N.Y.Georgetown University, Washington, D.C.George Washington University, Washing-
ton, D.C.Illinois Institute of Technology, Chicago,
Ill.New York University, New York, N.Y.University of Pittsburgh; Pittsburgh, Pa.Yeshiva University, New York, N.Y.
100
1122:
SUMMER STUDY
Michigan State University of Agricultureand Applied Science, East Lansing, Mich.(Statistics only)
Montana State College, Bozeman, Mont.University of North Carolina, Chapel Hill,
N.C.University of Pittsburgh, Pittsburgh, Pa.
Institutions at which doctor' s degreesspecially designed for the teachingof mathematics may be earned throughevening and/or Saturday study, orthrough summer study.
EVENING AND/OR SATURDAY STUDY
New York University, New York, N.Y.
SUMMER STUDY
New York University, N.Y.Pennsylvania State University, University
Park, Pa.University of Texas, Austin, Tex.
Jt
APPENDIX C. COMPUTERS
Institutions with digital computers on campus in 1961;make and model number of each computer, and
year of installation, if known
AlabamaAuburn University, AuburnUniversity of Alabama, University
Arizona
Arkansas
California
Colorado
Arizona State University, TempeUniversity of Arizona, Tucson
University of Arkansas, Fayetteville
California Institute of Technology, PasadenaCalifornia State Polytechnic College, San Luis ObispoChico State College, ChicoClaremont Men's College, ClaremontHarvey Mudd College, ClaremontLos Angeles State College, Los AngelesPomona College, ClaremontSacramento State College, SacramentoSan Diego State College, San DiegoSan Jose State College, San JoseStanford University, Stanford, Palo AltoUniversity of California at DavisUniversity of California at Berkeley (does not include
computers in use by Lawrence Radiation Labora-tory and other AEC projects)
University of California at Los Angeles
University of California at RiversideUniversity of Southern California, Los Angeles
Colorado State University, Fort CollinsUniversity of Colorado, Boulder
University of Denver, Denver
ConnecticutWesleyan University, MiddletownYale University, New Haven
DelawareUniversity of Delaware, Newark
District of ColumbiaAmerican UniversityGeorge Washington University
Florida
Georgia
Hawaii
Georgetown University
Florida State University, TallahasseeUniversity of Florida, Gainesville
Georgia Institute of Technology, AtlantaGeorgia State College of Business Administration,
AtlantaUniversity of Georgia, Athens
University of Hawaii, Honolulu
101
113
IBM 650, (1959)Remington Rand Solid State 80, (1961)
G. E. 304, (1960)IBM 650, (1957)
IBM 650. (1960)
Burroughs 220Bendix G-15. (1960)IBM 1620 ( to be available 1961-1962)Bendix G-15, (1960)IBM 1620 (expected by Sept. 1961)IBM 650, (1961)Bendix G-15, (1958)LGP-30. (1961)IBM 650, (1960)IBM 650IBM 650, (1957); Burroughs 220. (1960)IBM 1620, (1961)IBM 701, (1956); Bendix G-15, (1959);IBM 704, (1959); IBM 1620, (1961);IBM 1620 on orderSWAC (at least 10 years old); IBM (7090,(1961); IBM 1401, (1961); IBM 1401,expected in January 1962, Variable LogicComputer under construction.IBM 1620Remington Rand Solid State 80, (1961);Minneapolis Honeywell 800. (1961)
IBM 1620, (1961)Bendix Digital Computer, part no.G-15-D
serial no. 155, (1958)Burroughs 205, (1955)
LGP-30, (1960)IBM 650; IBM 7070 on order
Bendix G-15. (1958)
3 Royal McBee CPC computersThe Logistics Computer, (1953); Abel,
(1951)2 Burroughs E-101
IBM 650IBM 650
UNIVAC 1101; Burroughs 220; IBM 650
IBM 305 RAMACIBM 650, (1960)
IBM 650, (1959)
Appendix C.--Continued
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maryland
Illinois Institute of Technology, ChicagoNorthwestern University, EvanstonSouthern Illinois University, CarbondaleUniversity of Illinois, UrbanaUniversity of Chicago, Chicago
Indiana University, Bloomington
Purdue University, Lafayette
Rose Polytechnic Institute, Terre HauteUniversity of Notre Dame, Notre DameValparaiso University, Valparaiso
Iowa State University, AmesState University of Iowa, Iowa City
Kansas State University, ManhattanUniversity of Kansas, LawrenceUniversity of Wichita, Wichita
University of Kentucky, LexingtonUniversity of Louisville, Louisville
Louisiana Polytechnic Institute, RustonLouisiana State University, Baton RougeTulane University, New Orleans
University of Maryland, College Park
MassachusettsBoston University, BostonHarvard University, CambridgeLowell Technological Institute, LowellMassachusetts Institute of Technology, Cambridge
(does not include computers in use at the Lincolnand Mitre Laboratories)
Michigan
Northeastern University, BostonUniversity of Massachusetts, AmherstWorcester Polytechnic Institute, Worcester
General Motors Institute, FlintLawrence Institute of Technology, SouthfieldMichigan College of Mining and Technology, HoughtonMichigan State University, East LansingUniversity of Detroit, Detroit
University of Michigan, Ann ArborWayne State University, Detroit
MinnesotaCarleton College, NorthfieldSt, Olaf College, NorthfieldUniversity of Minnesota, Minneapolis
MississippiMississippi Southern College, HattiesburgMississippi State University, State CollegeUniversity of Mississippi, University
MissouriDrury College, SpringfieldLincoln University, Jefferson CitySt, Louis University, St, LouisUniversity of Missouri, ColumbiaWashington University, St, Louis
IBM 650IBM 650, (1958)IBM 650, (1959)ILLIAC; IBM 650UNIVAC I; MANIAC 111; 2 IBM's 1620;
LGP-30
IBM 650, (1956); IBM 709 System andAuxiliary Tape Equipment on order
Burroughs 205; Remington Rand Type 80
Bendix G-15D, Alphanumeric, (1960)IBM 610IBM 610
1BM 650, (1957); CYCLONE, (1959)IBM 7070, (1961)
IBM 650, (1958)IBM 650; IBM 1620 on orderIBM 610, (1959)
IBM 650IBM 1620, (1960)
LGP-30113M 650IBM 650, (1958)
IBM 1620; LGP-30; IBM 1401 on order
IBM 650UNIVAC 1; IBM 650RPC-4,000 Computer on orderIBM 704; 2 IBM 650; 4 LPG-30; Bendix
G-15; TX-0
IBM 650, (1959)IBM 1620 to be installed in 1962IBM 610, (1959)
IBM 1620Burroughs E -101Bendix G-15DMYSTIC, 1 AS type, (1956)Burroughs E-102, (1956): IBM 1620,
(1961)IBM 704, (1959); IBM 709, (1960)IBM 650 RAMAC
IBM 610, (1959)IBM 610 (Jointly with Carleton College)UNIVAC 1103, (1958)
Have on order RPC 4,000IBM 650, (1958)IBM 650, (1958)
LGP-30, (1959)IBM 1620, (1961)IBM 610; IBM 1620, (1961)Burroughs 205, (1960)IBM 650
1
I
Appendix C. -- Continued
MontanaMontana State College, Bozeman
NebraskaUniversity of Nebraska, Lincoln
New HampshireDartmouth College, HanoverUniversity of New Hampshire, Durham
New JerseyNewark College of Engineering, NewarkPrinceton University, PrincetonRutgers The State University, New BrunswickStevens Institute of Technology, Hoboken
New MexicoUniversity of New Mexico, Albuquerque
New YorkCity College, New YorkClarkson Institute of Technology, PotsdamColumbia University, New York
Ct.rnell University, IthacaFordham University, New YorkNew York University, New YorkPolytechnic Institute of Brooklyn. BrooklynPratt Institute, BrooklynRensselaer Polytechnic Institute, TroySyracuse University, SyracuseUniversity of Rochester, Rochester
North CarolinaDuke University, Durham
Ohio
Oklahoma
Oregon
University of North Carolina, State College, RaleighUniversity of North Carolina, Chapel Hill
Case Institute of Technology, Cleveland
Fenn College, ClevelandJohn Carroll University, ClevelandMiami University, OxfordOhio State University, ColumbusOhio University, AthensUniversity of Cincinnati. CincinnatiUniversity of Dayton, Dayton
Western Reserve University, Cleveland
Oklahoma State University, StillwaterUniversity of Oklahoma. Norman
Oregon State University, CorvallisUniversity of Oregon, Eugene
PennsylvaniaBucknell University, Lewisburg
Carnegie Institute of Technology. PittsburghDrexel Institute of Technology, PhiladelphiaLafayette College, EastonLehigh University, BethlehemPennsylvania State University. University ParkTemple University, PhiladelphiaUniversity of Pennsylvania, PhiladelphiaUniversity of Pittsburgh, PittsburghVillanova University, Villanova
Puerto RicoUniversity of Puerto Rico, Mayaguez
103
113
IBM 650
Burroughs 205, (1960)
LGP-30, (1959)IBM 1620, (1961)
IBM 1620 being acquiredIBM 650; IBM 7090 on orderIBM 650. (1957)IBM 1620 System. (1961)
CRC 102-A, (1957); MANIAC I fromLos Alamos (Not yet operative)
LGP-30, (1960)IBM 1620, (1961)IBM 650, (1954); IBM 650. (1958);IBM 1620, (1961)Burroughs 220. (1959)Bendix G-15, (1959)IBM 704IBM 650IBM 1620. (1961)IBM 650, (1958)IBM 650. (1959)IBM 650
IBM 650-653, being replaced by IBM7070
IBM 650, (1956)UNIVAC 1105, (1959)
UNIVAC I, (1958); Burroughs 220,(1960)
Burroughs 205, (1960)LGP 30-66, (1960)IBM 650IBM 704, (1958)LGP-30IBM 650, (1958)National 304; Burroughs 205;
Burroughs 220G. E. 225, (1961)
IBM 650IBM 650
ALWAC 111 E, (1957); IBM 1620, (1961)IBM 1620
Burroughs E-101. (1958); IBM 1620,(1961)
IBM 650. (1957)IBM 650IBM 607LGP-30, (1957)IBM System 650 RAMAC, (1959)IBM 650UNIVAC IIBM 7070IBM 1620, (1961)
IBM 650, (1958)
Appendix C.--Continued
Rhode IslandBrown University, ProvidenceUniversity of Rhode Island, Kingston
South CarolinaClemson College, ClemsonUniversity of South Carolina, Columbia
Tennessee
Texas
Utah
Vermont
Virginia
Christian Brothers College, MemphisTennessee Polytechnic Institute, CookevilleUniversity of Tennessee, KnoxvilleVanderbilt University, Nashville
Agricultural and Mechanical College of Texas, CollegeStation
Howard Payne College, BrownwoodLamar State College of Technology, BeaumontRice University, Houston
Southern Methodist University, Dallas
Texas Technological College, Lubbock
Texas Western College, El PasoTrinity University, San AntonioUniversity of Houston, HoustonUniversity of Texas, Austin
Brigham Young University, ProvoUniversity of Utah, Salt Lake City
University of Vermont, Burlington
University of Virginia, CharlottesvilleVirginia Polytechnic Institute, Blacksburg
WashingtonUniversity of Washington, SeattleWashington State University, Pullman
West VirginiaWest Virginia University, Morgantown
Wisconsin
Wyoming
Marquette University, Milwaukee
University of Wisconsin, Madison
University of Wyoming, Laramie
104
116
IBM 7070 System, (1960)IBM 610
RPC-4,000LGP-30, (1959)
IBM 1620 on orderIBM 1620IBM 1620, (1961)IBM 650, (1959)
IBM 650, (1956); IBM 709, (1961)
LGP-30, (1960)LGP-30, (1958)A computer built by Rice University
and similar to MANIAC II; LGP-30UNIVAC Scientific 1103; UNIVAC
Solid State 90; UNIVAC 120
CRC 102-A (1959); Litton 20-40, (1960);IBM 1620, (Dec, 1961, tentative)
Bend lx G-15-JLPG-30IBM 650Control Data Corporation 1604, (1961);Control Data Corporation 160, (1961)
IBM 650, (1958)Burroughs 205
IBM 1620, (1961)
Burroughs 205, (1960)IBM 650, (1958)
IBM 709, (1960)IBM 650, (1956); IBM 709, expected in
1961
IBM 610, (1958); IBM 650, (1960)
IBM 650, (1958); plan to change toIBM 1620 in September, 1961Control Data Corporation 1604, (1961);
3 IBM 1620, (1961)
Bend lx G-150
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