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FOCUS is published by theMathematical Association of America inJanuary, February, March, April, May/June,August/September, October, November, andDecember.

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ISSN: 0731-2040; Printed in the United Statesof America.

FOCUSJanuary 2003

Volume 23, Number 1

4 Remembering Henry L. Alder (1922-2002)By Gerald Alexanderson

7 Lowell W. Beineke Named Editor of The CollegeMathematics Journal

8 A Year in the Life of the MAA: The StatisticsBy Ann Watkins

10 NSF’s Advanced Technological Education ProgramBy Victor Katz

12 NSF Beat: Opportunities at the National Science FoundationBy Sharon Cutler Ross

13 Report: 14th General Assembly of the InternationalMathematical UnionBy Harry Waldman, based on a report by Donald G. Saari

14 Short Takes

15 Letters to the Editor

17 Memories of Arnold RossBy Glenn Stevens

18 Being a Mathematics Educator in a Department of MathematicsEileen Fernandez

On the cover: Lake Fibonacci is a recently created reservoir at the Maryland Science andTechnology Center, located in Bowie, MD. The lake's remarkable centerpiece is a mas-sive, yet elegant fountain that spurts water as high as 36 feet into the air. Created as amathematical sculpture by artist and mathematician Helaman Ferguson, the fountain ismade up of more than 45 tons of Texas granite, layered in alternating colors and rising toa height of 18 feet. It is supported by a concrete and steel platform atop pilings pounded40 feet into the lake floor. For more on Lake Fibonnaci see Ivars Peterson's Oct. 21, 2002MathTrek column on MAA Online at http://www.maa.org/mathland/mathtrek_10_21_02.html. Photograph courtesy of Helaman Ferguson.

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May/June August/September OctoberEditorial Copy March 15 July 8Display Ads March 25 July 10 August 20Employment Ads March 11 June 11 August 13

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Arthur Benjamin, ofHarvey Mudd College,and Jennifer Quinn, ofOccidental College,have been selected asthe new editors of MathHorizons, beginningwith the September2003 issue. Their termwill last five years.

Professor Benjaminearned his B.S. inApplied Mathematicsfrom Carnegie Mellon and his PhD inMath-ematical Sciences from JohnsHopkins. Since 1989, he has taught atHarvey Mudd College, where he iscurrently Chair and Professor ofMathematics. He has served as Editor ofthe Spectrum book series for MAA, andcurrently serves on the editorial boardsof Mathematics Magazine and the UMAPJournal. In 2000, he received the MAA’sHaimo Award for Distinguished Collegeand University Teaching. His researchinterests include game theory andcombinatorics, with a special fondness

for Fibonacci numbers. In addition tospending time with his wife and twodaughers, he enjoys tournamentbackgammon, racing calculators, andperforming magic.

Jennifer Quinn truly feels as if she hasled a charmed life. She had the privilegeof earning a B.A. from Williams College,an M.S. from the University of Illinois,Chicago, and a Ph.D. from the Universityof Wisconsin, Madison. She cannotimagine a professional career that doesn’tinclude doing mathematics and teaching

Arthur Benjamin and Jennifer Quinn Named New Editors

of Math Horizons

University of Memphishttp://troy.msci.memphis.edu/cbms

Free Boundary Problems in Partial Differ-ential Equations and ApplicationsMay 18–22Wayne State Universityhttp://www.math.wayne.edu/~gzlu/cbms/cbms.html

Stochastic Partial Differential Equationsand their ApplicationsMay 19–23Illinois Institute of Technologyhttp://www.iit.edu/~duan/SPDE.html

Every year, the Conference Board of theMathematical Sciences (CBMS) and theNational Science Foundation (NSF)sponsor Regional Research Conferencesin various areas of mathematics. Theconferences are intended to stimulate in-terest and activity in mathematical re-search. Each lasts five days. About 30funded participants are invited to eachconference, ranging from established re-searchers to graduate students and othernewcomers to the field. Five conferenceswill be offered this year:

Expansion Methods in CombinatoricsMay 13–17

CBMS Announces 2003 Regional Research Conferences

The Web of ModularityJune 3–7University of Illinois at Urbana-Champaignhttp://www.math.uiuc.edu/cbms/

Fully Nonlinear Equations in GeometryJune 23–27University of Notre Damehttp://www.nd.edu/~cbms/

See http://www.cbmsweb.org/NSF/2003_conf.htm for more information.CBMS is also calling for proposals forconferences for next year; see http://www.cbmsweb.org/NSF/2004_call.htm.

Jennifer Quinn Arthur Benjamin

students. In 1993, shejoined the faculty atOccidental College inLos Angeles where shecurrently chairs themathematics de-partment.

Quinn has served asNewsletter Editor forthe Southern Cal-ifornia Section of theMAA, is an AssociateEditor for Math-

ematics Magazine, and is completing hersixth and final year on the board of theSpectrum book series. In 2001, she washonored to receive the DistinguishedTeaching Award for the SouthernCalifornia section of the MAA. Herresearch interests include combinatorialproof, graph theory, and combinatorialmatrix theory. Other pursuits includetoo much committee work, homerenovations, and raising a beautifulmillennium baby boy.

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Remembering Henry L. Alder (1922-2002)

By G. L. Alexanderson

If one were asked, “ Who would be bestdescribed as representing the MAA?”, thename that would leap to mind is, “HenryAlder,.” From 1956, when he was electedChair of the Northern California Section,until his death, Henry was given one sig-nificant responsibility after another in theSection and at the national level. He per-formed these tasks splendidly, always con-scientiously and carefully, with meticu-lous attention to detail, and showing wis-dom, diplomacy, and tact. He truly be-lieved in the importance of the work ofthe Association. Through his many yearsof tireless service and his inviting othersinto the profession through his collegial-ity and mentoring, Henry Alder personi-fied the spirit of the MAA. Sadly for theMAA, his family, colleagues, and friends,Henry died of cancer on November 6,2002, at the age of 80, at his home inDavis, California.

Between 1960 and 1975, he was the na-tional Secretary of the MAA, and in rec-ognition of that outstanding service, hewas designated Secretary Emeritus, theonly person in MAA history to be so hon-ored. A few years later he was elected na-tional President for 1977-78. In 1960 hehad been approached by CarlAllendoerfer, then President of the MAA,about being nominated for Secretary. Heasked what the principal responsibilitieswould be. Allendoerfer told him that itwas largely the care and feeding of Presi-dents. Henry took that admonition seri-ously, but at the same time he realized thatthe Secretary has the potential for mov-ing an organization along. The Secretarycan hold the office for a significant pe-riod of time and provides the institutionalmemory of the organization. Presidentscome and go, but the Secretary often stayson.

Secretary and President were only themost visible offices that Henry Alder heldin the MAA. He served on innumerableMAA committees over the years, andwhen he was chair of a committee, things

happened. He chaired the Committee onthe Deborah and Franklin Tepper HaimoAwards for Distinguished College or Uni-versity Teaching of Mathematics and islargely responsible for the successfulimplementation of that important pro-gram, funded through an endowmentfrom another former MAA PresidentDeborah Tepper Haimo. He chaired thefirst committee on the Sliffe Awards andwas largely responsible for the formula-tion of that program by which we rewardteachers of the most successful teams par-ticipating in the American MathematicsCompetitions. Other committees Henrychaired most effectively include theGung-Hu Committee (the group thateach year nominates the winner of theDistinguished Service Award), the Coun-cil on Awards, and the Committee on the25-Year Member Banquet.

There is scarcely any aspect of MAA ac-tivities that has not been touched byHenry’s sage counsel and good judge-ment. In 1980 he received theAssociation’s most prestigious prize, theAward for Distinguished Service to Math-ematics. Earlier he had received the Lester

R. Ford Award for Expository Writing forhis beautiful article, “Partition Identi-ties—from Euler to the Present,” that ap-peared in the American MathematicalMonthly in 1969. This work described abroad range of ideas in partition theory,and “Present” in the title included workfrom some of his own research papers inthe Bulletin of the American Mathemati-cal Society and the Pacific Journal of Math-ematics. Certain generalizations of theRogers-Ramanujan identities involvewhat are now called Alder polynomials.When he published that paper in theMonthly the editor, Harley Flanders,wrote that Henry has probably contrib-uted more than anyone else to the presentvitality of this Association.” The samecould be said today.

Henry Ludwig Alder was born inDuisburg, Germany on March 26, 1922,but with Swiss citizenship. He and hisfamily moved to Zürich in 1933 where hefinished school and started his collegeeducation at the EidgenössischeTechnische Hochschule. In 1941 he trans-ferred to the University of California,Berkeley, where he received his B.A. inmathematics and chemistry in 1942. Heremained at Berkeley, with the exceptionof service in the U.S. Army Air Corps in1944-45, and wrote a dissertation underthe direction of the eminent numbertheorist, D.H. Lehmer, competinlg hisPh.D. in 1947. After one year as an in-structor at Berkeley, he moved to theUniversity of California, where he re-mained until his retirement, except for asabbatical in Zurich. At Davis he was arenowned teacher, both in his own fieldof number theory but also in statistics,an area in which he and his colleague,Edward B. Roessler, wrote a successfultextbook that ran through six editions.On his own campus he served as depart-ment chair, and chair of various commit-tees, including one on minority under-graduate research participation, anotheron culturally disadvantaged students.Statewide, he chaired the Board of Ad-

Henry L. Alder

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missions and Relations with Schools ofthe University of California system,among others.

Professor Alder served mathematicsacross a wide range, from school math-ematics through research. For the PacificJournal of Mathematics, he served on itsBoard of Governors from 1960 to 2002and, from 1970 on he was Chair of its In-vestment Committee. His interest inschool mathematics resulted in his ap-pointment to the California State Boardof Education, the first mathematician andfirst UC faculty member to receive suchan appointment. Another indication ofthe great range of his interests was hisservice as chair of the Council of Scien-tific Society Presidents in 1980, and from1956 to 1959 he was the first nationalpresident of Mu Alpha Theta, the nationalhigh school and junior college mathemat-ics club. I could give more examples ofhis many areas of service to mathematicsand to education; the list is long.

Those who knew Henry Alder well alwaysmarveled at how organized he was. Withan incredible memory he could call upprecedents and procedures like few oth-ers. Subsequent MAA secretaries came torely on Henry for advice on the handlingof bylaws changes, responding to legalquestions on incorporation, and such. Hewas a master of Robert’s Rules of Order.If someone was planning to take a pro-posal to the MAA’s Board of Governors,it was wise to be prepared for Henry’sanalysis. If he approved of the proposalhe would come up with a set of argu-ments (numbered of course) as to whyhe favored the proposal. On the otherhand, one had to be prepared for a com-parable list, seemingly thought out afterconsiderable study, of all the reasons thissame proposal was a bad idea.

In the Northern California Section he wasresponsible for procedural guidelinesenunciated early on but still used by theofficers today—for example, the “AlderRule”, now extended to our nationalmeetings, that says, “Don’t invite aspeaker for a meeting program unlesssomeone on the program committee hasheard the speaker and can vouch for thequality of his or her exposition.” He him-

self was an exceptionally able speaker, andaccording to reports from his students,an inspiring teacher. A colleague of mine,as an undergraduate at Davis, took fourcourses in number theory from Henryand says of his teaching, “Henry had theability both to awe students and put themat ease at the same time. His presencewould fill the room and his humor, his-torical anecdotes and charming phraseskept all of us at the edge of our seats. Hehad an uncanny knack for teaching stu-dents how to write good proofs, both byhis beautiful examples as well as by hisclear hints that made proof-writing seem

easy. Henry inspired me to become anumber theorist and I strive to live up tohis example today.” In 1976 he won theUC Davis Award for Distinguished Teach-ing. In 1999 he endowed a fund in theUC Davis Mathematics Department thatwill support a $2000 prize each year tothe mathematics graduate studentdeemed to be the best teacher. Additionalrevenue from the fund will be used toenhance undergraduate teaching.

When asked why the Northern Califor-nia Section of the MAA has been so suc-cessful, he immediately responded thatthere are four reasons (as usual, the re-sponse was spontaneous, but still the ar-guments were numbered): (1) a strongSecretary-Treasurer; (2) a good represen-tation of different kinds of schools—arotating system for choosing meeting sitesand officers, through research universi-ties, comprehensive state universities, lib-eral arts colleges, two-year colleges, andindustry [a practice probably due toHenry’s influence]; (3) high qualityspeakers, chosen for their ability to reachan audience; and (4) an executive boardwhere past officers stay on after theirterms of office and continue to contrib-ute, thus assuring continuity. He alwaysreminded his colleagues that at an MAAmeeting, a lecture should be given for thebenefit of the audience, not the benefitof the speaker. Up to the last year or so,Henry attended almost every Section Ex-ecutive Board meeting, and when theSection’s annual meeting was held inDavis last March, Henry was the personin charge of local arrangements. It wasan enormously successful meeting, atribute to Henry’s planning and consci-entious attention to detail. In 1998 theSectional Certificate of Meritorious Ser-vice was given to Henry at the Baltimoremeetings. It was appropriate that he wasrecognized in this way for his contribu-tions to the Section, even well after hehad received the Award for DistinguishedService at the national level.

Henry was a person of absolute probity,always fair to his colleagues and gener-ous with his time. In all my years of work-ing with him on many committees andboards, I never heard him speak harshlyof a colleague. On a proposed course ofaction he could be forceful in puttingforth his arguments, but they were neverad hominem. He never spoke in a mean-spirited way. He was serious, always sin-cerely promoting what he was convincedwas good for the organization, but he wasnot without humor. Ken Ross reports thatwhen he was elected Secretary of theMAA in 1983, Henry was “the first per-son to congratulate [him]” and then wenton to emphasize that “as Secretary, [Ken]

Henry Alder served as president of the MAAfrom 1977-78. This photograph hangs inthe stairwell of the MAA headquarters. Itis part of a gallery of portraits of MAApresidents.

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would have a great deal of power andpointed out that Lenin was Secretary ofthe Communist Party, never President.”

Henry’s manner of dealing with peopleset the tone for relations between MAAofficers, board members, and Washing-ton office staff that, I think, still prevails—one of civility and of concern for the feel-ings of one’s colleagues. He has left a last-ing mark on the quality of this great or-ganization. When he received the Distin-guished Service Award in 1980, the cita-tion included the following: “He has hadtremendous and profound influence onall of mathematics, and more than anyother person, he has charted the courseof the Mathematical Association ofAmerica for the past twenty years.” Thereare mathematicians who have addedgreatly to mathematics through their re-search activities. Still others have contrib-uted through their teaching. Finally, somemathematicians are willing and energeticworkers on behalf of the professional or-ganizations. But there are few among uswho fill all three of these roles. Thus it isappropriate that we today honor Profes-sor Henry L. Alder, an able researcher, an

honored teacher, and a man who hasmade unparalleled contributions of timeand energy to the professional activitiesof mathematicians.”

We can say the same today after morethan forty years. We shall miss him.

Let me close on a very personal note.Henry was responsible for my becominginvolved deeply in the activities of theMAA. I always thought of him as a men-tor. When I became MAA Secretary andlater President, when faced with a prob-lem I always thought, “What wouldHenry do?” I felt I was attempting to carryon, in some small way, the work that hehad done so well.

He is survived by his wife Benne, who isa professional actress; a son and daugh-ter-in-law, Lawrence and Janice Alder;two granddaughters, Allison andCatherine; two brothers and other fam-ily members.

Gerald L. Alexanderson has been both Sec-retary and President of the MAA.

Henry Alder served as secretary to the MAAfrom 1960-1975. This photograph is dis-played on the second floor of the MAA head-quarters building, together with portraits ofother MAA secretaries and treasurers.

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Lowell Beineke, Schrey Professor ofMathematics at Indiana University-Purdue University, Fort Wayne, Indiana,has been selected as the new editor of theCollege Mathematics Journal, beginningwith the January 2004 issue. He will servefor five years.

Beineke joined the MAA when he wasawarded a membership as a student atPurdue in the early 60s. Followinggraduation, he attended the Universityof Michigan, from which he received hisdoctorate in 1965. He then joined thefaculty of Purdue at the Fort Waynecampus (now IPFW), where he has spenthis entire professional career, movingthrough the ranks and being awarded theSchrey Professorship in 1986. Five yearsof that have been spent in England,including one on a Fulbright Exchangeat the (then) Polytechnic of NorthLondon and three sabbaticals at theOxford University MathematicalInstitute.

Beineke’s research has been in graphtheory. His thesis was on the thicknessof graphs and was written under thesupervision of Frank Harary. He isauthor of just over a hundred papers inthe field; some of his favorite areas aretopological graph theory, connectivity,tournaments, line graphs, and multi-dimensional trees. He and Robin Wilsonof the Open University have written andedited five books on graph theory, themost recent being Graph Connections,a collection of chapters relating graphtheory to various other areas ofmathematics. He referees numerouspapers every year and serves on theEditorial Board of the Journal of GraphTheory.

Although IPFW does not awarddoctorates, he has supervised four theses,three at Purdue West Lafayette and oneat Western Michigan University. Theseopportunities have provided one of thelinks between his teaching and research.While complementing one another, thetwo activities also compete for time.

Beineke says that if forced to give up oneor the other, he’s not sure which it wouldbe, although the day-to-day teachingwould probably win out. His favorite

Lowell W. Beineke Named to Be Editor of the

College Mathematics Journal

Lowell W. Beineke

Throughout his career, Beineke hasparticipated in many MAA activities,regularly attending national and sectionmeetings. He has served as bothPresident and Governor of the IndianaSection, and is currently the liaison forhis department and Advisor to the IPFWStudent Chapter (one of the CharterChapters). Among his honors, he isproud to have received both the Dis-tinguished Teaching and DistinguishedService Awards from the IndianaSection.

He is pleased to have this opportunityto edit the College Mathematics Journaland will try his best to maintain itsexcellence as a vehicle for thedissemination of mathematics forcollege educators.

“I am excited,” he said, “by the challengeof the position, but also recognize thatif the MAA goals for the CMJ are to bemet, it will require the assistance andcooperation of many, many others. So,along with the other editors, I ask youto please submit not only appropriatearticles, but also ideas and suggestions forarticles and authors. With yourcooperation, the excellence of the MAAjournals will continue withoutinterruption.”

In addition to his mathematical anduniversity lives, Beineke’s interestsinclude gardening, reading, running,cryptic crosswords, and travel. He and hisEnglish wife Judith have two children: theolder, Jennifer, is an Assistant Professorof Mathematics at Western New EnglandCollege, while her younger brother,Philip, is a graduate student in statisticsat Stanford.

Lowell W. Beineke

courses to teach are graph theory (ofcourse), geometry (including non-Euclidean), foundations of higher math,math history, and calculus (definitely!).

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A Year in the Life of the MAA: The Statistics

By Ann Watkins

A Year of Publications

American Mathematical MonthyTotal number of pages: 945Number of manuscripts submitted: 719Number published: 103Number of people who refereed manuscripts: ~ 300

Mathematics MagazineNumber of manuscripts submitted: 282Number published: 60Number of referee reports requested: 321Percentage received: 88%

The College Mathematics JournalNumber of CMJ authors: 77Number of CMJ referees who, on being asked what was hap-pening with the paper they had been sent ten weeks ago, repliedthat they had not looked at it, were not planning on looking atit, and didn’t know that they needed to tell anyone about that: 1

Number of new books published by the MAA: 23Number of those that are all-electronic: 1Average number of MAA books sold per month onamazon.com: 385

Average number of visits to MAA Online per day: 4,637Average number of pages hit per visit: 12

Number of articles published last year in MAA journals by MAApresident: 1Number of expository writing awards received by MAA presi-dent: 0

A Year of Membership

Number of full-time and part-time two-year college, four-yearcollege, and university mathematics professors: 48,015Total MAA membership: 32,558

Number of individuals who contributed to the MAA: 1,391Average contribution: $123.89

Number of MAA staff members: 35Ratio of members to staff: ~q 930/1Ratio for the AMS: ~ 180/1Ratio for SIAM: ~ 148/1

Number of full-time graduate students in mathematics: 26,168Number of graduate students who are MAA members: 2,419

A Year of Programs for Members

Number of new SIGMAAs approved: 3

Number of members of largest SIGMAA (RUME): 1264

Number of new outside grants funded: 14Total value of funded grants: $2,330,832

Number of professional development workshops: 8Number attending: 224

Number of U.S. citizens receiving Ph.D.s in mathematics: 532Number of new Project NExT Fellows: 71Number of Fellows so far: 626

A Year of Programs for Undergraduates

Number of junior and senior mathematics majors: 58,900Number of undergraduates who are MAA members: 1,199Number of undergraduates who receive Math Horizons: 17,000Number taking the Putnam exam: 2,954Number of active Student Chapters: 173

Number of students attending MathFest: 193Number of papers they presented: 107Number of mathematicians attending MathFest: 908Number of papers they presented: 116

A Year of the American Mathematics Competitions

Number of 8th grade and below students participating in theAMC 8: 169,654Number of 12th grade and below students participating in theAMC 12: 136,714Number of students participating in the USA MathematicalOlympiad: 325Number who came to Cambridge to take the USAMO: 202Number of students participating in the Mathematical Olym-piad Summer Program: 178

Rank of the U.S in the International Mathematical Olympiad.:3 out of 84Number of gold medals presented at the IMO: 39Percentage won by U.S. team: 10%

A Year of Governance

Number of pages in nine issues of FOCUS: 280Number of pages in agendas for two Board of Governor’s meet-ings: 241

Number of members in largest MAA section(Southeastern): 2065Number of members in smallest MAA section(Intermountain): 164Number of governors representing Southeastern Section: 1Number of governors representing Intermountain Section: 1

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Number of e-mails sent by the MAA president: 2817

A Year of Section Meetings

Number of section meetings: 38Average attendance per meeting: 144Average number of students per meeting: 41Average number of two-year college faculty per meeting: 10Largest attendance at a section meeting (Texas): 301Largest percentage of members attending a section meeting(Mississippi-Louisiana): 51%Largest number of student papers at a section meeting(Ohio): 38Number of times Pólya lecturer Ed Burger spoke atsection meetings: 6Number of chicken dinners eaten by MAA president atsection meetings: 7Number of blue-grass bands heard by MAA president atsection meetings: 1

A Year of National Meetings

Total attendance at winter meeting in San Diego: 4665Number who were students: 717Number of panel discussions: 50

Total attendance at MathFest in Burlington: 1239Number of states represented: 47Number of foreign countries represented: 10Percentage change in MathFest attendance in six years: +62%Percentage change in NASDAQ over same period: -22%

A Year of Complaints to the MAA President

Complaints about the letter from the MAA president askingpeople to give money to the MAA in their will: 2Complaints about the letter asking people to give money be-fore they die: 0

Number of e-mails complaining that the MAA president didn’trespond to a previous e-mail that requested no further com-munications from the MAA: 1

Most common complaint (having to speak on the same pro-gram as Pólya lecturer Ed Burger): 4

A Year of Thank-Yous

I receive many letters and emails thanking me for the work thatthe MAA does. Often these come from high school studentsgrateful for their experience with the American MathematicsCompetitions or from retired members who enjoy their jour-nals even more now that they actually have time to read them. Iwould like to add my thank-you to all of you for your dedica-tion and hard work towards advancing the mathematical sci-ences and for making the two years I’ve served as president pro-ductive ones for the MAA.

Number of minutes the MAA president enjoyed her job in thelast year: 525,600.

Ann Watkins’ term as MAA President ends after the January 2003Joint Mathematics Meetings.

1) The article in our December issue on Manjul Bhargava’s ap-pearing in the Popular Science list contained two unfortunateerrors. First, Bhargava’s thesis was not about the “Fifteen Theo-rem.” Second, the article’s title suggests that the “Fifteen Theo-rem” was the major reason for Bhargava’s selection as one ofthe “Brilliant Ten.” That is, of course, incorrect: the selectionwas based on all of Bhargava’s work so far.

2) In the article on Fibonacci’s Liber Abbaci in the Novemberissue, a typesetting error introduced extra plus signs and el-lipses into two of the formulas on page 7. They should read

and

respectively.

3) In the article on Heron’s formula in the November issue,the volume of the tetrahedron with base 1, 1, 1 and slant heights

2 , ,2 2 should be 5 / 12 not 5 6/ . (Corrected by theauthor and Peter Ross.)

We regret the errors.

Corrections

5 17 10 5 5 4 10 5 5 4 3 5 5 4 3 2⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅

4 10 5 26 4 3 5 26 4 3 2 26 4 3 2 5⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ,

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Which NSF educational program isthe main source of outside funding forprojects developed by community col-leges, supports improved education forthe high-technology industries that areso crucial to our nation’s economy, andhelps fund the creation of math curriculafor at least half of the nation’s prospec-tive elementary school teachers? The an-swer is the Advanced Technological Edu-cation Program (ATE). This program,established in 1992, has made grants thathave had an enormous effect in increas-ing the technical competencies of thou-sands of students in community collegesall around the country.

The ninth annual National ATE Princi-pal Investigators Conference was held inWashington on October 24-26, 2002.Entitled “Assessing the Impact,” theconference’s goals were to demonstratehow these grants have succeeded in theirmission over the years. Many of the cur-rent projects had booths in the exhibithall where they displayed some of theirwork and had a chance to share their ideaswith others. We will report here on someof the projects, and suggest that you con-tact the Principal Investigators or checkthe web sites of the projects of most in-terest to find out how you can either joinwith them or begin to replicate some oftheir ideas. Alternatively, if some of theideas here spark some new ideas of yourown, you should take the opportunity tosubmit proposals to the ATE programyourselves.

Project TEACH, centered at Green RiverCommunity College in Auburn, Wash-ington (Their website address: http://www.projectteach.org; email address:projectteach@grcc.ctc.edu), is a collabo-rative effort with Central WashingtonUniversity and six nearby school districts.Not only has the project developed newcourse materials for prospective K-8teachers, materials which emphasizeproblem solving and the use of technol-ogy, but it is also working hard to recruittalented students into teaching and toprovide practical and diverse early field

experiences. Furthermore, prospectiveteachers at Green River spend manyhours on Saturdays and in the summerworking with local 4th grade students inmathematics, thus gaining valuable expe-rience. One of the reasons that studentsattend community college is location nearthe student’s home and the low cost. Sincethese reasons often still apply after a stu-dent has completed two years, GreenRiver has arranged with Central Wash-ington University for the latter to conductjunior and senior level courses on its cam-pus to make it as convenient as possiblefor students to complete their teachingdegrees. And since the students’ field ex-periences are at nearby schools, theproject has found that once students havecompleted their degrees, they tend to getjobs in the immediate area, helping theseschools to get high quality teachers witha strong mathematics and science back-ground.

Prince George’s Community College(PGCC), in Maryland, is leading a simi-lar effort to develop and implement sci-ence and mathematics courses forpreservice elementary teachers inMaryland’s community colleges. In par-ticular, the college is working withMaryland’s four-year colleges to insurethat students with the new Associate ofArts degree in teaching will be able totransfer easily to any of those colleges tocomplete their degree. The courses atPGCC, like those at Green River, have aconstructivist and inquiry-based flavor,based on materials developed through theMaryland Collaborative for TeacherPreparation and consistent with NCTMand NCATE Standards. The faculty atPGCC is also working with local highschools to recruit students into the pro-gram. Interestingly enough, given that theneed for math and science-trained teach-ers is expected to be larger over the nextdecade than the capacity of Maryland’sfour-year colleges, plans are underway todevelop four-year teaching programs atsome of the community colleges them-selves. (Contact: Patricia Basili,basilipa@pg.cc.md.us).

The Community College of Philadelphia(CCP), which has a strong program inelementary mathematics, is using ATEfunds to develop a new degree option forstudents planning to be secondary math-ematics teachers. As part of this process,CCP is expanding its articulation agree-ments with many Philadelphia-area four-year colleges, so that students canseamlessly transfer into a Baccalaureateprogram. Two basic courses being devel-oped for the program are Teaching withTechnology and Problem Solving in Mathand Science. CCP graduates in this pro-gram will thus be expected to be expertsin the use of teaching technologies andalso have a large repertoire of problemsolving strategies. In order to recruit andretain students in the teaching program,CCP is developing an innovative market-ing strategy with the School District ofPhiladelphia in order to promote the pro-gram at college fairs. It also is creatingcustomized systems of advising andmentoring to help insure that studentscomplete the program. (Contact: MarciaEpstein, mepstein@ccp.cc.pa.us).

Although the projects above have limitedcomponents dealing with the training ofcommunity college faculty to prepareprospective schoolteachers, two nationalorganizations have ATE grants specificallydesigned for this purpose. The AmericanMathematical Association of Two-YearColleges (AMATYC) is conducting aproject entitled Teacher Preparation,Mathematics and Technology: A NationalDialogue. One major component of thisproject has been a series of regional con-ferences addressing the mathematics andtechnological preparation of prospectiveK-8 teachers at two-year colleges as wellas the broader issue of two-year collegeinvolvement in teacher preparation.These conferences addressed current re-search results in mathematics pedagogy,held dialogues on the mathematics thatprospective teachers should know, anddiscussed issues of course creation andarticulation with four-year institutions.But AMATYC also conducted two verysuccessful workshops in the summer of

By Victor J. Katz

NSF’s Advanced Technological Education Program

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2002 designed to help teachers at two-year colleges work with prospective el-ementary and middle school teachers.These workshops will be repeated at otherlocations in the summer of 2003. In ad-dition, with the experience gained inthese workshops, AMATYC will begin inMarch, 2003 to conduct Traveling Work-shops in Teacher Preparation. Thus, youcan ask AMATYC to come to your cam-pus to help your faculty deal with issuesin preparing teachers. For more informa-tion, check the website http://amatyc.dtcc.edu.

Another national project is being con-ducted by Phi Theta Kappa, the honorsociety for community colleges. Theproject, Preparing Tomorrow’s Scienceand Math Teachers: The CommunityCollege Response, involves teams fromseven community colleges with exem-plary teacher preparation programsmentoring colleagues at an additionaleighteen colleges. The mentoring teams,consisting of a community college edu-cator and a four-year college facultymember, are helping these eighteen col-leges replicate or adapt the knowledge,experience, and materials already devel-oped via site visits, conferences, and in-teractive technologies. They will soon beable to disseminate these activities na-tionally. Interestingly, among the seven“exemplary” programs are the three com-munity colleges whose projects are dis-cussed above. (Contact: Diane Eisenberg,nsf@ptk.org).

Among the most enthusiastic ATEawardees is the group of faculty fromSouth Carolina involved in the SouthCarolina ATE Center of Excellence,mainly from Piedmont Technical Collegeand Florence-Darlington Technical Col-lege (http://scate.org). The goal of the cen-ter has been to increase the quality, quan-tity, and diversity of South Carolina en-gineering technology graduates, and it issucceeding in its goals. The emphasis inthe new courses developed for the pro-gram is problem-solving, and the initialevaluation of the program shows that stu-dents graduating in it are far more confi-dent in their problem-solving skills thanstudents coming out of the regular pro-gram. The mathematics teachers in thisprogram have had to adjust their own

styles to meet the program’s goals. Thustheir teaching of technical mathematicsis far different from what it used to be.They are working more closely with thetechnology teachers, and teaching thenecessary mathematical skills when andas they are needed for solving importanttechnology problems. With some flex-ible scheduling, so that more mathemat-ics can be taught one week if needed andless another week, the students are moreengaged in the mathematics when it istaught and are becoming more capableof using it at the appropriate time. Theteachers too are more enthusiastic. Onetold me that she had been virtuallyburned out by teaching for several yearsin a traditional style with indifferent re-sults. Now, she is energized. Her studentsare succeeding at a much higher rate, andshe is very pleased with the outcomes.She has seen numerous students whoseinitial reaction to mathematics was“avoidance” being turned on by the sub-ject, and she has also seen students withlow self-esteem have their horizons raisedto the point that they are finding excel-lent technical jobs with their hard-wonskills. One of the goals of the program isto spread the teaching philosophythroughout the South Carolina commu-nity college system. So the lead mathteachers in the project are serving as men-tors throughout the system, to improvetechnical education all over the state.They welcome inquiries from other statesas well. (Contact: Lynn Mack,mack.L@ptc.edu).

Another highly successful ATE Center isthe New Jersey Center for Advanced Tech-nological Education, whose main officeis at Middlesex County College, (http://www.njcate.org). A key to their successhas been the partnerships they forgedwith corporations in New Jersey. Thesepartnerships allowed them to developnew programs that insured the employ-ability of their graduates. Just as in SouthCarolina, they used an integrated curricu-lum model, in which the teaching ofmathematics, among other subjects, wasproject centered. In particular, they de-veloped “just-in-time” methods of deliv-ery, so that students learned the math-ematics necessary to solve importantproblems, many coming out of genuineindustry needs. Although the mathemat-

ics courses for the various technical pro-grams cover the standard topics of tech-nical mathematics over a two-year period,the topics are all taught in relation to rel-evant problems. NJCATE is also workingwith a local school system to help themdevelop integrated technical high schoolcurriculum units based on their ownmodel.

Many other ATE projects are developingnew curricular materials to go along withthe project-centered approach to teach-ing mathematics, whether in mathemat-ics courses themselves or in interdiscipli-nary programs. For example, CapitalCommunity College in Hartford, CT, incooperation with the Kennedy SpaceCenter and AMATYC, produced two vol-umes of Mathematical Explorations, allbased on NASA space activities, to be usedin various mathematics courses. For ex-ample, the first Laboratory Technical Ac-tivity in the first volume is entitled “SpareParts of the Space Shuttle.” There are250,000 parts on a shuttle, some of whichare repairable and some of which are re-placed once they wear out. Decisionsmust be made as to how many sparesshould be on hand, either on the groundor on the shuttle, and when to order re-placements, especially of very expensiveparts, based on a probability of suffi-ciency equation. The activity, designed tobe worked on by a team, requires algebraand precalculus skills, some of which willprobably be developed as the activity isbeing used. Capital College is also pro-ducing a new series of books entitledMathematical Journeys, which consist ofLaboratory Activities designed to be usedeither in an interdisciplinary course or aninterdisciplinary club. For example, thereis a lab entitled “I’ve Got Your Number,”which explores several aspects of the cel-lular phone industry. The mathematics inthis laboratory includes geometry ofcircles and polygons, graphing tech-niques, introductory statistics, and piece-wise functions. Mathematical Journeyscontains detailed instructions on how tocreate a course out of the materials, withguides as the types of mathematical skillsnecessary for each unit and how thoseshould be introduced. There is even ma-terial on marketing such an interdiscipli-

continued on page 12

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nary course both to administrators, col-leagues, and students. (Web site: http://www.ccc.commnet.edu/MWP)

Other community colleges have also de-veloped mathematics course materialswhich meet their own needs, but whichwill probably also meet the needs of oth-ers. For example, Wake Technical Com-munity College created and tested class-room activities for integrating mathemat-ics and algebra-based physics (http://www.wake.tec.nc.us/math). In order tohelp students further in determiningwhat skills they will need in the work-place, Wake also developed a project ofWorkplace Research. Community collegeand high school instructors visited indus-tries throughout central North Carolina,

where they interviewed and videotapedtechnicians to determine and demon-strate what mathematical skills were be-ing used. Mathematical activities basedon these visits were then developed. Allof these industry “snapshots,” includingvideo clips, warm-up quizzes relevant tothe industry, and worksheets for furtherexploration are now available on a CD.Wake will be hosting an AMATYC work-shop in summer, 2003 dealing with Work-place Research.

Another project involving cooperationwith industry is the Middle School Ad-vanced Technology Education Project atCleveland State University, CuyahogaCommunity College, and Lorain CountyCommunity College, all in Ohio. This

project pairs middle school mathemat-ics, science and technology teachers with

engineering and technology profession-als. The teachers participate in variousworkshops and engage in project-basedlearning activities. In addition, they workwith their own students during the schoolyear on engineering challenges, wherestudents working in teams with profes-sors and engineers attempt to find inno-vative solutions to real world problems..This project has been helping teacherslearn better ways to integrate science andtechnology into the classroom, and hasdirectly helped numerous studentsthrough such additional activities as amiddle school discovery camp and work-study programs in local industries. (Con-tact: Terri Byrnes,m.byrnes@csuohio.edu)

For further information, go to the ATEwebsite: http://www.nst.gov/ATE.

continued from page 11

NSF Beat: Opportunities at the National Science Foundation

By Sharon Cutler Ross

Scientists, engineers, and educators whofill rotational assignments at the NSF area key element in providing “the talent andresources that are critical to meeting theNSF’s mission.” The Foundation con-tracts with rotators principally throughtwo programs: Visiting Scientists, Engi-neers, and Educators (VSEE) and the In-tergovernmental Personnel Act (IPA).Briefly, a VSEE rotator takes a non-paidleave of absence from his or her homeinstitution and receives a salary from NSF.Appointments are for up to one year withthe possibility of another year. Under theIPA, a rotator is on loan from her or hishome institution for up to two years asintermittent, part-time, or full-time staff.Again, an extension is possible. Both pro-grams have a mechanism, IndependentResearch/Development, to arrange fortime during the work year at the homeinstitution for continuing work withgraduate students or other ongoingprojects.

Mathematicians and mathematics educa-tors are most likely to serve in the Direc-torate of Human Resources in areas suchas the Mathematical and Physical Sci-

ences, Undergraduate Education (DUE),and Elementary, Secondary, and InformalEducation (ESIS). But the lines betweenareas are frequently crossed and a rota-tor can expect to wear many hats. “It’sperhaps as close as you can come to afunctioning interdisciplinary depart-ment,” says Lee Zia, a Program Directorin DUE. Zia, who presently has a perma-nent position at the Foundation, hasserved as a rotator. He cites the opportu-nities to see the workings of the NSF fromthe inside, to see the national picture inscience and mathematics education, andto help shape projects as his reason forapplying to be a rotator. Spud Bradley,ESIS Section Head for Instructional Ma-terials Development, gives similar reasonsfor his work at the Foundation. “Seeingthings from a national perspective, work-ing with national leaders, and helping toshape programs” are important factorsfor Bradley.

Many of the same qualities that make forsuccess in academia or industry are alsouseful in working at the NSF—good com-munication skills, especially writing; in-terest in new things; ease in dealing with

people; willingness to speak one’s mind.The pace at the Foundation is much fasterthan at a university, a different bureau-cratic style prevails, and thus there areadditional qualities that are helpful inmaking for a good experience as a rota-tor—a flexible mindset, a willingness todeal with interruptions, the ability towork under tight time constraints, andan ego that can relinquish ownership ofprojects and writing.

Washington, DC, obviously has much tooffer as a place to live. As NSF staffers,rotators have additional resources forprofessional development such as Con-gressional hearings and workshops andtalks sponsored by the National ResearchCouncil as well as those sponsored by theFoundation itself. The collegial atmo-sphere at the Foundation often leadspeople from their original interest incoming to the NSF into exploring andworking in other areas. A tour at the NSFhas the potential for career renewal or re-direction as well as providing a venue forcontributing to mathematics and scienceeducation in the nation.

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The 14th General Assembly of the In-ternational Mathematical Union (IMU)was held on August 17-18, 2002, inShanghai, China. The American delega-tion consisted of Salah Baouendi (Dept.of Math, University of California at SanDiego), Jennifer Chayes (MicrosoftCorp., Seattle), David Eisenbud (Direc-tor, MSRI, University of California, Ber-keley), Yum-Tong Siu (Dept. of Math.,Harvard University), and Donald Saari,(Chair, Dept. of Math, University of Cali-fornia at Irvine). Much of the General As-sembly business was carried out by fourcommittees, and the US was representedon each of them: Chayes served on theFinance and Dues committee, Eisenbudon the nominating committee, Saari onthe resolution committee, and Siu on theteller and credentials committee.

Several resolutions were passed.

Resolution. The General Assembly recom-mends continuing the tradition of the 1994,1998, 2002 ICMs by holding an EmmyNoether lecture at the next two ICMs (2006and 2010) with the selection of the speak-ers to be made by an IMU appointed com-mittee.

Background: This is the first of the threeresolutions proposed by the US NCM andintroduced by the US delegation. For sev-eral meetings of the GA, the US delega-tion has consistently but unsuccessfullyproposed resolutions to ensure the selec-tion of more women and minorities asmajor ICM speakers.

Resolution. The General Assembly of theIMU expects the Executive Committee todevelop a proposed mechanism to involvemembers from the National Committeesfor Mathematics, not on the ExecutiveCommittee, to assist in the selection ofslates. This Proposal should be put forth tothe 2006 General Assembly.

Background: It was felt during the meet-ing that people beyond those on the Ex-ecutive Committee should be involved in

the selection of slates of names for thenext Executive Committee.

Resolution. The General Assembly recom-mends the guidelines for receiving Collo-quia support from the IMU be further de-veloped and made available on the IMUwebsite. These scarce funds should go pri-marily to supporting mathematicians fromdeveloping countries and high quality in-ternational conferences that take place indeveloping countries.

Background: The issue here was to makemore precise procedures for IMU spon-sored conferences.

Resolution. The General Assembly of theIMU endorses the “Best Practices” docu-ment of the Committee on Electronic In-formation and Communication, also en-dorsed by the IMU Executive Committeeat its April 13, 2002, meeting. In particu-lar the Assembly endorses the provisionsdesigned to ensure access by mathemati-cians of the developing world to currentmathematical literature: the posting of thearticles on personal homepages and serv-ers and the practice now beginning withseveral publishers of making journal ar-ticles in electronic form freely accessible fiveyears after they have been published, oreven sooner.

Background:This was the second resolu-tion proposed by the US delegation.

Resolution. Notwithstanding these timesof heightened tension and security con-cerns, we urge a continuation of scientificexchange and publication. The IMU op-poses efforts either by governments, orga-nizations, or individuals to restrict contactsand interactions in the world mathemati-cal community. Specifically we opposeholding individual mathematicians liablefor the actions of their governments. TheIMU endorses the principles expressed inthe International Council for Science(ICSU) ARTICLE 5 of STATUTES.

Background: This was the third resolu-

tion proposed by the US NCM and in-troduced by the US delegation. This reso-lution reflects a worry that travel andother restrictions which have been im-posed, or suggested that they will be im-posed, on the free flow of responsible sci-entists and mathematicians will have anadverse effect on mathematics both herein the US and abroad. As an illustration,this includes concern about a May, 2002,ad which was placed in an Europeannewspaper urging a boycott, it includesconcern about visa problems and otherpossible restrictions imposed on math-ematicians wishing to work with col-leagues in the US.

In addition, two relevant items of legis-lation passed involved a a 10% dues in-crease and the selection of Spain for thesite of the 2006 International Congressof Mathematicians.

Finally, new officers of the IMU wereelected during the general assembly .They are:

President: John Ball (UK)Vice Presidents: Jean-Michel Bismut(France) andMasaki Kashiwara (Japan)Secretary: Phillip Griffiths (USA)

The newly elected Executive Council con-sist of: Andrey Bolibruch (Russia), Mar-tin Grotschel (Germany), Zhi-Ming Ma(China), Ragni Piene (Norway) (the firstwoman ever elected to the ExecutiveCouncil), Madabusi Raghunathan (In-dia).

Report: 14th General Assembly of the International Mathematical Union

By Harry Waldman, based on a report by Donald G. Saari

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That’s Wrong!

While we make every effort to getthings right, it’s inevitable that every oncein a while FOCUS and MAA Online willcontain mistakes. When that happens, weare always willing to run corrections (seepage 9, for example), so please let usknow when we’ve messed up. The quick-est way is to email focus@maa.org.Thanks!

New Officers for NCTM

The National Council of Teachers ofMathematics has announced the resultsof the 2002 election. Cathy L. Seeley ofCedar Park, TX will be President-elect for2003-2004, and will serve as NCTM Presi-dent in 2004-2006. New members of theNCTM Board of Directors were alsoelected: Cynthia Bryant of Salem, MO, M.Kathleen Heid of State College, PA, MariMuri of Cromwell, CT, and Anthony A.Scott of Elmwood Park, IL. Their termwill start on April 2003 and they will servefor three years. Kathy Heid, who is cur-rently a member of the MAA Board ofGovernors, will move from one board tothe other with hardly a break.

Fewer Math and Science Ph.D.s

According to an article in the Chronicleof Higher Education (Monday, November11, 2002; online, for subscribers only, athttp://chronicle.com/daily/2002/11/2002111101n.htm), the total number ofPh.D’s awarded in the United States hasdeclined sharply over the last few years.In fact, the 2001 number is the same asthe 1993 number. The decrease is mostlydue to fewer Math, Science and Engineer-ing degrees (down 6.5% since 1998).Doctorates in other fields decreased byonly 0.9% during the same period.On theother hand, the Chronicle points out thatthe percentage of doctorates awarded towomen has increased. The survey wasproduced by the University of Chicago’sNational Opinion Research Center; checkout their website at http://www.norc.uchicago.edu for more infor-mation.

DIMACS Reconnect ’03 Conferences

DIMACS, the Center for Discrete Math-ematics and Theoretical Computer Sci-ence at Rutgers University, sponsors Re-connect Conferences every year. They areintended to expose faculty to current re-search topics that are relevant to the class-room, to create the opportunity to writeclassroom materials based on such top-ics, and to “reconnect faculty to the math-ematical sciences enterprise by exposingthem to new research directions andquestions.” There will be three confer-ences in 2003: “Some Current Problemsin Coding Theory” will be held at SalemState College, June 15 -21, 2003; “Central-ity in Graphs with Applications to theTheory of Location of Facilities” at theIllinois Institute of Technology, July 16-13, 2003; and “Internet Algorithms: Mod-eling the Web as a Graph, with Applica-tions to Information Gathering andSearch” at DIMACS/Rutgers University,August 10-16, 2003. Funding for lodgingand meals is available through a grantfrom NSF. Visit http://dimacs.rutgers.eduor email reconnect@dimacs.rutgers.edufor more information.

Improving College andUniversity Teaching

A recent report from the National Re-search Council focuses on Evaluating andImproving Undergraduate Teaching in Sci-ence, Technology, Engineering, and Math-ematics. It argues that while the qualityof the research of scientists and math-ematicians is carefully evaluated, “theevaluation of teaching in these fields hasbeen haphazard and less exacting.” Inaddition “professors who excel in theclassroom are sometimes given little rec-ognition on their own campuses, let alonein the wider academic community.” Fi-nally, “faculty members and administra-tors often believe that it is nearly impos-sible to objectively gauge the effectivenessof teaching skills.” The NRC report arguesthat the tools for correctly evaluatingteaching effectiveness and the impact ofcurricula do exist and should be used bycolleges and universities. The report rec-ommends that colleges and universities

help faculty improve their teaching. It alsosuggests that “university leaders or gov-erning boards should create endowmentsto recognize faculty members who, overtime, have made significant contributionsto teaching.” The full report is online athttp://www.nap.edu/catalog/10024.html.

Summer Mathematics Program forWomen at Carleton

The Department of Mathematics atCarleton College plans to offer again thisyear their month-long summer math-ematics program for eighteen math-ematically-talented first- and second-yearundergraduate women. By introducingthem to new and exciting areas of math-ematics that they would not see in a stan-dard undergraduate curriculum, and byhoning their skills in writing and speak-ing mathematics, the program leaders en-deavor to encourage these women to pur-sue advanced degrees in the mathemati-cal sciences, and, more importantly, toincrease each woman’s confidence in herown abilities and connect them all into asupportive network to carry themthrough their undergraduate and gradu-ate education.

At the heart of the program are two de-manding, intense courses under the su-pervision of female faculty who are ac-tive in research and renowned for theirteaching. Besides the coursework, par-ticipants take part in a variety of math-ematical events: panel discussions ongraduate schools and careers, colloquiaon a variety of topics, recreational prob-lem-solving, and visits from at least oneREU organizer and the organizer of theBudapest Semester. The mathematicalpart of the program is balanced with op-tional weekend events including canoe-ing, hiking, picnics, and tubing.

Please refer students who you feel wouldbenefit from this program to the web pageat http://www.mathcs.carleton.edu/smp orhave them contact Deanna Haunspergerat Dept. of Math/CS, Carleton College,Northfield, MN 55057 (e-mail:dhaunspe@mathcs.carleton.edu). Theapplication deadline is February 21, 2003.

Short Takes

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January 2003

Another Article on Heron’s Formula

I enjoyed reading Reuben Hersh’s “A Nifty Derivation of Heron’sArea Formula” in the November 2002 issue of FOCUS. Hersch’sderivation, like other clever results in elementary mathematics,is one which is often rediscovered. I last encountered it (essen-tially the same derivation, but with a different proof) in RogerC. Alperin’s “Heron’s Area Formula” in the March 1987 issue (v.18, no. 2) of The College Mathematics Journal, pp. 137–8.

Roger B. NelsenLewis & Clark College

Generalizing Heron’s Formula

There actually is a nice “formula for the volume of a tetrahe-dron as a function of the lengths of the six edges,” but it’s justnot symmetric in all six edges, only in each of two subsets ofthree edges (which is consistent with the last paragraph inHersh’s article). It’s given on p. 13 of Pólya’s Patterns of Plau-sible Inference (Volume II of Mathematics and Plausible Reason-ing, 1954). With edges a, b, and c meeting in the same vertexand edge e opposite to a, f opposite to b, and g opposite to c, theformula is

(In standard notation the formula doesn’t look as ugly as theabove, especially taking into account the partial symmetry.) Onp. 45 of Pólya’s Mathematical Discovery, Volume I, 1981, he givestwo special cases of the formula (a trirectangular tetrahedronand a tetrahedron with e = a, f = b, g = c) where the formulasimplifies, and each he refers to as an “analogue to Heron’s theo-rem”. (Jerry Alexanderson suggested this last reference.)

Peter RossSanta Clara University

Letters to the Editor

144 42 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 22

2 2 2 22

2 2 2 22

V a b c b c e c a f

a b g a b c e b c a f

c a b g

= + + − + −

+ − − + − − + −

− + −

( )( )

( ) ( ) ( )( )

Letters commenting on material published in FOCUS (or re-sponding to other letters) are always welcome. Send them byemail to fqgouvea@colby.edu or by snail mail to FernandoGouvêa, Department of Mathematics, Colby College, Waterville,ME 04901. Letters will be edited for publication

René Thom, one of the most important mathematicians ofthe century and winner of the Fields Medal, died on October25 in his home in Bures-sur-Yvette, France. He was 79 yearsold.

Born in Montbéliard, Thom attended the École NormaleSuperieure between 1943 and 1946 and then quickly establishedhimself as an important mathematician. His work on cobordismand characteristic classes led to his being awarded the FieldsMedal in 1958. In 1963 he was made a permanent professor atthe Institut des Hautes Études Scientifiques (IHES) and re-mained there until his retirement in 1988.

Thom made many contributions to mathematics, philosophyof mathematics, and mathematics education, but since the 1970shis name has been most closely attached to “CatastropheTheory”, an attempt to use the theory of singularities as a toolto understand discontinuous phenomena in the real world.Thom argued for the wide applicability of this theory. Unfortu-nately, the projected applications failed to arise or were not quiteconvincing. Nevertheless, catastrophe theory is considered a sig-nificant precursor of the more recent work in “chaos theory.”

Thom was a critic of what he felt was sometimes an excessivefascination with proof. He argued that sometimes imprecise andunrigorous work contained fundamental insights. On the otherhand, he once asserted that “it is unethical for a mathematicalresearcher to use a result the proof of which he does not ‘under-stand’ (except for the specific case where he wants to disprovethe result),” a very high standard indeed.

Several important newspapers (including the New York Times,the Washington Post, the Guardian, and Le Monde) publishedmajor obituaries of Thom, several of which can still be foundonline. A biography can be found at http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Thom.html.

In Memoriam:

René Thom, 1923–2002

Have You Moved?

The MAA makes it easy to change your address. Pleaseinform the MAA Service Center about your change ofaddress by using the electronic combined membershiplist at MAA Online (www.maa.org) or call (800) 331-1622, fax (301) 206-9789, email: maaservice@maa.org,or mail to the MAA, PO Box 90973, Washington, DC20090.

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The Clay Mathematics Institute (CMI)presented the 2002 Clay Research Awardsat its Annual Meeting, held on October30, 2002, at the American Academy ofArts & Sciences in Cambridge, Massachu-setts. The Awards, presented by CMIPresident Arthur Jaffe and DirectorsLandon Clay and Lavinia Clay, went toOded Schramm, for his work on theLoewner equation, and to ManindraAgrawal, for his work on primality test-ing. Each winner was made a Clay Insti-tute Prize Fellow, and received a bronzemodel of the CMI logo, which is an el-egant sculpture “Figureight KnotComplement vii/ CMI” by sculptorHelaman Ferguson.

Agrawal, who was born in May 1966, hassince 2001 been a full professor at theIndian Institute of Technology in Kanpur,India. He has been active over the past

ten years in the field of decision theory,complexity, and the relation between thegeometry of sets and their informationcontent. For some years he has been in-terested in finding a polynomial time al-gorithm to test whether a given numberis prime. Although random algorithmscan solve this problem with high certaintyin polynomial time it remained a long-standing challenge to find a method thatworks in every case. Agrawal solved thisproblem in August 2002, working withtwo undergraduate students: NeerajKayal and Nitin Saxena. Their proof es-tablishes the correctness of a conjecturemade in 1999 by Agrawal and SomenathBiswas. (See the November issue of FO-CUS for an expository account of theAgrawal-Kayal-Saxena result.)

Oded Schramm came to the United Statesin 1987 as a graduate student in topol-

2002 Clay Research Award Winners Announced

ogy under William Thurston. After this,his work evolved into the frontiers ofproblems in combinatorics and analysis.Schramm is an example of a person us-ing training in one field to elucidate an-other one. Currently, Schramm works asa Senior Researcher in the extraordinarymathematics group at Microsoft inRedmond, Washington. Schramm’sgroundbreaking study of the stochasticLoewner equation led to the solution ofmany problems, by him, by his collabo-rators, and by others. It led to majorprogress in probability theory, in thetheory of percolation and of randomwalks, as well as in related topics of con-formal field theory.

For more information on the Clay Re-search Award and the winners, visit theirsite at http://www.claymath.org.

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January 2003

Arnold Ross entered my life in the formof a personal letter that came to my homein the central valley of California in thewinter of 1969, when I was just a sopho-more in high school. The hand-typed let-ter, which was addressed personally to me,and signed personally by Professor Ross,offered a warm invitation to join the com-munity of mathematicians by attending aneight week summer program at the OhioState University in Columbus, Ohio. Mydecision to accept that invitation provedto be a defining moment in my life. It wasnot only the beginning of a life devotedto mathematics. It was also the begin-nings of a friendship with Arnold thatwould continue until his recent death onSeptember 25, 2002 at the age of 96.

Over almost five decades, countless youngpeople with early promise for creative re-search in mathematics and science re-ceived such invitations from Arnold tojoin his program. Those of us who ac-cepted were treated to an unforgettableexperience of mathematical exploration.The program was built around a delight-ful collection of handwritten and mim-eographed problem sets designed byArnold himself. Through our work onthese problems we honed our powers ofindependent exploration and learned theart of skeptical conjecture, proof and dis-proof. Professor Ross’s famous exhorta-tion “to think deeply of simple things” hasbeen deeply etched in the psyches of allwho passed through his program. We allbenefited from his gentle reminders thatrich concrete experience precedes signifi-cant discovery, that “language is ourfriend,” and that good abstractionamounts to condensation of diverse ex-perience united by a few fundamentalideas. Arnold often said that “no oneleaves the program unchanged.” Indeed,at the end of the eight weeks we werementally exhausted and, as I can say frompersonal experience, many of us sworenever to return. However, once back inthe traditional school environment, theneed for more intellectual challenge be-came intense and we felt a yearning to goback.

Another personal letter from Arnold ar-rived in January of the following year in-viting us back for more advanced inves-tigations and asking us to “help” the newfirst-year students in the program.Arnold’s invitation was irresistible. Hehad a remarkable way of making each ofus feel special and he never failed to re-mind us of our responsibility to the restof the community. Altogether, I joinedArnold’s program for a total of five sum-mers, three times as a student and twiceas a counselor. Many of my peers wereinvolved even longer. Together we inter-acted not just with Professor Ross, butalso with his colleagues, including suchmemorable personalities as Kurt Mahler,Hans Zassenhaus, and Ivo Thomas. TheOSU mathematics department, whichArnold chaired for many years, welcomedus warmly into graduate seminars offeredin the summertime. I am especially grate-ful for an invitation from Professor JohnHsia to join his seminar on quadraticforms one summer. Through these inter-actions, the “children of the Ross Pro-gram” came to see research mathematicsas the work of a community of individu-als and we came to see ourselves as mem-bers of that community.

It has been said that Arnold Ross influ-enced American mathematics of the 20thcentury more than any other single indi-vidual. Such statements can be neitherproved nor disproved, but there is no

doubt that Arnold’s influence has beenprofound. A steady stream of outstand-ing scholars has flowed out of Arnold’sprogram since the very beginning. Manyof these individuals now hold researchpositions at many of the nation’s mostprestigious institutions—not just inmathematics, but also in a variety of fieldsranging from astrophysics to economics.

It is significant, I think, that Arnold madehis contribution to American mathemat-ics not through his own research contri-butions, but through the development ofhigh quality programs of mathematicseducation. Indeed, Arnold’s devotion tomathematics education ran much deeperthan the creation of the Ross Program forwhich he is best known. Arnold repeat-edly emphasized that the principles of hisprogram were relevant not just for theeducation of highly talented youngpeople. The basic principles that Arnoldrepeated so often and so consistently—that knowledge comes of experience, thatlanguage is a basic tool of mathematics,and that “the opposite of boredom is notfun,” are applicable to a broad spectrumof students. His insistence on this pointwas just one of many ways that his deeprespect for the potential of learners at alllevels manifested itself. Arnold himselfran a very successful program in the 60’sfor minority students in Columbus, Ohiothat he provocatively named HorizonsUnlimited. Moreover, his work deeply in-fluenced many others in mathematicseducation who have developed their ownprograms for young people from a widerange of backgrounds.

Arnold Ross was a deeply compassionateman whose energy and optimism seemedinexhaustible. He ran his summer pro-gram every summer from 1957 through2000, when he finally retired from theprogram at the age of 94. Until the veryend of his life, Arnold bore a mischievousgleam in the eye that reflected his untir-ing efforts to enrich the talents of youngpeople and to introduce them to the joysof a life of inquisitive exploration.

Glenn Stevens is Professor of Mathematicsat Boston University and is the director ofthe PROMYS program (http://www.promys.org), a program for highschool students inspired by the Ross Pro-gram.

Memories of Arnold Ross

By Glenn Stevens

Arnold Ross

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When I first accepted a position inMontclair State University’s Departmentof Mathematical Sciences, people asked,“Why are you working in a“mathematicsdepartment when your degree is ineducation?” My response then, whichremains true today, was simple: in orderto be a mathematics educator, one mustmaintain a solid footing in the classroomand in one’s area of education research.I was all too familiar with the dangers oflosing this footing. One foot out of theclassroom generates research that fails toserve education’s stakeholders (amongthem teachers, students, principals, ad-ministrators or parents). And a foot outof education research fails to spread ideasabout how to enhance the teaching andlearning of mathematics.

I have known since high school that Iwanted to be a mathematics educator(although I didn’t know at the time thatsuch a profession existed). I tried tobalance both disciplines through myeducation (a Masters in mathematics anda Doctorate in mathematics education).When I com-pleted my studies, Idiscovered that I qualified for positionsin both education and mathematicsdepartments. It was not an easy choice: Iwanted to teach mathematics but knewthat some mathematicians wereprejudiced against mathematicseducators. I worried about being able todo genuine research in mathematicseducation and about how my researchwould be viewed and whether it wouldbe valued. It has taken some work, but Ifeel I’ve found a good place for myself.Since others are in my position, I wantedto share some of the strategies I’ve hadthat have helped me maintain thedelicate footing required to be acontented educator in a department ofmathematics.

Use your classrooms as a forum for research

With opportunities to teach eithermathematics or mathematics educationcourses, mathematics educators have arich forum for doing research, completewith students and their genuineobstacles. I have successfully used this

strategy to generate papers on how toenhance the teaching of certain calculustopics, how to tweak certain instructionalformats to improve problem solving ingeometry amongst prospective teachers,and how to address students’ mis-understandings of functions in pre-calculus. Remember to get your students’written permission before you collectdata from them and be careful in writingup results in which you are bothresearcher and teacher.

Work with mathematicians and educators

I’ve had to work hard to achieve this, butthe payoff has been enormous. I haveserved on committees and doneprofessional conference work withprofessors in our university’s educationdepartment. I have also collaborated onresearch projects with mathematicians inmy department. As a result, I’ve metcolleagues who are not only valuableresources, but also good friends. Ofcourse, you do not have to stay withinyour university. I am collaborating on abook for middle school teachers, andhave applied for a grant, with twocolleagues from my graduate school days(in education) and one new colleague (inmathematics) who are from threedifferent universities.

Seek out the mathematics community’soutreach to education efforts

It is not unusual these days to see math-ematics projects dedicated to improvingeducation. One of my more rewardingexperiences was with the MAA’s ProjectNExT. One of this project’s manyobjectives is the initiation of youngfaculty into mathematics academic life.Not only did NExT provide me withforums for sharing work I had done inthe classroom, but it also exposed me tonumerous resources for enhancing myteaching, giving presentations, applyingfor grants, and maintaining balancebetween work and personal life. It is stillreassuring to find fellow NexTers (andtheir numerously colored dots) atmeetings of the MAA or AMS and toknow that I can use the NExT listserv to

share ideas and ask for advice on mattersof teaching and research.

Go to conferences in both disciplines

This is a tough one, mainly for financialreasons. Balance is the key. I take intoaccount where the meetings are and towhat extent what I have to offer matchesthe topics for paper session. Sharingrooms with friends will help you andyour department pay for this effort.

Talk about your work

Recently, I was talking to a statistician inmy department who described her initialskepticism and wariness at qualitativeresearch. (Most of my research inmathematics education is qualitative.)She told me that by hearing me (andothers) talk about our work and itstheoretical underpinnings, she has cometo value the role that this methodologycan play in generating research andenhancing statistical methods. I’ve alsohad colleagues tell me that they didn’tknow (until they met me and saw mywork) what research in mathematicseducation was like. They confessed toconceptualizing math-ematics educationas just mathematics teaching. They nowrealize it is a social science complete witha wide variety of theoretical frameworksand methodologies that can be used togenerate new education theories orinform practice at a wide variety of levels.So talk about your work, not just indepartmental seminars, but also at lunchor in the departmental lounge.

There is no choice that works foreveryone. Some mathematics educatorswill end up in departments of education.These strategies have helped make theoption of working in a mathematicsdepartment work well for me.

Eileen Fernandez is in her fourth year asan assistant professor of mathematics andmathematics education at Montclair StateUniversity in Upper Montclair, NJ.

Being a Mathematics Educator in a Department of MathematicsBy Eileen Fernandez

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January 2003

The MAA Online book review column,Read This!, continues to actively reviewbooks that are of interest to a wideaudience of mathematicians. Betweenthe Briefly Noted section and the full-length reviews, we have covered morethan 300 books, with many more tocome. All those reviews are still availableon MAA Online.

What have we reviewed recently? Here’sa partial list:

Chance, Luck and StatisticsBy Horace C. Levinson.Review by Charles Ashbacher.

The Math LifeA film by Wendy Conquest, Bob Drake,and Dan Rockmore.Review by Henry Cohn.

Fractals, Graphics, andMathematics Education

By M. L. Frame and B. B. Mandelbrot.Review by George Ashline.

Proofs Without Words II,By Roger B. Nelsen.Review by Robert C. Stolz.

The Education of a MathematicianBy Philip J. Davis.Review by P. N. Ruane.

Mathematical Olympiads: Problems andSolutions From Around the World,1999-2000Edited by Titu Andreescu andZuming Feng.Review by Mihaela Poplicher.

How to Ace the Rest of CalculusBy Colin Adams, Abigail Thompson,and Joel Hass.Review by Kevin Anderson.

All the Mathematics You Missed [ButNeed to Know for Graduate School],By Thomas A. Garrity.Review by Mariah E. Hamel.

Read This!

By Fernando Q. Gouvéa

The theme for this year’s mathematicsAwareness Week has just been an-nounced. It will be Mathematics and Art.FOCUS will have more detailed informa-tion in a future issue; for now, visit http://www.d.umn.edu/~jgallian/art.html foressays, links, references, possible speak-ers, and the MAM2003 poster.

Mathematics

Awareness Week

2003

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EMPLOYMENT OPPORTUNITIES

CALIFORNIA

CAL STATE POLYTECH. UNIV.,POMONADepartment of MathematicsFour tenure-track positionsMathematics Education (Two positions:Assistant Professor and Associate/Assistant Professor). Teachundergraduate courses in matheducation, collaborate with others oncampus involved in math education.Opportunity to teach lower and upperdivision math courses, provide in-serviceprograms for local schools, help todevelop master’s in mathteaching, advisestudents seeking secondary teachingcredential. Minimum qualifications:Doctorate in math education withmaster’s degree in mathematics (orequivalent) or Ph.D. in mathematics,with strong background in matheducation. ABD’s will be considered.Must know about trends in matheducation, uses of technology in matheducation. Preference to those able tosupervise student teaching. Mathematics(Two positions: Asst Prof ) Teachundergraduate, graduate, and servicecourses in math, participate incurriculum development, and adviseundergraduate and graduate students.Preference to those with expertise in oneor more of: algebra, control theory,differential equations, estimation theory,geometry, number theory, stochasticdifferential equations, topology.Minimum qualifications: Ph.D. inMathematics or Statistics. Completionof terminal degree by 9/03. All positions:Expected to serve on department anduniversity committees, engage inscholarly activities. Required: Evidenceof, or potential for, teaching excellence,directing master’s theses, engaging inscholarly activities, working with diversestudent body. Salary dependent onqualifications. Initial review ofapplications 1/8/03. Review will continueuntil position is filled or closed. Submitapplication form indicating position area(forms are available at http://www.csupomona.edu/~academic/

faculty/open_faculty_positions.htm),curriculum vitae, transcripts, andminimum of three reference letters toFaculty Search Committee, MathematicsDepartment., CSPU Pomona, 3801 W.Temple Ave., Pomona, CA 91768-4007;lmborchert@csupomona.edu; 909-869-4008; Fax: 909-869-4904; http://www.csupomona.edu/~math. AA/EEO.

GEORGIAGEORGIAGEORGIAGEORGIAGEORGIA

GEORGIA COLLEGE AND STATEUNIVERSITYDepartment Chair, Department ofMathematics and Computer ScienceApplications are invited for DepartmentChair. Department of Mathematics andComputer Science. At least five years ofteaching experience is required andadministrative experience is desirable.Applicants must have a doctorate inmathematics, computer science orrelated field. The department offersundergraduate degrees in mathematicsand computer science and minors inmathematics, computer science, actuarialscience and quantitative analysis and hasexcellent teaching and laboratoryfacilities. There are twenty-one facultypositions in the department distributedas follows: five computer science, twomathematics education, thirteenmatheamtics, and one chair. As theUniversity System of Georgia’sdesignated public liberal arts universityand a member of the Council of PublicLiberal Arts Colleges (COPLAC),GC&SU is committed to combining theeducational experiences typical ofesteemed private liberal arts colleges withthe affordability of public highereducation. GC&SU is an EqualOpportunity/Affirmative ActionEmployer. Review of applications willbegin December 6, 2002 and continueuntil the position is filled. For additionalinformation and the applicationprocedure, go to: http://www.gcsu.edu/facultyjobs.

FLORIDAFLORIDAFLORIDAFLORIDAFLORIDA

BROWARD COMMUNITY COLLEGEBroward Community College (BCC) isa large, three-campus, three-center urbaninstitution serving approximately 50,000credit and non-credit students inSoutheast Florida. BCC is the principalprovider of undergraduate highereducation for the residents of BrowardCounty. Through a wide variety ofdegree and certificate programs andcontinuing education courses, the collegeattracts a great diversity of students. Thecollege is also a source of culturalenrichment; a resource for communitydevelopment, business, and industry;and an avenue for continued skillupgrading and enhancement andretraining.A completed employment application,copies of graduate transcripts & letterof intent must be received by January31, 2003 to be considered foremployment.

Mathematics Faculty, FOUR PositionsAvailable Master’s degree with 18graduate semester hours in Mathematicsrequired. Three positions at CentralC a m p u s ( # 2 4 7 ) :Dedication and enthusiasm for teachinga must. Applicant should be willing toteach the entire span of Math coursesfrom Pre-Algebra to Calculus III. Ap-plicant will contribute time and effort toacademic endeavors at the department,campus and college levels. Willing andable to incorporate technology in theclassroom and must be open to newteaching strategies to enhance studentsuccess.

One position at North Campus (#117):Experience teaching both collegepreparatory and college levelMathematics courses with anunderstanding of the needs and concernsof community college students. Musthave experience using appropriatetechnology and must be willing to workwith varying instructional modalities.

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January 2003

Upon selection, official transcripts willbe required.Salary ranges (based on degree & yearsof experience) are: Master’s (18 gradsemester hrs in discipline), $31,963-$41,552; Doctorate (24 grad semester hrsin discipline), $37,716- $47,305.

Applications available: http//:www.broward.edu/jobs/bccjobs.jsp or800-682-3646 or 954-201-7338. Submitapplication packages to: BrowardCommunity College/ HR, 225 E. Las OlasBlvd., Ft. Lauderdale, FL 33301. BCC iscommitted to the principle of diversity.We are interested in receiving ap-plications from a broad spectrum ofpeople including women, minorities,veterans, & disabled individuals.

UNIVERSITY OF SOUTH FLORIDA

The Department has two non-tenure-earning, nine-month (teaching)Instructorship positions available on ourmain (Tampa) campus. These positionsare annually renewable. Minimumqualifications include Ph.D. (orequivalent) in Mathematics or a closely-related field earned by August 25, 2003,and documented interest and ability inundergraduate teaching. Applicants withthree years of experience teachingundergraduate students are preferred.Further details of these positions include:

Equivalent of 12-hour teachingload.Course-release time may be earnedfor course supervision and/or coursedevelopment. Instructors will beprimarily teaching general-educationmathematics courses to Freshmen andSophomores.

By February 15, 2003, send applicationmaterials (including AMS Cover Sheetand curriculum vitae) and have threeletters of reference, at least two of whichaddress teaching, sent to:

Instructor Search CommitteeDepartment of MathematicsUniversity of South Florida4202 East Fowler Avenue, PHY114Tampa, FL 33620-5700

Inquiries about these positions may besent to mathsearch@math.usf.edu.Note: Members of the Search Committeewill be attending the joint meetings in

January in Baltimore. The University ofSouth Florida is an affirmative action,equal opportunity, equal accessemployer. Applications from women andminorities are encouraged. According toFlorida law, applications and meetingsregarding them are open to the public.For disability accommodations, pleasecontact the department at (813) 974-2643 at least five days in advance.

MASSACHUSETTS

WILLIAMS COLLEGEThe Williams College Department ofMathematics and Statistics invitesapplications for two positions inmathematics and one position instatistics, beginning fall 2003, all at therank of assistant professor (inexceptional cases, more advancedappointments may be considered). Weare seeking highly qualified candidateswho have demonstrated excellence inteaching and research, and who will havea Ph.D. by the time of appointment.

Williams College is a private, residential,highly selective liberal arts college withan undergraduate enrollment ofapproximately 2,000 students. Theteaching load is two courses per 12-weeksemester and a winter term course everyother January. In addition to excellencein teaching, an active and successfulresearch program is expected.

To apply, please send a vita and have threeletters of recommendation on teachingand research sent to the HiringCommittee, Department of Mathematicsand Statistics, Williams College,Williamstown, MA 01267. Teaching andresearch statements are also welcome.Evaluations of applications will begin onor after November 25 and will continueuntil the positions are filled. WilliamsCollege is dedicated to providingawelcoming intellectual environment forall of its faculty, staff and students; as anEEO/AA employer, Williams especiallyencouragesapplications from womenand underrepresented minorities. Formoreinformation on the Department ofMathematics and Statistics, visit http://www.williams.edu/Mathematics.

MICHIGANMICHIGANMICHIGANMICHIGANMICHIGAN

GRAND VALLEY STATE UNIVERSITYGrand Valley State University, inAllendale, Michigan, is acceptingapplications for the position ofPostdoctoral Teaching Fellow, withemployment to begin in August 2003.Candidates must have a doctorate in theMathematical Sciences or MathematicsEducation by August 2003 (completednot earlier than May 2000).

The fellowship is a two-year visitingposition with a renewal option for a thirdyear. This position is designed to offercandidates the opportunity to developbroad instructional and scholarlypotential in a department committed toexcellence in the teaching and learningof undergraduate mathematics. Fellowswill have the opportunity to teachundergraduate courses and work in closementoring relationships withdepartment faculty. In addition tostructured mentoring centered oninstruction, fellows will explore avenuesfor scholarship through interactions withcurrent faculty, and present a monthlyseminar in their area of professionalexpertise.

For more information, includingresponsibilities of the position, andimportant details on how to apply, seeour position description at http://www.gvsu.edu/math/jobs.html. Reviewof completed applications will beginFebruary 17, 2003.

NORTHERN MICHIGANUNIVERSITYThe Department of Mathematics andComputer Science invites applicationsfor two tenure-track positions inmathematics at the rank of assistantprofessor beginning with the 2003-2004academic year. Successful candidatesmust have a Ph.D. in an area of themathematical sciences by August, 2003.For more information, visit our web sitea t h t t p : / / m a t h . n mu . e d u / c a re e r /position.html. EEO/AA

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MONTANA

ROCKY MOUNTAIN COLLEGEThe Department of Mathematics atRocky Mountain College invitesapplications for a tenure-track positionbeginning fall, 2003. The successfulcandidate will need a strong backgroundin analysis, and demonstrate obviousenthusiasm and talent for undergraduateteaching both at the introductory andupper levels. Classes taught will include,but are not limited to, differentialequations, vector analysis, advancedcalculus, complex variables andtopology. The candidate will also beexpected to teach part of the traditionalfour-semester calculus sequence. Thesuccessful candidate must be committedto undergraduate teaching with ademonstrated ability to teach effectivelyto students of varied interests andbackgrounds. A Ph.D. or ABD inmathematics is required, and thesuccessful candidate will play a large rolein shaping the future direction of theprogram. In their applications,applicants should address their interestsin teaching in an undergraduate, liberal-arts environment that emphasizes closefaculty-student interaction.Applications will be screened beginningFebruary 15, 2003. Send letter ofapplication, statement of teachingphilosophy, curriculum vitae, and threeletters of recommendation which addressthe candidates interest in andcommitment to excellent teaching, to:Bob Robertson, Director of Personnel,Rocky Mountain College, 1511 PolyDrive, Billings, MT 59102. E-mailinquiries to wiensd@rocky.edu. AA/EOE

NEW JERSEY

RUTGERS UNIVERSITYDIMACS Reconnect ’03 Conferences:Current Research Relevant to theClassroomThe Reconnect ’03 Conferencessponsored by DIMACS (the Center forDiscrete Mathematics and TheoreticalComputer Science) are geared towardsexposing faculty teaching under-graduates to current research topicsrelevant to the classroom, involving them

in writing materials useful in theclassroom and reconnecting them to themathematical sciences enterprise byexposing them to new research directionsand questions. The three programs:“Some Current Problems in CodingTheory” at Salem State College, June 1521, 2003; “Centrality in Graphs withApplications to the Theory of Locationof Facilities” at Illinois Institute ofTechnology, July 16 13, 2003; “InternetAlgorithms: Modeling the Web as aGraph, with Applications to InformationGathering and Search” at DIMACS /Rutgers University, August 10 16, 2003.Applicants accepted to participate willreceive lodging and meals through NSFfunding. For more information or anapplication form, visit our web site athttp://dimacs.rutgers.edu/reconnect/.Or, contact the Reconnect ProgramCoordinator, atreconnect@dimacs.rutgers.edu or (732)445-5928.

NEW YORK

PACE UNIVERSITYDyson College of Arts and SciencesDepartment of MathematicsThe Department of Mathematics, DysonCollege of Arts and Sciences, PaceUniversity invites applications for a full-time, tenure-track position at theAssistant Professor level to beginSeptember 2003. Applicants should havea Doctorate degree in Mathematics,Applied Mathematics, orStatistics. All fields of research will beconsidered. Responsibilities includeteaching undergraduate courses inmathematics, developing curriculum,maintaining an active research programand sustaining scholarly activities. Thesuccessful candidate must have a strongcommitment to undergraduateeducation, and present evidence ofexcellence in teaching and research. Theposition will be located at campuses inboth New York City and WestchesterCounty, a northern suburb.

Founded in 1906, Pace University is aprivate comprehensive university thatoffers more than 300 majors and 3,000courses within six undergraduate and

graduate colleges/schools. Its diversestudent population is comprised of 9,000undergraduates and 5,000 graduatestudents. Located in New York City andWestchester County, Pace draws itsstrength from being a unified institutionthat offers students a choice of severalcampus locations, each with its owndistinctive atmosphere. For moreinformation, visit our websites at: http://webpage.pace.edu/mathny/ and http://www.pace .edu/dyson/academics/mathwest/

Candidates for the position shouldsubmit a letter of application, acurriculum vitae, an AMS StandardCover Sheet, a teaching statement,research statement, and three letters ofrecommendation sent separately to: Prof.G. Taiani, Chair, Search Committee,Dept. of Mathematics, Pace University,1 Pace Plaza, New York, NY 10038.Review of applicants began November30th and will continue until the positionis filled.

Pace University is an Equal Employmentand Affirmative Action Employer, M/F/H/V, committed to ensuring a diverselearning and working environment.Women and minorities are encouragedto apply.

NORTH CAROLINA

GUILFORD COLLEGEPosition Description – Mathematics––For Fall, 2003Guilford College, a private liberal artscollege affiliated with the Society ofFriends, invites applications for a tenure-track position in mathematics beginningin August of 2003. Completion orimminent completion of a Ph.D. inmathematics is required. Interest in andability to teach creatively in lower-levelcourses such as pre-calculus, elementarystatistics, mathematics for teachers, andmathematics for the liberal arts throughupper-level courses for mathematicsmajors is required. The MathematicsDepartment teaches courses that servicescience, business, education, andcomputer studies students among others,and all candidates must be committed to

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working effectively with the broad rangeof student interests and abilities thisencompasses. Preference will be given tocandidates with interests in computerstudies, interdisciplinary teaching, anddirecting independent studies of varioussorts (including undergraduateresearch). Responsibilities includeteaching a minimum of 12 credit hoursper semester, continuing scholarlyactivity (broadly interpreted), advisingstudents, college committee service, andteaching as needed in the eveningcontinuing education program.

A complete application includes a letterof interest, a personal statement onteaching, a vita, graduate transcripts, andthree letters of recommendation (at leasttwo of which explicitly support teachingexcellence or its potential). All materialsshould be sent to Search Committee,Department of Mathematics, GuilfordCollege, 5800 W. Friendly Ave.,Greensboro, NC 27410. Applicationmaterials should arrive by February 21,2003 for first consideration.

Guilford College seeks applications frompeople representative of diversity basedon age, race, gender, sexual orientation,disabilities, ethnicity, religion, nationalorigin, career and life experiences, socio-economic background, geographic roots,as well as members of the Society ofFriends. EOE/AA

PENNSYLVANIA

CALIFORNIA UNIVERSITY OFPENNSYLVANIAMathematics Education: Department ofMathematics and Computer Science.Duties will include teaching introductoryand upper level undergraduate andgraduate courses in mathematics and anapplications-based elementary educationmathematics sequence (MAT 120/130);seeking external funding to supportresearch interests, facility upgrades, and/or outreach programs; serving as aliaison with the College of Education toensure course compatibility of contentand teaching methodology withelementary and secondary education

certification programs; and developingcollaborative partnerships witheducational and/or commercial entities.An earned doctorate in mathematicseducation is required; a master’s degreein mathematics, teaching experience atthe elementary or secondary level, andexperience with university programs thatprovide collaborative college credit at thehigh school level is preferred. Teachingassignments may involve travel toregional sites and/or distance learningformats. See our websiteat’www.cup.edu/employment forapplication information. Cal U is AA/EEO.

TENNESSEETENNESSEETENNESSEETENNESSEETENNESSEE

TENNESSEE TECHNOLOGICALUNIVERSITYDepartment of MathematicsOne tenure-track instructor positionstarting 8/03.

Minimum master’s in mathematicsrequired. College mathematics teachingexperience preferred. Evidence ofexcellent teaching required.

Duties: Teaching lower division courses,advising, outreach, scholarly activityand/or service.

Initial screening January 22, 2003, openuntil filled.

For complete job description andapplication procedure, seewww.math.tntech.edu or contact

Brian O’ConnorSearch Committee ChairpersonBox 5054 TTUCookeville, TN 38505

AA/EEO

TEXAS

TEXAS LUTHERAN UNIVERSITYDepartment of Mathematics invitesapplications for a tenure-track assistantprofessorship beginning August 2003.

Requirements include Ph.D. inmathematics by appointment date,ability to teach a wide range ofintroductory and advancedundergraduate courses, and acommitment to establish a researchprogram for undergraduate students.Submit letter of application, cv,statement of teaching philosophy, andfive references (names, addressesincluding email, telephone) to: DeanJohn T. Sieben - College of NaturalScience and Mathematics, TexasLutheran University, 1000 W. Court St.,Seguin, TX 78155; fax (830) 372-6095,phone (830) 372-6007, e-mailjsieben@tlu.edu. Review of applicationswill begin January 15, 2003 and continueuntil the position is filled. TexasLutheran University is an equalopportunity employer and encourageswomen and minorities to apply. Webpage: www.tlu.edu.

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