ContinuNewsletter of the Department of Mathematics at the University of Michigan Summer 2001

UMOn July 31, 2001, Al Taylor stepped down as department Chair after six successful years in the postion. Trevor Wooley has

been selected as the new Chair. Due to Trevor’s scheduled sabbatical leave for the 2001-02 academic year, AlejandroUribe, the current Associate Chair for Academic Affairs, will serve as the interim chair for the coming year. You should

hear about Alejandro’s experience as Chair in the next ContinuUM. In the two “Notes from the Chair” columns, Al reflectson his chairmanship, and Trevor lays some plans for the future of the department.

The Future of theMathematics Department

The Mathematics Department atMichigan has experienced extensivechange in virtually all aspects of its mis-sion over the past several years, and weare fortunate indeed that, through AlTaylor’s commitment and balanced lead-ership through six of the last seven years,almost all of these developments havebeen for the good. As Al begins somewell-deserved relief from administrativeduties, it seems an opportune moment tohighlight some of the developments andchallenges that we expect to see in the fu-ture. Fortunately for me, the “future” doesnot begin until July of 2002! The Depart-

ment is very fortunate that Alejandro Uribe has agreed to serve asChair during my long-awaited year of leave next year.

Competing with Peer Departments

One of my regular complaints in recent years has been that theresources provided to us by the College barely enable us to main-tain our status within the Big Ten, let alone compete with the topten departments. The good news is that this situation is changingfor the better. In the final years of Al’s term as Chair, increased re-sources were forthcoming from LS&A. In addition, we have justsecured a significant new package of resources that, starting nextyear, will incrementally address issues involving salary and teach-ing so crucial in a competitive hiring environment. Taken together,these resources will allow us to concentrate our competitive en-ergy on the top ten departments, and offer prospects of enteringthe elite five departments nationally.

As one contemplates the difficulties of competing with thevery strongest departments, one is struck by the scale of financialresources available to highly endowed private schools. However,the size and quality of the department at Michigan provides a criti-cal mass of excellence that offers an extraordinarily stimulatingenvironment unavailable to smaller departments, no matter howwell-endowed. What we seek to do in the future is to exploit this

Reflections on SixYears as Chair

This is a piece I’ve looked forward towriting for some seven years now, my fi-nal one for the “Notes from the Chair”column. At the end of July, I’ll have fin-ished my two terms as Chair and am ex-cited about returning to my normal careerof teaching and research. AlejandroUribe will assume the chairmanship nextyear, filling in for Trevor Wooley, whohas agreed to serve a 3-year term as Chair,the 2002-2005 academic years, after hereturns from a year’s leave in Cambridgeand Bonn.

I don’t believe the Dean could havemade any better choice of Chairs to keepthe department on its upward trend. My opinion is confirmed bythe selection of three new Associate Chairs to join the leadershipteam, Tony Bloch for graduate affairs, Dick Canary for educa-tion, and Mel Hochster for faculty appointments. Other majorleadership jobs are being filled by Toby Stafford (Chair of theFaculty Recruitment Committee), John Stembridge (DoctoralChair), and Ralf Spatzier (Undergraduate Chair). This leadershipteam is remarkable for its youth and vitality!

While we have for decades been a democratic department withimportant decisions being made on a near consensus basis, thenew team reflects the fact that administrative work and responsi-bility must be shared to a much greater degree than ever before.The youth of the team reflects the fact that the department has im-proved to one in which almost every faculty member has an activeresearch program, most of which are increased in impact by re-ceiving highly competitive external research funding. Faculty,especially young faculty, can’t afford to de-emphasize their re-search work for several years to spend large amounts of time onthe important administrative work that is necessary to keep a largedepartment functioning smoothly. Therefore, the new Chairs haveobtained some incremental resources to enable active young fac-ulty to take on these tasks while maintaining their research

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Bioinformatics:Math’s Role in the Life Sciences Initiative

Bioinformatics sits at the intersection ofmolecular biology and computer science,two disciplines which have undergonerevolutionary scientific-technological de-velopment during the past few decades. Po-sitioned on the interface of two rapidlydeveloping intellectual arenas, bio-informatics is experiencing intensive devel-opment as well as explosive growth ininterest and demand.

Improving techniques in molecular biol-ogy yield extensive information about themolecular components of living cells. Thisinformation includes determination of thegenetic make-up (the DNA) of organismsand provides precise information about pro-teins that are active in cells. This informa-tion about DNA and proteins comes asexact information about molecular se-quences, and also as information aboutthree-dimensional structure which is veryimportant in determining the way in whichthe DNA or protein functions. Technologi-cal advances have made molecular technol-ogy commonly accessible. The result hasbeen a flood of information about the mo-lecular composition of DNA and proteinsfrom a wide variety of organisms. Articlesin the popular press about genome sequenc-ing have given some indication of the revo-lution in available information, but givelittle indication of the magnitude of dataavailable as biologists worldwide produce aconstant flow of information about the mo-lecular structure of the genes and proteinsthat control living cells.

As valuable and as plentiful as this in-formation is, it only provides a “parts cata-log” for a variety of organisms withoutexplaining how these parts work or fit to-gether. Little is known about the integratedsystem—what makes a living cell, or how acell will respond to a novel environment ora specific change in its genome. DNA givesthe blueprint for the design of various pro-teins, but what controls the processwhereby proteins are expressed from this

blueprint under different conditions? Giventhe DNA blueprint for a protein, how dowe predict the three-dimensional shape thatthis protein will eventually assume, ashape which largely governs its function inthe cell? This growing bank of molecularinformation leaves us well short of under-standing the principles that govern the in-teractive biological system.

A key goal of bioinformatics is to con-struct the integrated behavior of the intactorganism in relation to its underlying mo-lecular determinants (the genome). Mo-lecular biology takes the first step towardssuch an understanding with the measure-ment of molecular features of a living cell.The next few steps lie more on theinformatics side, steps that may be mostreadily made by mathematicians, computerscientists and statisticians. These includemining of the molecular data to filter andselect out interesting features. Then math-ematical modeling of how the cell/organ-ism, as an integrated system, is acting onthe molecular information identified in theprevious step as lying in the genome and inprotein structure. Computer science is pro-viding us with more and more powerfultools to do this analysis— hardware archi-tectures and efficient algorithms for sym-bolic analysis, scientific computation,graphical interpretation and data manage-ment.

Michigan is one of a few institutionsthat are playing a leadership role inbioinformatics. With a truly interdiscipli-nary effort rooted in the Medical Schoolbut including faculty in the Departments ofMathematics, Biology, Chemistry and theColleges of Pharmacy, Engineering andPublic Health, we are launching a graduatedegree in bioinformatics and expanding thenumber of bioinformatics faculty positionsby ten to fifteen campus-wide. More aboutthe newly formed program can be found atits web site www.bioinformatics.med.umich.edu.

-Professor Phil Hanlon

ProfessorPhil Hanlon

Collegiate Chair andLSA Associate Dean

As described in the article to the left,Phil Hanlon is spearheading Math’s par-ticipation in the Bioinformatics portion ofUM’s life sciences initiative. In additionto these activities, Hanlon has beennamed the DonaldJ. Lewis CollegiateProfessor of Math-ematics, 2000-05.He has also beenselected to be theAssociate Dean ofFinance and Plan-ning for the Collegeof Literature, Sci-ence and the Arts, a position he assumedin the winter of 2001.

Hanlon completed his undergraduatedegree at Dartmouth and received hisPh.D. from the California Institute ofTechnology in 1981. He taught at Massa-chusetts Institute of Technology and Cali-fornia Institute of Technology beforejoining UM in 1986. He became a pro-fessor in 1990. Hanlon is an extremelywell regarded mathematician, and has re-ceived recognition over the years to in-clude the NSF Presidential YoungInvestigator Award, a Sloan Fellowship, aGuggenheim Fellowship, and Universityhonors including the Henry RusselAward, the LS & A Excellence in Educa-tion Award, and a Thurnau Professorship.

Considered a world leader in alge-braic combinatorics, Hanlon’s expertisehas been used in various arenas. Combi-natorics describes the study of patterns.Typically Hanlon applies combinatorialmethods and results to problems in alge-bra or alternatively applies algebraictheory to combinatorial problems. Hisleadership and expertise in this area hasbeen recognized by (among others) theNational Security Agency. He has servedon the NSA Advisory Board since 1994,and also chaired the Math Section since1994. Hanlon served as Chair and authorof a report on the technical challengesfacing NSA and the role mathematicscould play in addressing the fundamental

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The second annual Marjorie LeeBrowne Colloquium was presented as partof the department’s recognition of MartinLuther King Day. The event honors Dr.Marjorie Lee Browne, the University ofMichigan’s first and the nation’s second Af-rican-American woman to earn the Ph.D. inmathematics.

The department was honored to host Dr.Evelyn Boyd Granville as this year’sspeaker. Dr. Granville is the nation’s firstAfrican-American woman to earn the Ph.D.in mathematics.

Dr. Granville has led an inspirationallife as a scientist, educator and person. Shewas born in Washington, DC in 1924, thesecond child of William and Julia Boyd.She came of age in segregated Washingtonduring the Depression, but reports neverhaving been aware that her family lackedthe basic necessities of life. Instead her par-ents emphasized to her the value of hardwork and education.

After graduating summa cum laudefrom Smith College in 1945, Dr. Granvillebegan graduate school in mathematics atYale. (Although she’d also been accepted atUM, Yale offered her a scholarship.) AtYale, she was twice awarded a JuliusRosenwald fellowship and was also hon-ored with a U.S. Atomic Energy Fellowshipfor her final year. Her doctoral dissertationon the properties of Laguerre series in thecomplex domain was supervised by Profes-

sor Einar Hille, a distinguished analyst. In1949, Dr. Granville became the first Afri-can-American woman in the history of theUnited States to be granted the Ph.D. inmathematics.

Following the receipt of her Ph.D., Dr.Granville enjoyed a remarkable careerworking as a mathematician and educator inacademia, government and industry. Sheheld academic positions first at the NewYork University Institute of Mathematics(now known as the Courant Institute) andFisk University, before moving to a positionas a mathematician at the National Bureauof Standards, and later at IBM. At IBM, Dr.Granville played an exciting and fundamen-tal role in the dawn of the computer age, es-pecially as it was being applied to celestialmechanics. For example, she was part ofthe team of scientists responsible for writ-ing the computer programs that tracked thepaths of vehicles in space on NASA’sProject Vanguard and Project Mercury.

In 1967, Dr. Granville made a major ca-reer change by accepting a professorship inmathematics at California State University,Los Angeles. Here she discovered a newpassion: the education of K-6 teachers andstudents. She was a key participant in sev-eral special projects for K-6 education, in-cluding the Miller MathematicsImprovement Program. Her textbook (withJason Frand), Theory and Applications ofMathematics for Teachers (Wadsworth,1975, 1978) became a standard for the

“new math” and wasadopted at over 50 col-leges and universities.

Upon retiring fromCSULA in 1984, Dr.Granville and her hus-band moved to a com-munity near Tyler,Texas. Her talent andenergy did not go unno-ticed: She received invi-tations to join thefaculty at a local publicschool, at Texas Col-lege, a small historically

black college in Tyler, and also at the Uni-versity of Texas at Tyler.

In her Colloquium talk entitled“Strengthening the K-12 Curriculum in Sci-ence and Mathematics: An Absolute Must,”Dr. Granville detailed some of her personalexperiences in past and recent years con-cerning mathematics education in thiscountry. Private industries and governmentagencies in the United States are finding itimpossible to recruit enough technicallyqualified personnel to fill existing jobopenings. Dr. Granville recounted how in1998-99, she partcipated in an outreachprogram to middle school students. Theprogram, sponsored by Dow Chemical, em-phasized to the students the importance ofmath and science in their future careers. Dr.Granville stressed that math provides stu-dents with the skills employers look forwhen hiring workers: logical thinking,problem solving abilities along with a vari-ety of problem solving strategies, and cre-ative thinking.

While Dr. Granville was showing themiddle school students why math was im-portant, she wondered if there were enoughwell trained math and science teachers tohelp them develop these skills. The effec-tiveness of the math and science curriculawas also in question. Are the teacher train-ing programs designed to produce effectiveteachers in math? Considering that the testscores of U.S. students in mathematics andscience rank low in comparison with stu-dent performance in many other countries,the answer is likely NO, particularly in ur-ban schools.

Students develop an attitude towardmath, good or bad, at an early age. There isa scarcity of well trained, inspiring teachersto help foster positive attitudes at an earlyage. Effective teacher training is a must,combined with continued career develop-ment opportunities.

Dr. Granville believes that a strong na-tion needs a first rate public educationalsystem starting in kindergarten. “Strengthcomes from…an intelligent citizenrytrained to think rationally and equipped tosolve problems.”

Institutions of higher learning mustwork with local and state agencies respon-sible for the K-12 curriculum in math andscience and with those institutions respon-sible for teacher training standards to effectchanges that ensure that the pool of quali-fied workers will be sufficient to meet fu-ture demands.

Successful MLK Day Colloquium

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Bob Megginson presents aframed poster to EvelynBoyd Granville. MathDepartment photo.

Professor Hyman Bass presented theinaugural lecture of the Roger C. LyndonCollegiate Professorship in Mathematics.He began with biographical remarks aboutthe man for whom this collegiate chair isnamed, Roger C. Lyndon. Lyndon waseducated at Harvard, where he earned aB.A. in 1939, an M.A. in 1941, and a Ph.D.in 1946. He was an instructor and assistantprofessor at Princeton University prior tojoining the faculty at the University ofMichigan as assistant professor. He waspromoted to associate professor in 1956and to professor in 1959. Lyndon retired in1988 and died in June of that year.

During his career, Lyndon gainedworldwide recognition for his seminal con-tributions to logic and group theory. As anundergraduate he found and corrected aflaw in philosopher Willard Quine’s foun-dations of mathematical logic. His contribu-tions to group cohomology were initiated inhis thesis, where, among other things, heanticipated spectral sequences, which are offundamental importance to groupcohomology.

Both Bass and Lyndon devoted much oftheir research careers to group theory,sometimes described as the mathematicaltheory of symmetry. Group theory measuresthe symmetry of an object as the set of allways that we can change that object and yetleave it the same. While mathematical sym-

metry may seem a somewhat exotic notion,it finds its way into virtually all branches ofmathematics and science.

In his lecture “Mapping the Borderlandsbetween Mathematics and Education,” Bassexplored instances where researchers havecrossed the boundary between mathematicsand education, much as he is doing in hisposition at UM. His work with DeborahBall of the School of Education, crosses theborderlands between the mathematicalknowledge and practices of the discipline,and those of the mathematics classroom,particularly at the elementary level. He pre-sented three historically significant ex-amples of work in the borderlands, andtheir impact on the discipline.

Felix Klein, Turn of the 20th Century

Felix Klein was notable for his deepand enduring interest in mathematics edu-cation at the turn of the 20th century. Hewas a great mathematical synthesist work-ing at Göttingen, where he devoted substan-tial attention to developing ideas about thepre-college mathematics curriculum. Hehoped to provide a vision of school math-ematics that would offer teachers a perspec-tive on the discipline that would enablethem to make better choices about presenta-tion and representation of important math-ematical topics. Klein appreciated thespecial cognitive complexity of teaching.

When addressing university-trained math-ematicians, he declared “…what high re-gard one must have for the performance ofthe elementary school teachers. Imaginewhat methodical training is necessary toindoctrinate…children with the principlesof arithmetic! Try it with your universitytraining; you will not have great success!”

In his extensive work on the schoolmathematics curriculum, Klein exemplifiedwhat Bass calls the cultural exchangemodel of interaction. He was respectful andhumble. He sought to bring a unifying dis-ciplinary perspective to considerations ofcurriculum, but did not seek to determinethat curriculum.

Bourbaki and the New Math

This example also involves mathemati-cians developing visions of the curriculum.In the 1930s, a group of mathematiciansrecognized the need to modernize math-ematics instruction in the French universi-ties. They undertook to reform the basiccourses of instruction. What began mod-estly quickly escalated into a monumentalenterprise to write collectively a compre-hensive account of the foundations of all ofcontemporary mathematics. These volumeswere published under the pseudonym ofNicolas Bourbaki. Unlike earlier influentialencyclopedic productions, Bourbaki under-took to actually develop the mathematics,from the foundations up, with detailed rig-orous proofs, and a globally unified con-ceptual and linguistic structure. Bourbakiserves as an incomparable reference workthat has greatly influenced university levelmathematics education around the world.

None of the brilliant mathematical de-velopments of the post WWII period mani-fested themselves in the school curricula. Inthe 1960s, a number of mathematiciansturned their attention to efforts to export toschools the new kinds of mathematicalthinking, such as that exemplified byBourbaki. This was the period that is nowreferred to as the “new math.” Elementaryversions of university level courses weredeveloped, founded on the formalism of settheory, with prominent attention to namingand studying the properties of algebraic op-erations. Calculus descended to the highschool curriculum. While the new math wasnot entirely misguided, pedagogically, it

Bass Delivers Collegiate Chair Lecture

continued on page 94

Chair Al Taylor, Professor Hy Bass and LS&A Dean Shirley Neuman priorto the Collegiate Chair lecture. UM Photo Services.

Department Hosts Middle School StudentsEach fall, the echo of their voices and

energetic footsteps can be heard aroundEast Hall. These groups are not incomingfreshmen, but middle school students visit-ing the department in conjunction with theUniversity’s King/Chavez/Park (K/C/P)Program. The K/C/P Program is run by theUniversity’s Office of Academic Multicul-tural Initiatives. The goal is to helpunderrepresented students prepare for col-lege by learning about college admissionrequirements and procedures, attendingpresentations by staff and faculty in se-lected academic units, and engaging inother activities designed to expose them tothe campus environment. K/C/P is a largestate initiative with many programs andcomponents.

Students from middle schools in De-troit, Ann Arbor, Willow Run, Ypsilanti,Pontiac, Flint, Adrian, Hazel Park, Monroe,Van Buren Township and other school dis-tricts in southeastern Michigan, visit theUniversity of Michigan for a day long se-ries of activities. Students also have the op-portunity to participate in a classroomsetting at UM.

Professor Robert Griess organizes theMathematics Department’s components ofthe program. Griess sees the opportunitiespresented by the program to be long range.“Minorities are not greatly represented inmathematics and math-related fields. Thereare many interesting career possibilities. Ifwe and our math presentations catch theimagination of these kids, we would expectto see increasing numbers of minorities inmathematics.”

Once a week during the fall, groups ofapproximately 15 students arrive at theMathematics Department for their hour-long visits. Department hosts for the pro-gram range from graduate students toprofessors. Each host is responsible forcreating a program for the students that caninclude a tour of the building, a visit to thelibrary, visiting classrooms, viewing anddiscussion of the computer facilities, andusually a demonstration or exercise inmathematics. It is important that the stu-dents understand the significance of amathematics education, and how it can beused in many professions. The host can

also thwart any misconceptions the stu-dents have about studying math in theircollege careers.

One of Griess’s presentations involvedcombinatorics and sequences of numbers.He had the students label four pennies withthe numbers 1 through 4. The studentswere then asked to write down how manydifferent combinations of numbers theycould make from those four numbers (1-4).Next, they were asked to take away thenumber 4 penny, and determine how manydifferent combinations of numbers theycould make with the numbers 1-3. They didthe same for 2 pennies and one. In the end,it was the method of sequencing that thestudents learned, and how it was easier todetermine the answers using this methodthan just randomly arranging the pennies.

The students who participated in themathematics programs this fall formed avariety of opinions about the mathematics

they practiced. Some of the comments ontheir evaluations show that the presenta-tions were a success. Here are some of thestudents’ responses to the question “whatdid you learn”:

• there is more to math than plus,minus, and divide;

• that you need math for a lot ofthings;

• that you don’t really know how toadd like you really think you do,and that it is not as easy as youmight see it will be.

“I think the K/C/P program offers themembers of this department the opportu-nity to have an impact on the future of ourdiscipline,” Griess says. “If we can reachyoung minds and show them the value ofcontinuing their education—in math or an-other subject—then we have succeeded.”

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A group of students from Barbour Middle School in Detroit work with Bob Griess on acombinatorics problem. Math Department photo.

programs. It is very gratifying to me to seesuch high quality teachers and researchersdoing the jobs that will continue to improvethe quality of our education and researchprogram.

When finishing a job, it’s natural tolook back and think about what’s gone well,what hasn’t, and what one thought of thework. Ever since agreeing to serve as Chairin 1994, I have been waiting for some veryunpleasant disaster to strike that I’d have todeal with. I’m still waiting and with lessthan a month to go (as of this writing), it’spretty clear that none is going to happen! Iattribute this to the great shape and thetrends that had been put in place under DonLewis’s decade of chairing the department.Don has the record of being the best Chairof a math department I’ve ever known. Ifthere was a theme to my years as Chair, itwas to continue to support the many goodthings that were already happening.

It’s also the case that serving as Chair isa very interesting job. The job of professoris good because one can keep learning newthings every day; by this scale, the job ofbeing Chair is very good! One gets to meetand work with colleagues from around theUniversity to help make Michigan a betterplace for students and faculty. I have beenvery impressed with the quality and dedica-tion of colleagues I’ve met, dealt with, andlearned from. This includes Chairs andheads of other units as well as the Deans ofour College. As a faculty member, one of-ten shares Dean jokes—like the one wherethe irate parent calls to complain about thelousy teacher her child has and demands tospeak with “no one lower than the Dean;”whereupon the Dean’s secretary responds,“Madam, there is no one lower than theDean.” But the truth is, at least in the Col-lege of LS & A at Michigan, the Deans andAssociate Deans have all been very intelli-gent and committed faculty who highlyvalue and support the educational and re-search missions of the University.

As to what’s gone well, the list is simplytoo long to cover except in the barest detail.

Strengthening and Broadening theDepartment

We’ve recruited outstanding faculty inboth core areas of mathematics and new ar-eas of applied mathematics. As you haveread in this newsletter over the years, fac-ulty honors and recognition for research,the analog for a math department of the All-America selections for the football team,have never been greater. Faculty honors foroutstanding educational work have alsonever been greater.

Freshman-Sophomore Program

Many faculty continue to work hard atimproving our freshman-sophomore pro-gram, being sure we have a wide array ofcourses so that every Michigan freshmanhas an appropriate course to help themlearn the mathematics they need to succeedin whatever career they choose. We areworking hard to find ways to use theinternet to enhance and improve the coursesas well as teach more of the technology stu-dents need to learn.

Junior-Senior Program

We’ve added many new courses (e.g.mathematical biology) and give a lot of fac-ulty attention to the undergraduate majorprogram, including our annual Career Day(for which we depend on the generous helpof many alums) and Awards Ceremony.New degree opportunities have also beenadded as well as the possibility of minoringin mathematics.

Graduate Program

Much more fellowship support thanever before is available through our NSFVIGRE grant, the largest such grant in thecountry. A new doctoral program in Appliedand Interdisciplinary Mathematics has beenadded along with our participation in theMasters Program in Financial Engineering,both of which give more opportunities toMichigan graduate students.

Outreach Program

Many more faculty than ever before areinvolved with outreach programs to highschool students and teachers, with at leastthree such programs in place. I’m especially

proud of the Michigan Math Scholars pro-gram, expanded this year to include all thenatural science departments at Michigan,intended to give talented high school stu-dents a taste of the excitement of doingmath and/or science research.

I’d like to take credit for all these greatthings happening, but the truth is that I hadalmost nothing to do with any of them ex-cept to serve as a cheerleader. Instead, Imust thank all the people who worked asheads of major committees and programs. Afar from complete list includes MelHochster, Ralf Spatzier, Igor Dolgachev,Toby Stafford, David Barrett, CharlieDoering, Peter Scott, Dick Canary, RobLazarsfeld, Curtis Huntington, MortBrown, Pat Shure, Phil Hanlon, DanBurns and Carolyn Dean. They did the ac-tual work. As to “running the department,”most of the credit for this has to go to theAssociate Chairs, Paul Federbush, JimKister, Andreas Blass, Berit Stensones,Alejandro Uribe, and especially PeterHinman who served so many years as As-sociate Chair for Education and the Under-graduate Program Director.

I can’t forget Jeffrey Rauch, who, ashe did once before for Don Lewis, steppedin to serve as Chair for a year, perhaps ourmost successful recruiting year of the lastdecade, when I took a sabbatical leave. Infact, Jeffrey has done a big administrativejob just about every year. We have a greatfaculty and just about everybody pitches into do the work.

So, you can see I’ve had a great timeserving as Chair. Nevertheless, I am happyto turn it over to others, as it is tiring andI’m out of ideas. I’ll be taking a term ofleave this fall to concentrate once again onthe excitement of doing research in math-ematics and then return to teaching and re-search in January. However, I’ll be here,ready to help out the new departmentalleaders when called upon, just as DonLewis has always been there for me when Ineeded help. I’ll do all I can to help Trevorand Alejandro continue to make us the verybest math department for research ANDeducation in the country!

- Professor B. Alan Taylor

Taylor, continued from page 1

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competitive advantage in order to increasethe number of our star-rated groups of re-searchers. Already, we have highly visiblesuch groups in algebraic geometry, numbertheory, several complex variables, and alge-braic combinatorics, and we will seek tobuild new groups, both on long-standingstrengths as well as in new areas. The morerecent moves by the department into ap-plied, interdisciplinary and emerging math-ematics (including financial mathematics,mathematical biology, computer science,mathematics education) will form an inte-gral part of this thrust.

The increasing competitiveness in thequality of our permanent faculty has beenaccompanied by a corresponding increasein the vigor of our Postdoctoral program.We currently have over 50 postdoctoratesworking in the Department, a level onemight even consider too vigorous! Such alarge pool of energetic young talent pro-vides both an attractive research scene forfaculty and graduate students, but also astimulating environment for our under-graduates—especially those taking part inour REU (Research Experiences for Under-graduates) program. It is somewhat hum-bling to note how large a slice of NorthAmerica’s future faculty members aretrained here at Michigan.

Our graduate students are increasinglycompetitive with the very strongest inNorth America, and we will increasinglyseek to find resources to bring the very besthere to Michigan. Our new AIM (Appliedand Interdisciplinary Mathematics) Ph.D.program, in particular, offers to augmentthe opportunities available as we look to-wards placing our graduates increasinglyoutside the academic world.

One might surmise from my commentsthus far that we are on the brink of enteringElysium, and so I offer some cautionarynotes (the bad news!). First, we certainlyface increasing outside pressure for ourbest young faculty, and also when we seekto hire senior faculty, from well-endowedcompetitors. Moreover, the new appliedand interdisciplinary areas, in which we in-creasingly seek to hire, frequently requirehiring packages and resources going sub-stantially beyond those usually available tomathematics. We will increasingly need tofind outside sources, in addition to pressur-ing the College, in our attempts to rise tothese challenges.

Similarly, at the postdoctoral and gradu-ate level we find ourselves pressured oncompensation, teaching load and resources,largely on account of the new VIGRE pro-gram funded by the National Science Foun-dation. This program has substantiallyexpanded the availability of competitivepostdoctoral and graduate student packagesto U.S. citizens, and thus we find ourselvescompeting for recruits with many morewell-funded programs than hitherto. Tocompete effectively, we will need to find away to create additional independentlyfunded postdoctoral and graduate positions(along the lines of our current HildebrandtAssistant Professorships).

Education

Perhaps the biggest and most immediateissue that will influence our educationalmission in mathematics is the increasingrole of computers. The future will undoubt-edly bring increased integration of comput-ers and teaching. Our challenge will be toenhance the experiences of both studentand instructor as this transformation occurs.It is obvious that proper use of technologycan enhance our undergraduates’ experi-ences in the classroom (and outside too!).Faculty, on the other hand, are all too famil-iar with the large investment of time, moneyand energy involved in designing coursesthat properly exploit available technology.However, following such initial investment,it is possible to achieve the first educationalgoal, and also save time for faculty to in-crease course development.

Computers also play a role in anotherimportant aspect of educational change that

will confront us over the next several years.As a public institution, we have a duty toprovide mathematical training to meet theneeds of the “New Economy,” broadly con-strued. We must train students in areas ofmathematics increasingly demanded by em-ployers in computer science, financialmathematics, bioinformatics, etc., both atundergraduate and at graduate levels. Thisobligation offers challenges, but also pos-sible rewards. In common with departmentsacross the nation, we are experiencing acontinued decline in the number of math-ematics majors enrolled in our program.Perhaps by embracing the challenge oftraining for the above emerging areas, wewill make progress on reversing this trend.

Summary

While it is satisfying to observe that weare more competitive than ever as a depart-ment, both in research and teaching, weface serious pressure in recruitment, espe-cially so far as postdoctorates and graduatestudents are concerned. We will seek to be-come leaders in applied, interdisciplinaryand emerging areas of mathematics beyondthe core areas more familiar to the depart-ment, and we will be forced to adapt tochanging technology, both in terms of ourteaching practices, and in order to addressthe increasing importance of mathematicsin underpinning the new economy. This allseems quite daunting! However, all of thesechallenges offer excellent opportunities forthe Mathematics Department to developand improve further. Check out your copiesof ContinuUM to monitor our progress!

- Professor Trevor Wooley

Math ProblemAssistant Professor Harm Derksen has developed math problems for competitionssuch as the International Math Olympiad. Here is one of his problems to challenge

your math skills. The answer is elsewhere in this newsletter.

Wooley, continued from page 1

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Suppose that 1 < x < 2. Prove that the sequence

bxc; b2xc; b3xc; b4xc; : : :

contains in�nitely many powers of 2. (For any real

number y, byc denotes the largest integer � y.)

With the support of the Office of theProvost and the College of Literature, Sci-ence and the Arts, the program formerlyknown as Michigan Math Scholars (MMS,a.k.a., Math Camp) expanded into Michi-gan Math and Science Scholars (MMSS).The 2001 summer program offered highschool students challenging mathematicsand statistics courses as well as courses inastronomy, biology, chemistry, geology andphysics. High school students (ages 14-18)from both the United States and Canadafound that their courses went well beyondthe basic textbooks and classroom experi-ences, giving them a hands-on approachalong with a glimpse of the exciting re-search possibilities in both mathematics andscientific fields. MMSS offers high schoolstudents the opportunity to explore mathand science at the cutting edge, with labora-tory research, field work and computerlaboratories.

The mathematics courses that were of-fered in MMSS 2001 included The Natureof Infinity, taught by Professor AndreasBlass, Interactive Statistics, taught by Pro-fessor Martha Aliaga, and MathematicalTheory in Biology, taught by ProfessorsTrachette Jackson and Patrick Nelson. Pro-fessor Sergey Fomin taught Codes, Ciphersand Secret Messages, an introductorycourse to cryptology, and Professors HughMontgomery and Carolyn Dean taughtnumber theory to aspiring mathematiciansin a course titled Exploring NumberTheory: From Ancient Greece to InternetSecurity.

Science courses offered included Envi-ronmental and Medical Microbiology, Ge-nome Sequences and Human Health,Mysteries of Embryology, The Large ScaleStructure of the Universe, Michigan Rocks!The Geology of Southeastern Michigan, AJourney through Modern Molecular Sci-ence—an Introduction to Chemistry, andRoller Coaster Physics. All of thesecourses were taught by outstanding Univer-sity of Michigan faculty members who notonly love their subjects of study, but alsolove teaching their subjects to enthusiasticstudents.

All MMSS participants get a great ideaof what studying at a major research univer-

sity is like along with getting to know thebeautiful city of Ann Arbor and other stu-dents interested in the same subjects. BothMMS and MMSS alumni report that thisprogram assisted them in selecting theircollege majors and even in selecting an aca-demic institution to attend. Many alumniare outstanding students today at the Uni-versity of Michigan and plan to pursue ca-reers in mathematics, science, medicine andengineering.

The MMSS administration, directed byProfessor Dan Burns, is working on final-izing the dates for the 2002 summer pro-gram and creating an exciting combinationof math and science courses for the futureMMSS curriculum. Some possibilities in-clude Introduction to Logic, The History ofScience and Ethics, Neuro-Psychology andAbstract Geometry. The more popularcourses from 2001 such as The Nature ofInfinity, Cryptology, Microbiology andRoller Coaster Physics will be offered aswell in 2002. For future inquires or to beadded to the Michigan Math and ScienceScholars mailing list for a future brochurecomplete with application information,please call (734) 764-0335 or send email tommss@umich.edu. Visit the MMSSwebsite at www.math.lsa.umich.edu/mmss/for more information and updates about thisamazing summer program for high schoolstudents.

- Annie Marshak Dowling MMSS Program Coordinator

2001 Michigan Math andScience Scholars Program

problems. His report is being used as thebasis for attacking mission-critical issuesfacing the NSA for the next 10 years.

More recently, Hanlon’s research hasinvolved computational genomics, as de-scribed in the accompanying article. Hiswork in biomathematics is bringing newideas to search for genetic information inthe huge new databases that are emerging.

Within the department, Hanlon hasbeen a caring, challenging teacher andmentor. He has had eight students completetheir doctoral theses and is currently direct-ing four others. Students flock to hisclasses. He constructed a new combinato-rics curriculum at both the undergraduateand graduate level, and developed an inno-vative class for non-mathematics concen-trators (Math 175 Cryptography) that wasthe first to utilize the department’s nowwidely recognized interactive group modeof instruction. In an effort to reach out tothe broader Michigan community, Hanlonconceived and implemented the MichiganMath Scholars Program (Math Camp), pro-viding an intensive summer program forhigh school students. This program hasproved to be a superb recruiting tool.

Hanlon is committed to serving the de-partment, college and University. In thecollege, he has been an Executive Commit-tee Member, and on the Search Committeefor the new Dean. He is a member of theBoard in Control of Intercollegiate Athlet-ics, and was one of two faculty asked toserve on the search committee for AthleticDirector. He has been a member of theLife Sciences Advisory Committee, mem-ber and Chair of the Rackham DivisionalBoard, and was on the Faculty AdvisoryCommittee on Information Technology.

Hanlon, continued from page 2

8

MMSS Program participants study the environmental history of a glacial kettle lake byexamining the sediment core at Pickerel Lake, MI. Geology Department photo.

was naively conceived. It was designedmainly by mathematicians with the subor-dinate participation of educators. It vastlyunderestimated the learning opportunitiesthat teachers would need to work with thisradically new mathematical content. Hencethe enactment of the new math curriculawas sometimes ineffectual.

Reforms, Debates & Collaborations atthe Turn of the 21st Century

We are amid a major period of educa-tional reform in mathematics. Widespreadconcerns about weak mathematics achieve-ment have led to claims about the poorquality of teachers, teaching, and curricu-lum. Critics also point the finger at inad-equate professional education and poorassessments. A significant difference inthe contemporary concerns is the pro-claimed aspiration to achieve high levelmathematics learning for all students.

One stream of activity in this area is asubstantial effort at curricular and peda-gogical reform. The major initiatives, how-ever, did not emanate from the disciplinaryexperts in mathematics and science. In-stead, the initiatives came from the teach-ers’ professional organization—theNational Council of Teachers of Math-ematics (NCTM). Starting in 1989, theNCTM promulgated mathematics standardsfor curriculum, teaching, and assessment.

The National Science Foundation fol-lowed this initiative by funding projects fordevelopment of standards-based curricularmaterials for the schools. By the late1990s these new curricula had been pilotedand were in the first stages of adoption inschools around the country. It was onlythen that their nature and significance be-came vivid to large numbers of teachers,students, and parents. Reactions were di-verse and often passionate. Suddenly edu-cational improvement in mathematicsbecame a widespread concern, enteringpolitics and the media.

A second, more diffuse, and less pub-licly visible development is the gradualemergence of interdisciplinary collabora-tions of mathematicians with educationalpractitioners and researchers. Some ofthese are directed at interventions for theimprovement of instruction—curriculumdevelopment, construction of assessmentinstruments, professional development ofteachers, etc.

Others aim to generate new fundamen-tal knowledge and understanding about thenature of mathematics instruction and itsentailments. Specifically, the researchBass and Ball are leading here at UM isaimed at what has come to be recognizedas one of the central problems in U.S.mathematics education: the mathematicalcontent knowledge of teachers, particularlyat the elementary level.

Research has amply documented theshallow and fragile mathematical knowl-edge and skills of many U.S. teachers.What is not well understood is how to ad-dress the problem of teachers’ mathemati-cal knowledge in ways that would improvestudent learning. The most natural sound-ing approaches—to require more tradi-tional mathematics courses, for example amathematics major—have proved disap-pointing.

What is the useful and usable math-ematical knowledge that teachers need foreffective instruction? The topics and skillsspecified by the curriculum offer a piece ofthe answer, but this is hardly enough. Tra-ditional approaches have been to situate theschool curriculum within the discipline,and to amplify the ambient mathematicalideas from a broader and deeper math-ematical perspective. Although this makessense for the curricular questions, it has notproved as useful for determining the math-ematical knowledge that it takes to teach.

In the Bass and Ball work, instead oflooking to the discipline, and importing itsperspectives into the classroom, they di-rectly examine teaching practice. Theyask, what is the nature of the work ofteaching? What mathematical resourcesdoes it draw upon, in what forms, and inwhat ways are they used? To mathemati-cally prepare mathematics teachers, oneshould understand the mathematical entail-ments of their work. This is how the math-ematical preparation of physicists,engineers, economists, and biologists is de-signed. Bass and Ball are engaged in a re-lated endeavor by studying the work ofmathematics teaching and seeking to un-cover the mathematical resources—knowl-edge, skills, sensibilities—on whichteaching depends.

This approach seems so natural and rea-sonable that one can well ask why it hasnot happened long ago. A major reason isthat teaching is difficult to observe, to rep-resent, and to analyze. What makes thework possible now is the existence of arich, digitized data base of primary recordsof teaching practice, consisting of video,transcripts, student work, teacher’s journal,and many other artifacts, for an entire yearof teaching of a third grade class.

Analyzing these records in detail ad-dresses the following questions:

• What kinds of mathematicalknowledge—ideas and proce-dures, practices, sensibilities—isentailed by the work of teaching?

• In what forms do teachers need tohold such mathematical knowl-edge? Where and how in thecourse of their work do teachersuse these sorts of mathematicalknowledge?

• How can teachers be helped to de-velop such knowledge?

One focus has been the process of stu-dents learning the principles of reasoning.Here it is important to notice the movesand guidance furnished by the teacher inthe direction of such performance. Thechildren are able to reason because theyhad been learning to do so all year.

Among the things that Bass and Ballare discovering about the mathematicalknowledge needed for teaching are:

• that what matters is its use (for ex-ample, in hearing and interpretingstudents’ thinking, in revisingtasks, in managing discussion,etc.);

• that it has to be substantially un-packed, in contrast with the waysthat mathematicians hold suchknowledge;

• that knowing connections acrosstopics and stretching out to wherestudents are headed matters.

The improvement of mathematics edu-cation (like that of science education andliteracy) is an urgent national need. Theproblems are complex and they inherentlydemand multi-disciplinary approaches foreffective treatment.

Bass, continued from page 4

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The department has made significantprogress in recruiting and hiring manyyoung faculty members. This year the de-partment welcomed several new tenured ortenure-track faculty. Profiles of the six newdepartment members are below.

Associate Professor Brian Conrad re-ceived his Ph.D.from Princeton Uni-versity in 1996. Heis considered one ofthe best young alge-braic number theo-rists in the fieldtoday. With col-leagues at other uni-versities, he iscompleting the re-maining cases of the Shimura-Taniyamaconjecture of the rational numbers. The im-portance of this result was highlightedwhen Andrew Wiles’s proof of Fermat’slast theorem hinged on an incomplete proofof the Shimura-Taniyama conjecture. Hisresearch in this area is groundbreaking, andhe has the potential to be a truly excep-tional leader in the field. Conrad is also asuperb lecturer and excellent teacher. Thisyear he has taken over the UndergraduateMath Club. Each week numerous math ma-jors meet for pizza and pop in the Nesbittundergraduate commons room, and hear apresentation by a faculty member. It hasgrown to a truly successful endeavor.

Assistant Professor Harm Derksen re-ceived his Ph.D.from the Universityof Basel in 1997.He has done distin-guished work inconstructive invari-ant theory, represen-tation theory, affinegeometry and sym-bolic computation.Derksen has madethree major research contributions. He ob-tained a polynomial bound for the degreesof generators of invariant rings of reductivegroups, and introduced a new and simplealgorithm for finding such generators via aGröbner basis calculation. He found the

first holomorphic actions of reductivegroups on complex affine space which arenot holomorphically linearizable. Recently,he gave a new proof of the “saturation con-jecture” for multiplicities of irreducible rep-resentations in a tensor product ofirreducible representations of the generallinear group. His teaching background in-cludes working with Dutch participants ofthe International Mathematics Olympiad.

Assistant Professor Trachette Jacksonreceived her Ph.D.from the Universityof Washington in1998. She works inbiomathematics, par-ticularly in theanalysis of systemsof nonlinear partialdifferential equa-tions that modelproblems in physiology such as cancer andcellular dynamics. She works on real bio-logical and medical problems, using realdata from experimentalists. At UM, Jack-son will be developing interactions with mi-crobiology, immunology, and the CancerCenter. She is a gifted lecturer who empha-sizes interactive teaching techniques in herclasses.

Associate Professor Bruce Kleiner re-ceived his Ph.D.from the Universityof California-Berke-ley, in 1990. Hewas a faculty mem-ber at the Universityof Pennsylvania andthe University ofUtah before comingto UM. His initialfield of research wasdifferential geometry, and in his thesis heclassified four-dimensional manifolds withpositive curvature and a continuous symme-try. Soon thereafter he proved a major re-sult about isoperimetric inequalities. Hecontinued his research in the area ofnonpositive curved manifolds and mani-folds without conjugate points. Kleiner’srecent work is in the field of combinatorialgroup theory. His main result in the field is

Several Outstanding YoungFaculty Members Appointed

the proof of the Margulis conjecture, con-cerning quasi-isometries of higher-ranksymmetric spaces.

Assistant Professor Peter Miller re-ceived his Ph.D.from the Universityof Arizona in 1994.He studies appliedmathematics, in par-ticular nonlinearwaves. His majorwork has dealt withthe nonlinearSchrödinger equa-tion, particularly inconnection with optics and nonlinearwaves. His study of optics is important andtimely, and constitutes one of the main sci-entific foundations of the computer andcommunications revolution. Miller willhave the opportunity for interdisciplinaryinteraction with faculty from electrical en-gineering and computer science.

Associate Professor Chris Skinner re-ceived his Ph.D.from Princeton Uni-versity in 1997. Heis considered one ofthe most outstandingyoung number theo-rists practicing to-day. Skinner hasbeen publishing inmathematics since1989, his freshmanyear here at UM. His undergraduate thesiswas solicited for publication in the DukeMathematical Journal. Upon completion ofhis Ph.D., he received a three-year appoint-ment at Princeton’s prestigious Institute forAdvanced Study, where he was awarded anOstrowski Fellowship and a Clay Math-ematics Institute Fellowship. Skinner’smost significant contributions are to thetheory of diophantine equations in manyvariables over number fields, non-vanishingof twists of L-functions, and Galois repre-sentations and their application to modular-ity questions associated especially withelliptic curves.

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Three-Year Faculty AppointmentsThe department welcomed 29 new as-

sistant professors for the 2000-01 academicyear—a record! New assistant professorsare listed here with their doctoral institu-tions and area of speciality. Hildebrandtand VIGRE apointments are also indicated

Mahdi Asgari - Purdue, Number Theory(Hildebrandt)

Tibor Beke - M.I.T., Topology

Thomas Bieske - University of Pittsburgh,Geometric Function Theory (VIGRE)

Gilberto Bini - Universita La Sapienza diRoma, Commutative Algebra/AlgebraicGeometry

Marcin Bownik - Washington University,Harmonic Analysis

Ana Bravo - Autonomous University ofMadrid, Commutative Algebra

Stephen Bullock - Cornell University,Differential Geometry

Daniel Chan - M.I.T., Algebra

Mark Dickinson - Harvard, AlgebraicGeometry (Hildebrandt)

Anton Dzhamay - Columbia University,Partial Differential Equations/Math Physics

Gavril Farkas - University of Amsterdam,Algebraic Geometry

Tatyana Foth - Pennsylvania StateUniversity, Automorphic Forms

Angela Gibney - University of Texas-Austin, Algebraic Geometry (VIGRE)

Hans Johnston - Temple University,Numerical Analysis

Boris Kalinin - Pennsylvania StateUniversity, Dynamical Systems

Tao Luo - Institute of Mathematics,Academia Sinica, Non-Linear DynamicalSystems

Patrick Nelson - University of Seattle,Math Biology

Thomas Nevins - University of Chicago,Algrbraic Geometry

Ronghua Pan - Institute of Mathematics,Academia Sinica, Partial DifferentialEquations

Benjamin Richert - University of Illinois,Commutative Algebra/Algebraic Geometry

Oliver Roth - University of Würzburg,Complex Analysis

Victoria Sadovskaya - Pennsylvania StateUniversity, Differential Geometry

Eric Schippers - University of Toronto,Complex Analysis

Mark Skandera - M.I.T., PermutationStatistics (VIGRE)

Michael Sullivan - Stanford University,Differential Geometry (VIGRE)

Kaushal Verma - Indiana University,Complex Analysis

Thomas Weston - Harvard, AlgebraicNumber Theory (Hildebrandt/NSFPostdoctoral Fellow)

Ming Yang - Columbia University,Probability

Gang Yu - University of Georgia, NumberTheory

Several faculty members received pro-motions this year. To Professor: AlexanderBarvinok, Dick Canary, Sergey Fominand Karen Smith. To Associate Professor:Brian Conrad.

The following faculty members havebeen invited to speak at the next Interna-tional Congress of Mathematicians to beheld in the summer of 2002 in Beijing:Tom Hales, Juha Heinonen, TobyStafford, Trevor Wooley.

Hyman Bass was awarded the Excel-lence in Research Award from LS&A.

Anthony Bloch is co-chairing the 2001SIAM Conference on Control and its Ap-plications.

Daniel Burns and Robert Megginsonreceived Excellence in Education Awardsfrom LS&A, acknowledging their specialcontributions to undergraduate education.

Brian Conrad was awarded an NSFCAREER Award.

Brian Conrad and Chris Skinnerwere named Alfred P. Sloan Research Fel-lows. An extraordinarily competitive award,

Fellows are selected from the very best sci-entists of their generation.

William Fulton was elected a ForeignMember of the Royal Swedish Academy ofSciences.

Angela Gibney was awarded an out-standing dissertation award from the Uni-versity of Texas for her thesis, one of onlyfour so honored out of over 800 graduatesfrom the University of Texas.

Gene Krause received the Excellencein Concentration Advising Award fromLS&A. This award recognizes his long andexemplary record as a concentration advi-sor for students pursuing a teaching certifi-cate in mathematics within the College.

Robert Megginson was inducted intothe Native American Science and Math-ematics Wall of Fame. This is an honor sitemaintained at the Southwest Indian Poly-technic Institute in Albuquerque to recog-nize Native Americans whose careers havemade significant contributions to both theirfields of study and the advancement ofother Native Americans in science andmathematics. The site currently honorstwelve Native Americans.

Kristen Moore was awarded theAmerican Fellowship from the AmericanAssociation of University Women Educa-tional Foundation. This award is highlycompetitive, with only 18 fellowships forall of the arts and humanities, social sci-ences, and natural sciences.

Krishnan Shankar received the Marga-ret and Herman Sokol Postdoctoral Fellow-ship Award in the Sciences, recognizing hisoutstanding work in research and teaching.

Pat Shure was awarded the 11th AnnualLouise Hay Award for Contributions toMathematics Education by the Associationfor Women in Mathematics. The awardcites Pat “not only on the breadth of hercontributions to mathematics education,but also on her reputation as a superbteacher and an inspiring role model for hercolleagues and students.”

Karen Smith won the 2001 Ruth LyttleSatter Prize from the American Mathemati-cal Society. The prize honors outstandingcontributions to mathematics research by awoman in the previous five years. She re-ceived the prize for her work in commuta-tive algebra, and her more recent work thatbuilds new bridges between commutativealgebra and algebraic geometry.

Faculty Kudos

11

Faculty ProfileSeveral Complex Variables

For the past few years the departmenthas been fortunate to have a special groupof assistant professors who are extremelyactive in the general research area of sev-eral complex variables. These four havebeen responsible for some exciting collabo-ration with senior faculty as well as otherassistant professors. Each has a uniquebackground and area of interest. Here weinclude brief profiles of the four facultymembers.

Mattias Jonsson received his Ph.D.from the Royal Institute of Technology inSweden. His current research interests arein the areas of dynamical systems, financialmathematics, complex analysis and ergodictheory. His research in higher-dimensionalcomplex dynamics involves the ergodicproperties of iterates of holomorphic mapsof complex manifolds, in particular com-plex projective space Pk. Jonsson hasworked on joint projects in this area withcolleagues at Notre Dame, Penn State andin Paris. In the area of financial mathemat-ics, he is studying optimal trading strategiesand other stochastic control problems.

During his work here, Jonsson has beenable to participate in numerous interna-tional conferences, including the Ph.D.Euroconference on Complex Analysis andHolomorphic Dynamics in Spain, and theInternational Conference on DynamicalSystems in Brazil. Jonsson was part of theorganizing committee for the 1999 Mid-west Several Complex Variables confer-ence honoring Al Taylor’s 60th birthday.He is active in the Ann Arbor Juggling ArtsClub, and can often be spotted on the Diagplying his art with other club members.

“Michigan has a good research environ-ment for postdocs,” Jonsson said. “I havebenefited from the extremely active re-search and the many seminars andoportunities for mathematical discussions.”

The department is fortunate thatJonsson has accepted an offer of a tenure-track position.

Dror Varolin received his Ph.D. in1997 from the University of Wisconsin.He is interested in many areas of math-ematics, all centered around some aspect ofgeometry. His primary work has been inseveral complex variables, complex dynam-ics, algebraic and analytic geometry, and

some control theory and Lie theory (mostlyconnected to geometric problems). Varolinhas collaborated with several people in thedepartment and elsewhere, including JohnErik Fornæss, Mattias Jonsson, RobLazarsfeld, Alex Schuster, Karen Smithand Arpad Toth.

In addition to his many teaching re-sponsibilities during his time at UM,Varolin has organized numerous seminars,including the weekly Several ComplexVariables seminar, the Quantum Mechanicsseminar and the Nevanlinna Theory semi-nar. He was an organizer for two MidwestSCV conferences in 1999. “Michigan hasa very active faculty, and I’ve developedsome great research topics with other fac-ulty members,” Varolin says.

Varolin is active with the Ann ArborSoccer Association. His team placed thirdlast year, and he hopes to have better luckthis year.

He will stay in the department next yearto participate in the Special Year in Com-plex Analysis.

Sophia Vassiliadou received her Ph.D.from the University of Notre Dame in1997. Before coming to UM in 1998, shewas a postdoctoral fellow at the MaxPlanck Institute in Germany. Her researchinterests are in the areas of several com-plex variables and partial differential equa-tions. In particular, she is interested inproving the existence and regularity resultsfor solutions to the , ∂ b

, and ∂ -Neumann problems on nonsmooth do-mains. Vassiliadou has worked with JohnErik Fornæss on a question of local L2-

solvability for ∂ on a singular surface andwith David Barrett on a problem related tothe Bergman kernel of a nonsmooth modeldomain. She credits these collaborationswith opening some new horizons in her re-search and forcing her to think in a moregeometric way. Vassiliadou’s future re-search projects involve trying to under-stand the geometry of singular varieties andanalyzing symmetric spaces.

Vassiliadou is impressed with thestimulating atmosphere of the department.“What I really liked about Michigan is thatyou can feel that math is being done in thisplace. There are so many seminars andactvities on various subjects that you canget an idea of what’s going on in manyfields, not just your own.”

Vassiliadou plans to stay in the depart-ment for one semester next year, then shewill join her husband in the MathematicsDepartment of the University of Toronto.

Kaushal Verma is completing his firstyear here at UM, after receiving his Ph.D.from Indiana University in 1999. His mainresearch interests include mapping prob-lems in Cn, holomorphic correspondences,pluripotential theory and complex dynam-ics. His thesis work involved understand-ing the reflections principle in severalcomplex variables and its applications tostudying the boundary behavior ofholomorphic mappings and analytic sets.More recently his interests have broadenedto include the dynamical study of Henonmappings in C2, in particular their struc-tural stability.

Verma is also impressed and enthusedby the research environment at Michigan.“There are many dynamic researchers inthe department, and I am impressed by thenumber and variety of seminars and talks.”

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l-r: Kaushal Verma, Sophia Vassiliadou, Dror Varolin, Mattias Jonsson.Math Department photo.

∂

Two Faculty Members RetireJack Goldberg, Associate Professor of

Mathematics, retired from active facultystatus in May, 2000. He received his B.S.degree from the City College of New Yorkand his M.S. and Ph.D. degrees from theUniversity of Illinois at Urbana-Champaign. Goldberg joined the UM math-ematics faculty in 1961.

Goldberg’s research has been in com-plex variables and special functions. Hedirected four dissertations in these areas.In 1969-70, Goldberg was a visiting associ-ate professor at Robert College in Istanbul,Turkey. In 1981-82, he returned to Turkeyas a Fulbright Scholar at Bugazici Univer-sity in Istanbul.

Best known as a popular, dynamicteacher involved in curriculum develop-ment, Goldberg was active in bringing com-puters into the classroom. In 1980 hereceived the Amoco Foundation GoodTeaching Award from UM. He has writtenfour textbooks stemming from his teachingon linear algebra, matrix theory, differentialequations and other topics in applied math-ematics.

An active member of the department,Goldberg was an Associate Chair from1975-77, and served on several Universitycommittees, including the Board in Controlof Intercollegiate Athletics. He has beengranted emeritus status by the Regents.

Donald J. Lewis, Professor of Math-ematics, retired from active faculty status inMay, 2000. Lewis received his B.S. fromthe College of St. Thomas and his M.S. andPh.D. from UM. Prior to joining the UMfaculty in 1961, he was an instructor atOhio State, an NSF fellow at the Institutefor Advanced Study in Princeton, and a fac-ulty member at Notre Dame. Lewis waspromoted to Professor in 1963.

Lewis’s research lies in the area of num-ber theory concerned primarily withDiophantine problems, and encompassesthe theory of algebraic number fields andfunction fields, and arithmetic geometry.While a number of his results have beenimproved in recent times, it is characteristicespecially of his earlier work that he wasthe first to obtain any kind of result on aproblem, and that this decisive progresscleared the way for subsequent develop-ments. The work in his thesis concerning

the local solubility of cubic forms, however,remains definitive. One of Lewis’s main in-terests was the development of young math-ematicians, and he directed 24 doctoraltheses.

Lewis served as Chair of the departmentfrom 1984-94. He was noted for his leader-ship in University affairs. This includedservice on the Executive Committee of theCollege of Literature, Science and the Arts,on the University Budget Priority Commit-tee, and on search committees for theDeans of Literature, Science and the Arts,of Engineering, and the Vice President forResearch. He has received numerousawards, including a Distinguished FacultyAchievement Award from UM, anAlexander von Humboldt Pries Award, andthe Distinguished Public Service Awardfrom the American Mathematical Society.As Chair of the Math Library for manyyears, Lewis was instrumental in getting itclassified as a Level 5 library.

From 1995-99, Lewis was based inWashington, D.C., as the Director of theDivision of Mathematical Sciences of theNational Science Foundation.

He has been granted emeritus status bythe Regents.

Emeritus Faculty andFriends Gather

In May, 2001, the department hosted aluncheon for emeritus faculty and friendsof the department. More than 45 people at-tended the luncheon, which was an oppor-tunity to renew acquaintances, greetlong-time colleagues, and find out aboutcurrent departmental happenings.

The program for the day began withcurrent Chair Al Taylor and incomingChair Trevor Wooley sharing recent de-partmental highlights, and future plans.(See the Chair’s Notes columns for furtherdetails.) Associate Professor Chris Skinnerpresented the mathematical portion of theprogram “Right triangles, a million dollars,and number theory at Michigan.”

Everyone in attendance agreed that theluncheon was a wonderful opportunity toshare current achievements with the facultywho helped to make the department what itis today. Hopefully, an event such as thiswill be repeated on an annual basis.

Jack McLaughlin1923-2001

Professor Emeritus Jack E.McLaughlin passed away on January 12,2001. Born in Idaho in 1923, McLaughlinreceived his B.S. from the University ofIdaho in 1944, and his Ph.D. from the Cali-fornia Institute of Technology in 1950.

McLaughlin joined UM as an Instructorin 1950, was promoted to Associate Profes-sor in 1958 and to Professor in 1963. Heretired from the Department in 1994. Hewas considered an excellent and demandingteacher, especially of honors students whosought his courses to measure their ability.McLaughlin guided these students as chairof the honors program for several years. Hehad a unique success in impressing under-graduates with the beauty of math and thepleasure of discovery after intense effort.He directed nineteen doctoral theses, andmany of his students have become leadersin their fields of interest.

In 1986, he received the Amoco Foun-dation Good Teaching Award. In the lettersof recommendation submitted by his formerstudents, a great number of them citedMcLaughlin as the best and most inspiringteacher they had in their academic careers.The mastery of the subject he displayed inhis teaching influenced many of his stu-dents to pursue a career in mathematics.

McLaughlin’s research ranged widely,encompassing several subfields of alge-bra—lattice theory, finite groups, and com-mutative algebra. He discovered one of thesporadic finite simple groups, that of order898,128,000, which now bears his name.He also participated in the discovery of amodule of finite projective dimension witha negative intersection multiplicity. Hiswork on group cohomology, most of whichpassed on through the writings of his stu-dents, has had an important impact on thefield. He was well respected by his col-leagues in the field. Paul Halmos, his UMcolleague, once said that there are a numberof ways to tackle a mathematical problem,but when all else fails, ask McLaughlin.

While enjoying the intellectual chal-lenges of mathematics, McLaughlin had toovercome the physical challenges of mul-tiple sclerosis. He lived with the disease forthe last 30 years of his life. McLaughlin’sphysical challenges rarely limited him in histeaching, research or academic activities.

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Fall 2000 marked the first full semesterof activities for the VIGRE (Vertical Inte-gration of Research and Education) pro-gram in the department. The currentprogram provides financial support for 30graduate students and 4 postdoc assistantprofessors, and allows the department tooffer professional development activitiesdesigned to foster close contact betweenstudents, postdocs and permanent faculty.The program reduces the teaching respon-sibilities for participants, allowing them toprofit more fully from the rich mathemati-cal life of the department. Additional ac-tivities, including a large number ofresearch experiences, will be offered to un-dergraduates. While the activities de-scribed below are designed for andsupported by the VIGRE program, theyclearly are of benefit to all members of thedepartment.

Numerous activities have been de-signed and implemented to foster interac-tion between graduate students, postdocsand senior faculty within the department,and include opportunities for undergradu-ate participation in research. Here is a de-scription of the current seminars andgroups developed as part of the VIGREprogram:

VIGRE Seminar: Intended for ad-vanced undergraduates and graduate stu-dents, these talks by internal and externalspeakers are related to diverse applicationsof mathematics, career possibilities in themathematical sciences and importanttrends within mathematics itself.

Open Problem Seminar: Intended forpostdocs and advanced graduate students,participants present open problems in theirarea of research. The goal is to helpyounger colleagues develop independentresearch agendas. Seminars are held ineach of four areas: algebra, analysis, ap-plied mathematics and geometry-topology.

Graduate Student and Postdoc Pro-seminars: The two separate seminars areinformal meetings under the leadership of asenior faculty member. The basic idea ofthe graduate student seminar is to exposeparticipants to different aspects of themathematical profession, and are largelycultural and non-technical in nature. Thepostdoc seminar leader helps younger col-leagues development professional “street

smarts,” with topics including how to sub-mit papers for publication, how to apply forgrants and jobs, what the American Math-ematical Society does, etc.

Integrated Working Groups: Faculty,postdocs, graduate students and under-graduates meet to work on a common areaof mathematics or a problem. The twogroups that were held this year focused onthe topics of Mathematical Fluid Dynamicsand Non Linear Systems, and NumericalAnalysis.

Undergraduate REU Summer Pro-gram: Undergraduate math majors workon research projects with faculty members.The participants met once a week duringthe summer and coordinated with twoVIGRE graduate trainees. The graduatecoordinators gave talks on mathematics,gave advice on applying to graduateschool, and organized guest speakers.

Undergraduate Math Club: Thisgroup of undergraduate math majors meetswith a faculty mentor who facilitates math-ematical discussion and organizes guestspeakers.

Graduate student Jesse Otero is an up-per level student participating in theVIGRE program. He was a graduate stu-dent in the depart-ment in 1994-5,and returned to hisgraduate studies in1998. During hishiatus, Oterotaught high schoolalgebra and geom-etry in Florida. Heand JessicaSidman were thecoordinators of theundergraduate REU program last summer.

Otero embraced mathematics becausehe excelled in the subject and enjoyedstudying it. He is currently working withCharlie Doering and has benefited greatlyfrom the various VIGRE activities. “Thesupport provided by the program allows memore time to work on research and otheractivities. I have particularly enjoyed theIntegrated Working Group in MathematicalFluid Dynamics and Non Linear Systems.The group is class-like, and allows for par-ticipation of all levels. I found it a very

beneficial way to learn.” Otero is currentlydeveloping a student applied math seminar.He plans on continuing research with Pro-fessor Doering in the area of mathematicalfluid dynamics and problems of heat trans-port in turbulent flows.

Assistant Professor Angela Gibney’s in-terest in math was fostered at a young age,since her mother studied the subject. Sheunderstood earlythat mathwas inter-esting, and was atthe heart of mostsciences. Gibney re-ceived her Ph.D.from the Universityof Texas, Austin.She was recentlyawarded UTA’sOutstanding Disser-tation Award.

Gibney feels that the VIGRE programoffers an ideal opportunity to teach, whilestill having the time to participate in the in-tellectual life of the department. The de-partment houses some of the premierefaculty members in her area of interest, al-gebraic geometry. “Teaching only oneclass per semester makes scholarshipeasier. I want to get as much as possibleout of my experience here, and this allowsfor the time to do research, as well as expo-sure to the other mathematicians.” She hasalso enjoyed the non-math presentationsabout job seeking and the career planningprocess, that can benefit all members of thedepartment.

Gibney is currently working with Assis-tant Professor Gavril Farkas on research.She would like to develop a Saturdaymorning math group designed to reach thegeneral public, including high school stu-dents. “Since VIGRE emphasizes partici-pation of all levels in the field ofmathematics, this would allow us to reachstudents prior to their enrollment in col-lege, as well as emphasize to the commu-nity the significance of math in all areas ofscience.”

VIGRE Activities Enrich the Department

14

Recent PhD RecipientsDariush Ehsani completed his disser-

tation “The Solution of the d-bar NeumannProblem on Non-Smooth Model Domains”under the direction of David Barrett. Hewill be an assistant professor at TexasA&M University.

Florian Enescu completed his disserta-tion “A Study of F-Rationality and F-Injectivity” under the direction of MelHochster. He will be an assistant professorat the University of Utah.

Sara Faridi completed her dissertation“Closure Operations on Ideals” under thedirection of Karen Smith. Faridi is an as-sistant professor at George WashingtonUniversity, in Washington, D.C.

Patrick Hagerty completed his disser-tation “Radiation Induced Instability” un-der the direction of Anthony Bloch. Hewill be an assistant professor at the Univer-sity of Arizona.

Eric Hall completed his dissertation“Generic Extensions of Permutation Mod-els of Set Theory” under the direction ofAndreas Blass. He is a postdoc at PurdueUniversity.

Jason Howald completed his disserta-tion “Calculations with Multiplier Ideals”under the direction of Robert Lazarsfeld.Howald will stay on as a lecturer at Michi-gan for one more year.

Melinda Koelling completed her dis-sertation “Dynamics of Generalizations ofthe Toda Lattice” under the direction ofAnthony Bloch. She will be an assistantprofessor at Rensselear Polytechnic Insti-tute.

Ian Pulizzotto completed his disserta-tion “Heat Flow in a Random Medium andHomogenization” under the direction ofJoe Conlon.

Mihnea Popa completed his disserta-tion “Linear Series on Moduli Space ofVector Bundles on Curves” under the di-rection of Robert Lazarsfeld. He will be anassistant professor at Harvard.

Kimberly Retert completed her disser-tation “Noncommutative Curves inGrothendieck Categories” under the direc-tion of Toby Stafford. She will be an assis-tant professor at Texas A&M University.

Timothy Schwider completed his dis-sertation “The Classification of EssentialLaminations in Dehn Surgeries on the Fig-ure Eight Knot” under the direction ofPeter Scott.

Kendrick Smith completed his disser-tation “The Mod 2 Cohomology of someClassifying Spaces of Compact LieGroups” under the direction of Igor Kriz.He is an assistant research scientist in theUniversity of Michigan Information Tech-nology Division.

Craig Sutton completed his disserta-tion “Applications of RepresentationTheory to Dynamics and Spectral Geom-etry” under the direction of Ralf Spatzier.Sutton will be an assistant professor atDartmouth University.

Rachel Weir completed her disserta-tion “Canonical Divisors and InvariantSubspaces in Weighted Bergman Spaces”under the direction of Peter Duren. Shewill be an assistant professor at VirginiaPolytechnic Institute.

Dennis Keeler received the Sumner B. Myers Prize for the best Ph.D. thesis inmathematics for the year 2000. He was also one of only nine recent Ph.D. recipientsuniversity-wide to receive a Rackham Distinguished Dissertation Award. Keeler iscurrently a Moore Instructor/NSF Postdoctoral Fellow at MIT.

For his dissertation “Noncommutative Ample Divisors,” Keeler examined ampledivisors in ordinary commutative algebraic geometry. The ample divisor is used to rep-resent the variety in a particularly useful form and can be used as an analytical startingpoint. Keeler tackled the following questions that have been raised regarding ampledivisors: Under what conditions can an algebraic variety be expected to have a divi-sor? Are “left-handed” and “right-handed” noncommutative ample divisors different?Keeler proved that there are no differences between these two types of noncommuta-tive ample divisors. He also outlined criteria for an ample divisor. Many of his resultshave been published in the Journal of the American Mathematical Society.

Outstanding Dissertation Recognized

GraduateProgram NewsThe Mathematics Graduate Program

continues its success in recruiting and re-taining students. For the 2000-01 academicyear, there were 116 active students in thePh.D. and Masters programs. In March2001, the Department hosted anotherGraduate Recruiting weekend. Fourteenstudents attended the weekend, and ten ad-ditional students visited the department atother times. Twenty students have been ac-cepted to the graduate program for fall2001.

Rackham Predoctoral Fellowship

A mathematics student has again beenawarded a Rackham Predoctoral Fellow-ship for the 2001-02 year. An extrememlycompetitive fellowship, only 60 areawarded each year. Eduard-WilhelmKirr, who is studying under the directionof Anthony Bloch, received the fellowshipfor his dissertation “Resonance Phenom-ena in Hamiltonian Partial DifferentialEquations.” Kirr is developing a method ofinvestigating autonomous Hamiltonian sys-tems subject to time dependent perturba-tions. His study analyzes the couplingbetween the bound states and the radiationmodes of the unperturbed Hamiltonian. In-stability of the natural oscillations and theirdecay rate is obtained, and concrete appli-cations in quantum mechanics, optics andtelecommunications are presented.

Outstanding Graduate StudentInstructors

Elliot Lawes and Rachel Weir wereawarded the department’s OutstandingGraduate Student Instructor award for theyear 2000-01. Elliot has taught three differ-ent introductory calculus classes during thepast four years. He is studying under thedirection of Tom Hales. Rachel, who suc-cessfully defended her dissertation underthe direction of Peter Duren, has alsotaught three different intoductory calculusclasses during various semesters in her aca-demic career.

Million Dollar Friend

Graduate student Haggai Elitzur wasthe “phone a friend” for a contestant on“Who Wants to be a Millionaire” this year.He correctly answered the final $1,000,000question and his friend won the top prize!

15

New Undergraduate Programin Risk and Finance

The Departments of Mathematics andEconomics have developed a new interdis-ciplinary undergraduate concentration infinancial economics and mathematics.Modern finance uses mathematical meth-ods to study the behavior of firms and indi-viduals in asset markets, the marketdetermination of asset prices, and links be-tween financial market outcomes and theoverall economy. Finance addresses howfirms and households manage their affairswhen faced with risk and uncertainty. Italso addresses how risk affects overall eco-nomic outcomes.

The area of risk and finance is a naturalsubject for a joint program between eco-nomics and mathematics.

The disciplines share a common meth-odological perspective that uses rigorousmodeling in the formulation and solutionof problems.

The economic questions of finance—which involve the simultaneous modelingof risk and choices over time—require spe-cific advanced mathematical techniques.

Finance is an area in which the applica-tion of mathematics to understanding hu-man behavior has been especiallysuccessful. Principles derived from math-ematical reasoning have become a standardpart of the tools used on Wall Street and infinancial centers around the world.

A concentration in risk and financelinks well with the departments’ existingstrengths in areas such as actuarial scienceand macroeconomics.

The Departments of Mathematics andEconomics have collaborated to develop anew curriculum. It will be directed at topstudents who combine an interest in riskand finance with strong motivation for rig-orous analysis. A special feature of theprogram, which distinguishes it from busi-ness school programs, is that it will be situ-ated within a broader liberal arts context.

The program will be staffed by eco-nomics and mathematics professors whohave an interest in finance, but who areclosely integrated into their respective dis-ciplines.

Students in this program will receivethe benefits of a liberal arts degree, whichinclude exposure to a wide range of disci-plines and the central role of language andexpression as part of the educational expe-rience.

The new concentration will require sub-stantial resources. Funding is needed tohire faculty with broad interests in teachingand research in finance and the analysis ofrisk.

New specialized courses and a programof internships will be offered to build onthe departments’ strong base of existingcourses and programs.

There is widespread student interest inthe economics and mathematics of risk andfinance, and our alumni/ae have urged us todevelop such a program to respond to andsupport that interest.

Career Day 2000The department hosted another successful Mathematics Career Day conference in

October. Over 75 students participated in the event. Both graduate and undergraduatestudents were able to meet with representatives from business, education andacademia, and discover the opportunities available in business for mathematicians. Ev-eryone involved in the event agreed that it was a successful and worthwhile afternoon.

Alumni participants:

Eric Breck '98 - Computational Linguist, Boston, MA

Julie Frohlich '97 - Math Teacher, Troy School District

Kimberly Hartzfeld '93 - Manager, Anderson Consulting

David Kaprelian '85 - Consultant, Towers Perrin

Ed Kimball '71 - Principal Consultant, PricewaterhouseCoopers

Daniel Maki '66 - Chairman, Mathematics Department, Indiana University, Vice-President, CDT

Dick McLaughlin '62 - Technical Supervisor/Software Engineer, Bell Laboratories(retired)

Robert Nelson '75 - President, Airflow Sciences Corp.

Andrew Nobel '97 - Consultant, Anderson Consulting

Carmen Saleh '95 - Management Consultant, PricewaterhouseCoopers

16

Solution to Math Problemby Harm Derksen

Define for all n. Then for all n and wehave

.If for some n, then for all and weare done.

We may assume that for all .Suppose that there exists a con-stant N such that for all . Thisleads to a contraction because asand for all m. We conclude thatfor infinitely many positive integersm .

If , then

and where .

De�ne an := 2n=x � b2n=xc

for all n. Then 0 � an < 1 for

all n and we have

an+1 =

�2an if an <

1

2,

2an � 1 if an �1

2:

If an = 0 for some n, then

b2m=xcx = 2m

for all m � n and we are done.

We may assume that an 6=

0 for all n � 0. Suppose that

there exists a constant N such

that am � 1=2 for all m � N .

This leads to a contradiction be-

cause am = 2m�NaN ! 1 as

m ! 1 and am < 1 for all

m. Thus we conclude that am >

1=2 for in�nitely many positive

integers m.

If am �1

2, then

0 < (b2m=xc+ 1) x� 2m

= (1� am)x <1

2x < 1:

and bbmxc = 2m where bm =

b2m=xc+ 1.

The department’s team for the WilliamLowell Putnam Mathematics Competitionplaced 14th out of more that 434 teams par-ticipating in the event. The individual com-petition included 2818 students from acrossNorth America. This year’s team was com-prised of Chetan Balwe, who received anhonorable mention distinction for placingin the top 50 in the individual competition,Robert Easton, who individually placed inthe top 500, and Rishi Raj, who also re-ceived an honorable mention distinction forplacing in the top 50 in the individual com-petition. UM student Thomas Dunlap alsoplaced in the top 500.

Winner of the 18th Annual University ofMichigan Undergraduate MathematicsCompetition was Tomas Sirgedas. Tiedfor second place were Justin Altman,Amy Kimball, and Vivek Shende.

The William LeVeque Award in Num-ber Theory was presented to Jesse Kass.The award recognizes a student who is atmost a junior and excels in the study ofnumber theory.

The following students received EvelynO. Bychinsky Awards, designed to recog-nize underclassmen who show exceptionalpromise in mathematics:

Jeffrey AllottaRobert EastonAndrew JohnsonKalman NanesVivek Shende

The award for Outstanding GraduatingSenior went to Gabriel Kerr.

Bertrand Guillou received the SumnerMyers Award in Analysis, which recog-nizes a student who is at most a junior andexcels in the study of analysis.

Stacey Barbosa received the Leon P.Zukowski Prize for outstanding service inthe Math Lab.

Outstanding Achievement in Mathemat-ics Awards went to the following seniors:

Nicholas EhartAlan GrantJoseph MarsanoDiana MurrayJonathan NgMegan PowellBrian ReedBelal SabkiJennifer SingleLudmilla Teng

The Margaret S. Huntington Prize inActuarial Science was awarded to the fol-lowing first year students:

Kristen BarbosaBrian Chi Yan ChanValerian JoneZubin KapadiaJessica LobenherzFatih OzsolakAnne PiontekMarina PolishchukTyler RichardsonShiu May Young

The Irving S. Wolfson Award in Actu-arial Science was presented to GaryLevenbach.

Paul Kardosh received the Otto Rich-ter Memorial Prize in Actuarial Science.

Benjamin Singer received the Wirtand Mary Cornwell Award, recognizing astudent who, during the four previousyears, has demonstrated the greatest intel-lectual curiosity, given the most promise oforiginal study and creative work in math.

Undergraduate Award Recipients Actuarial ProgramHighlights

It was another eventful academicyear for the Actuarial students. Arecord number of firms visited thecampus during the fall semester pro-viding a number of interesting infor-mation sessions. The second annual“Mathematics Pizza Party for Under-graduates,” sponsored by CIGNA, washeld in October. In addition, studentswent on a day trip to visit Lincoln Na-tional in Fort Wayne in November (af-ter the examinations!). Recruiting wasvery active during the winter semesterwith most employers emphasizingsummer internship programs.

In conjunction with the 50th Anni-versary of the Conference of Consult-ing Actuaries, the American Academyof Actuaries sent a gift to the Univer-sity of Michigan, which was used tohelp fund fees for the professional ex-aminations of the Casualty ActuarialSociety and the Society of Actuaries.Because of gifts like this, we are ableto encourage more students to starttheir professional examinations.

The students helped to organize tu-toring sessions at a middle school inAnn Arbor in the fall, and participatedin the Detroit project during the wintersemester. In addition, there was activeparticipation in a number of intra-mu-ral sports. Unlike previous years, the“Underpaids” were victorious for thefirst time in a new sport for us—co-edinner tube water polo—where we wonsome richly deserved IM t-shirts.

- Professor Curtis Huntington

Yamina AceboDaniel AllenJustin AltmanKeith AndrewsDaniel BerebitskyRebecca BranchMatthew BuckmanJennifer ChaEmily ChengHendrik DoornJonathan EfronNicholas Ehart

Undergraduate Degree Recipients: December 2000, May 2001, August 2001Nathan FredericksWilliam GiffordDana GoldbergAnjela GovanAlan GrantLamont HamiltonTawni HarringtonNobuya HayashiKimberly HenlotterCarl HorwitzRyan HutchinsonEdwin Jung

Rebecca JurvaKathy KamPaul KardoshGabriel KerrJames KimEmily KonzenGarret Koski-BudabinLok-Yi KwokPaul LamSusan LeeJoseph MarsanoMarcus Matthews

Tim McMillenMichael McNamaraCherianne MilneBrian MonteithSiwatu MooreDiana MurrayJayjit NandwanaStefan NeboyskeyJonathan NgSara ParentHimani PatelMatthew Perry

Brian PoppenMegan PowellAnish RamachandranJoe RayBrian ReedBelal SabkiRichard SchierlohJoshua SchoreSusan ShortreedJennifer SingleSarah SnyderSarvesh Soi

Jeffrey SteinkrausBradley StetsonDavid StirrupJunichi TakayamaKuang TanSze TanLudmilla TengNicholas TrombettaWei VooNicole VulcanoChad Williams

17

William (Bill) J. LeVeque, former UMprofessor of mathematics (1949-1971) anddepartment Chair (1967-1970) has made agift to the department to establish an Excel-lence in Number Theory Fund. This endow-ment will be used to enhance the numbertheory program at Michigan by providingfunds for travel, seminar speakers, confer-ences and related activities.

LeVeque, the first number theorist onthe faculty, was instrumental in recruitingthe second, D. J. Lewis. Together they de-veloped a very strong program that is nowone of the world’s best. A steady stream oflong term visitors from England, Hungaryand Poland gave decided breadth and inter-national impact to the program.

LeVeque’s research areas included tran-scendental numbers, uniform distribution,and Diophantine approximation. His twovolume 1956 monograph “Topics in Num-ber Theory” was highly influential in thedevelopment of number theory in this coun-try, as was the MAA monograph “Studiesin Number Theory” that he edited.

In 1960 he conceived the idea of updat-ing L. E. Dickson’s “History of the Theoryof Numbers” that covered the subject fromantiquity to 1910. LeVeque assembled aWho’s Who in number theory, includingDavenport, Mahler, Erdos, Linnik, Turan,Renyi, and Deuring to work on the project,but the effort failed for lack of funding. In1974 he accomplished part of his goal bypublishing a six volume collection “Re-views in Number Theory” containing all re-

views in number theory that appeared inMathematical Reviews (MR) from 1940-1972 assembled by topic, for easy referenceand for ease in seeing historical develop-ments. The Special Libraries Associationgave him an award for this effort.

The Reviews were updated in 1984.This collection had a profound impact onthe subject and was referenced almost dailyby researchers.

In 1964, when Ann Arbor was chosenas the new site for MR, LeVeque took onthe task of relocation, finding space, as wellas recruiting and training a staff. In June1965, MR moved and LeVeque served asExecutive Director for the next 15 months,guiding MR to stability.

In 1977, LeVeque became ExecutiveDirector of the American Mathematical So-ciety—a position he held until his retire-ment in 1988. As Director he led the societyto become a major publisher of books andjournals, thereby putting it on sound finan-cial standing. He pioneered the use of com-puters in printing, funded the developmentof LaTex, and played an encouraging rolein the computerization of the MR data base,which made MathSciNet possible.

While an immensely imaginative andsuccessful administrator, LeVeque neverlost his love and interest in number theory.His generous gift will help number theoryto flourish at Michigan, and the current fac-ulty members in number theory greatly ap-preciate his contribution.

LeVeque Gift Funds Number Theory

Alumna Karen K. Uhlenbeck (BS '64,PhD '68 Brandeis) was awarded the Na-tional Medal of Science. She was one of 12American scientists and engineers to re-ceive the medal, that was presented at a cer-emony in December in Washington, D.C.

In announcing the National Medal ofScience winners, former President BillClinton declared “These exceptional scien-tists and engineers have transformed ourworld and enhanced our daily lives. Theirimagination and ingenuity will continue toinspire future generations of Americanscientists to remain at the cutting edge ofscientific discovery and technological inno-vation.”

Uhlenbeck, who holds the Sid W.Richardson Foundation Regents Chair inMathematics at the University of Texas atAustin, conducts research in geometry andpartial differential equations and studies ap-plications of geometry to large-scale prob-lems in high-energy physics. She isinterested in the ways complex mathemati-cal concepts find uses in research in otherareas of science, such as ecology, molecularbiology and the structure of materials.

Uhlenbeck received the National Medalfor Honor, the highest honor conferred onU.S. scientists, for her pioneering contribu-tions to global analysis and gauge theoryresulting in advances in mathematical phys-ics and the theory of partial differentialequations. Cited as one of the founders ofgeometry based on analytical methods, shewas also recognized for her leadership as amentor for women and minorities in math-ematics education.

“I feel very humble, as many greaterscientists have received this award,”Uhlenbeck said. “I hope that my acceptancewill serve as encouragement to youngwomen scientists and mathematicians.”

Uhlenbeck has taught at UT Austinsince 1987. She was born in Cleveland andgrew up in New Jersey. Prior to her ap-pointment at UT Austin, she held facultypositions at University of California Berke-ley, University of Illinois and University ofChicago. In addition to receiving numerousawards, honors and fellowships, includingmost recently a Guggenheim Fellowship for2002, Uhlenbeck received the UM Alumnaof the Year Athena Award in 1984.

Alumna ReceivesMedal

Professor and Mrs. CameronCourtney have established the Cameronand Jack Courtney Graduate Fellowship inthe Department of Mathematics. The fel-lowship is named after Cameron Courtney,who received his Ed.D. in 1965, and hisson John (Jack) Courtney, who receivedhis Ph.D. in 1993. Funded through a chari-table remainder trust, the fellowship willprovide financial assistance to a deservinggraduate student.

Cameron was a student of Phil Jones atUM, and spent 24 years teaching at UM-

New Graduate Fellowship EstablishedFlint and Dearborn campuses. When he de-cided to pursue his graduate education atUM, he was married with a child. He isgrateful for the financial assistance he re-ceived during his studies, and that is thereason he has established a graduate fellow-ship.

Jack Courtney worked with ChristophBorgers in Numerical Analysis. Jack wasthe first student to finish in the ScientificComputing option that had just been estab-lished. He is now on the faculty of Michi-gan State University.

18

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