Harvey Mudd MathematicsDepartment Garners AMS Award

458 NOTICES OF THE AMS VOLUME 53, NUMBER 4

Ten years ago the mathematics department at Har-vey Mudd College was a very good departmentknown for excellent teaching and for innovationslike its “clinic” in which student teams work onmathematics problems from industry. The de-partment was doing well, and likely there wouldhave been no complaints had it remained as it was.Instead, the department has over the past decadebrought itself up to a new level to become one ofthe best places in the nation to be an undergrad-uate mathematics major. The quantitative mea-sures of the department’s success went through theroof, with the number of majors tripling and morethan half of them going on to graduate school. Butwhat really changed is how the department unifieditself around its core mission of promoting teach-ing and scholarship in ways that inspire faculty andstudents alike to do their best work. For its out-standing performance, the Harvey Mudd mathe-matics department this year received the first-everAMS Award for an Exemplary Program or Achieve-ment in a Mathematics Department.

How did the department get to where it is today?One important factor is that it built upon itsstrengths, one of which is the Harvey MuddMathematics Clinic. Professor emeritus Robert

Borrelli was deeply involved with the clinic from itsinception in the 1970s, and other faculty—StavrosBusenberg, Courtney Coleman, and Henry Krieger—served as directors of the clinic up to the 1990s. Theclinic teams up senior mathematics majors to workon mathematical problems supplied by industry.These are real-life problems, messy and ill posed,and a crucial factor in making the program workwas the ingenuity of the Harvey Mudd faculty in figuring out how to distill the problems down toworkable projects for the student teams. During the1970s and 1980s the faculty introduced other in-novations as well; for example, Borrelli and Colemanencouraged their students to experiment with soft-ware for solving partial differential equations at atime when not much of this kind of software wasaround. This experimentation evolved into the ODEToolkit, now available on the Web. Borrelli andColeman also founded an interdisciplinary studentresearch journal called Interface.

In the mid-1990s the department, facing a bigwave of retirements, seized the opportunity toreinvent itself. A key step was hiring Michael Moody,a mathematical biologist from Washington StateUniversity, to take over as department chair. “Hewas a wonderful leader, very charismatic, with lotsof ideas,” noted Lesley Ward, who came to HarveyMudd in 1997. “He would see what should be donein the future and then lay out the steps to getthere.” Moody set for the department what hecalled an “animating goal”: To be recognized as one the very best undergraduate programs in thecountry.

During Moody’s six years as chair, from 1996until 2002, the department hired eight new pro-fessors; the total number of faculty is twelve. Heand Arthur Benjamin, who had come to HarveyMudd in 1989, worked as a team to do much of the hiring. Moody recalled that he and Benjamin resonated on what they wanted: “We wanted peo-ple who would mesmerize and inspire students in the classroom and have a passion for their math-ematical work.” In addition, the department waslucky in the timing of its hiring. Current chair Alfonso Castro, who came to Harvey Mudd three

Harvey Mudd mathematics department, fall 2005. Left toright: J. Milton (visitor), H. Krieger, F. Su, A. Benjamin,

A. Castro, D. Yong, L. de Pillis, L. Ward, S. Martonosi, S. Frantz,A. Bernoff, W. Gu, J. Jacobsen, M. Orrison, and D. Goroff. Not

pictured are M. Raugh, B. Schade, and C. Connelly.

APRIL 2006 NOTICES OF THE AMS 459

years ago, noted that because the 1990s were toughyears for job seekers in mathematics, the depart-ment was able to hire junior people who under different circumstances would likely have gone totop research universities. “These young faculty notonly bought into the mission of quality teaching atthe undergraduate level, they also established afirst-rate presence in the research community,” hesaid. Some of the candidates sensed the depart-ment’s newfound dynamism and were attractedby the prospect of contributing to the building ofa new department. “That was exciting to me,” notedFrancis Su, who came to Harvey Mudd in 1996.

Young, newly hired faculty were given big re-sponsibilities early on. Soon after Ward came toHarvey Mudd, she and Su, together with senior faculty member Henry Krieger, took on the task ofrestructuring the department’s core curriculum.This two-year collection of courses is taken by allHarvey Mudd students. After consulting with otherdepartments about what their majors needed to getout of the core mathematics curriculum, Krieger,Su, and Ward reconfigured the four, semester-longcourses into eight courses that run half a semes-ter each. They also added to the core a new coursein statistics and probability and introduced a strand in discrete dynamical systems. “This boughtus huge credibility inside the institution,” Moodynoted, because the other departments felt thattheir concerns were heard and taken into account.He took flak from some senior faculty who con-sidered the changes too radical, but he was notperturbed. “I grew up in a system where assistantprofessors were seen and not heard to a large ex-tent,” he noted. “But they have creativity and energy,and if you leaven that with an experienced personwho has a light hand on the tiller, they’ll do greatthings. Plus they’ll be invested in it.”

Also around this time the department revampedthe mathematics major. Over the years the majorhad morphed into a system with several differenttracks, and there would sometimes be just one ortwo students per track, leaving them feeling some-what isolated. The department now has a single, uni-fied major centered on a core set of six advancedcourses. Students take electives to customize theirown programs in consultation with faculty advisors.In addition, the department launched two new majors: the joint major in computer science andmathematics that started in 1998 and a major inmathematical biology that started in 2001.

Every senior major in the department must takepart in a “senior research experience”, which canmean either participating in the mathematics clinicor writing a senior thesis. The strong traditionbuilt up over thirty years of running the clinicserved the department well when directorship ofthe clinic passed in 1999 from Borrelli to then-newly hired faculty member Michael Raugh.

(Raugh also cre-ated and servesas the directorfor a version ofthe clinic at theInstitute forPure and Ap-plied Mathe-matics at theUniversity ofCalifornia, LosAngeles.) Therange of topicscovered in theHarvey MuddMathemat i csClinic is enor-mous; in recentprojects, stu-dents have worked on such topics as gene expres-sion data, global positioning system algorithms,soliton-like water waves, and cryptography.

The department set about revitalizing its seniorthesis by raising standards and by introducing additional structure, such as having students participate in a weekly seminar in which they give talks to each other about their work as it pro-gresses. Small changes like preparing hardboundcopies of theses and storing them on shelves wherestudents can browse through them help to conveythe message that the department believes that writ-ing a senior thesis is a serious and substantial un-dertaking. At the end of the year, all graduating se-niors must participate in “Presentation Days”, athree-day, collegewide miniconference in whichstudents from all departments present talks abouttheir work. “The fact that we as a college decidedit’s more important to have three days of presen-tations than three more days of lectures says a lot about how the college values undergraduate research,” commented Ward.

But is it really possible to involve undergradu-ates in mathematics research? Absolutely, said Su.“I believe undergraduates at any level can do re-search,” he said. “There are many kinds of researchexperiences. In terms of serving a student, what isvaluable for the student is learning to inhabit theresearch process.” The goal is to give the studentsan experience in mathematical discovery that allowsthem to understand what research is like. Su notedthat even in a deep field where there are not manyeasy problems lying around—say, differential geom-etry—there are nevertheless problems that under-graduates can sink their teeth into. For example, hiscolleague Weiqing Gu has come up with problemsin M-theory and string theory that boil down tospecific systems of partial differential equations.Without possessing extensive background, an undergraduate can work on solving such systems

In the HMC Mathematics Clinic, teams ofstudents work with faculty and companyliaisons to solve open-ended real-worldproblems. Here Lisette de Pillis (standing,left) supervises a network optimizationproject for ESRI Corporation.

460 NOTICES OF THE AMS VOLUME 53, NUMBER 4

and makeprogress onunderstand-ing them ana-lytically andg e o m e t r i -cally. Theproof that thedepartment’sa p p r o a c hworks is inthe publica-tions: Since2002 at leasttwenty pa-pers havebeen pub-lished, manyof whichwere basedon senior the-ses and writ-ten jointly byfaculty andstudents, andmany stu-dents havepublished pa-pers on theirown. Thereare otherproofs aswell. HarveyMudd mathe-

matics major Joshua Greene received the 2002AMS-MAA-SIAM Morgan Prize for outstanding re-search by an undergraduate, and another HarveyMudd student, Aaron Archer, was a runner-up forthis distinction in 1998.

Of course, for the students to have a meaning-ful research experience, the faculty themselveshave to be engaged in research. And at HarveyMudd, they are. The department’s publication out-put is impressive, and several faculty are supportedby research grants from the National Science Foun-dation (NSF). The Keck Foundation provided a three-year grant for the Center for QuantitativeLife Sciences, which is codirected by mathematicsfaculty member Lisette de Pillis and a biology fac-ulty member. The center has developed new coursesin mathematical biology, hosted research visitors,and funded two dozen multidisciplinary summerresearch projects. The Harvey Mudd mathematicsfaculty has also been represented in major researchconferences: Gu was an invited speaker at the International Congress of Mathematicians in Bei-jing in 2002, and four other faculty—Ward, Su, de Pillis, and Andrew Bernoff—have been courselecturers at the Park City Institute for Advanced

Study summer mathematics conferences. In 1999the department began organizing its own annual,one-day regional research conference. With topicsranging over analysis, algebra, geometry, mathe-matical biology, and scientific computing, the conferences typically attract fifty to seventy-fiveparticipants. Although this is a bona fide researchconference, with experts in the field presentingtheir latest work, Harvey Mudd students are en-couraged to attend just to soak in the atmosphere.“We always have significant student attendance atthe conferences,” Moody remarked.

Hand in hand with the emphasis on research andscholarship is the department’s strong commit-ment to excellence in teaching. As Ward put it, atHarvey Mudd “it’s okay to spend a lot of time onmaking your classes great.” As at other places, thecollege is trying to come to grips with how to doc-ument good teaching. Student evaluations are used;also, when an individual comes up for promotionor reappointment, he or she must get other facultymembers to write letters of recommendation focused on teaching. But what really seems to makethe biggest difference in the department’s teach-ing is a highly developed sense of collegiality andcollective responsibility. “We are really generousand free in sharing teaching ideas,” Su noted. Herecalled that when he was teaching a certain coursefor the first time, his colleague Art Benjamin lenthis lecture notes to Su. It has become a traditionto hand down one’s lecture notes. Su has developeda large collection of what he calls “Fun Facts”, interesting tidbits about a wide variety of mathe-matical topics that can be presented in about fiveminutes at the beginning of a lecture to awaken students’ interest and expand their ideas of whatmathematics is. Su started sharing the “Fun Facts”over the Web, and now other professors are usingthem. On a daily basis the faculty discuss witheach other many teaching issues, large and small.“If we go to lunch, we are as likely to be discussingteaching as research,” Ward remarked. The collegehas no teaching awards, but Harvey Mudd mathe-maticians have received such awards at the na-tional level: In 2000, Benjamin received the HaimoAward of the Mathematical Association of Amer-ica, and in 2004 Su received the MAA’s Alder Award.

The department’s efforts to renew itself havemade a big difference in its ability to attract stu-dents into mathematics. “The students picked upa different feel” from the mathematics depart-ment, Moody noted. “They could tell we really cared about them.” The number of mathematics ma-jors increased from a low of ten in 1993 to aboutthirty per year in recent years. The class of 2006has forty-one majors, nearly one quarter of HarveyMudd seniors (this number includes computer sci-ence/mathematics and mathematical biology ma-jors). The number of women has also increased, and

Jon Jacobsen and Francis Su demonstrate thefluid dynamics of a vortex cannon (the stable

toroidal ring will blow out the candle Su isholding). Many HMC math faculty use physical

demonstrations in their lectures.

Weiqing Gu (standing) advising a team ofstudents on a summer research project

concerning tumor modeling andimmunotherapy for cancer patients. The

project was supervised by Lisette de Pillis.

APRIL 2006 NOTICES OF THE AMS 461

women now account forabout one third of all math-ematics majors, the sameproportion in which womenare represented in the Har-vey Mudd student body.(With the hiring in fall 2005of Susan Martonosi, the pro-portion of women in themathematics departmentfaculty is also one third.)Among students who fin-ished the mathematicsmajor between 2002 and2005, about 60 percent wenton to graduate school, andmany were accepted in thetop mathematics graduateprograms in the country. Inthe past five years, nineteenHarvey Mudd mathematicsmajors were awarded theprestigious NSF GraduateResearch Fellowships, andanother sixteen were namedhonorable mentions. Majorswho do not choose graduateschool are heavily recruitedby business, industry, and government.

Not only has the department attracted moremathematics majors, it has also attracted morenonmajors to take part in its programs. For ex-ample, sixty to seventy students—about 10 percentof the Harvey Mudd student body—take part in theweekly Putnam Seminar, in which the studentswork on practice problems for the Putnam Com-petition. The seminar is led by Bernoff and Su, whohave put the emphasis on having fun solving prob-lems rather than on honing an elite team. In theprocess, the department does manage to hone anelite team: Harvey Mudd has placed in the top tennationwide in the Putnam Team Competition in fourof the past five years and is the only undergradu-ate college to have made it into the top five in thelast thirty years. High participation by nonmathe-matics majors also occurs in the MathematicalContest in Modeling and the Interdisciplinary Con-test in Modeling (both of which are sponsored bythe Consortium for Mathematics and its Applica-tions). Harvey Mudd has done very well in both com-petitions, and the winning teams have often com-bined mathematics majors and nonmajors alike.

Even with all the energy and attention the de-partment puts into its own programs, it neverthe-less manages to find ways to reach out beyond thecampus. In 2000 mathematics faculty member Dar-ryl Yong, together with three Harvey Mudd facultyfrom other departments, started an outreachprogram in Pomona High School, which is in a low-

income neighborhood.This program brings Har-vey Mudd students into theschool’s classrooms, whichare populated mostly byLatino students, to lead ac-tivities designed to inspireinterest in mathematics,science, and engineering.In 2004 mathematics fac-ulty members Michael Or-rison and Jon Jacobsentraveled to Jamaica to leada workshop designed toenrich the mathematicalbackground of Jamaicanteachers. They plan tooffer the workshop againin 2006.

Harvey Mudd recentlyhired mathematicians inits top two administrativeposts: Daniel Goroff camefrom Harvard Universityto become vice presidentand dean of faculty in July2005, and Maria Klawe willcome from Princeton Uni-

versity to take up the post of president in July2006. And a couple of years back, the college losta faculty member who went on to an administra-tive post—namely, Michael Moody, who is now thedean of faculty at Franklin W. Olin College of En-gineering, an innovative engineering school thatopened its doors in 2002. Moody was thrilled whenthe department received the AMS Award for Ex-emplary Achievement and also felt a pang of home-sickness. “I’m so proud of the department,” hesaid. “I can’t imagine a more deserving group of peo-ple—I am completely biased of course!—but theyreally are incredibly dedicated to mathematics andto the community they have created.”

Where does the department go from here? Howdoes it sustain its success? Moody pointed to theneed to continue to develop programs that bringfaculty together as teams so that they set aside dif-ferences and work toward a common good. Su saidhe has seen exactly this happening organically inthe department: One faculty member gets an ideato try something new, and he or she convinces col-leagues to come on board. If too many ideas pro-liferate, the department will have to prioritize, butfor now Su is happy to let things develop in thisorganic way. “But whatever we do, our mission isto engage undergraduates in research and discov-ery,” Su said. “That will always be central.”

—Allyn Jackson

Harvey Mudd College students before(above) and after the 2005 Putnam exam.

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