New Cross-disciplinary Graduate Programs Up and Running at U.S. Universities

November 1, 1999

At the heart of the National Science Foundation's IGERT (Integrative Graduate Education and Research Training) program, evident even on a quick reading of the official program announcement (, which includes links to all IGERT programs established to date), are some intriguing concepts: "innovative, research-based graduate programs," "broadly prepared PhDs with multidisciplinary backgrounds," "broad spectrum of career opportunities."

In August, NSF announced the second round of IGERT awards (a total of $54.5 million over five years to 21 doctorate-granting institutions in the U.S.), and this fall, the first students at the 17 first-round institutions began their studies. The program, according to NSF director Rita Colwell, is producing "a culture change and new perspectives, for both students and faculty, on the role of researchers and their career opportunities."

For SIAM, all this seems to be very much in the spirit of its 1995 (NSF-funded) Report on Mathematics in Industry. The report presents the results of an in-depth study of the relation between the knowledge and skills needed for success in industry (or government or business), as perceived by both mathematicians and their managers, and the extent to which graduate programs were seen as producing those qualities. An overwhelming 90% of SIAM's survey respondents believed that change in graduate education was needed. To learn about changes being introduced at IGERT institutions, SIAM News looked into two of the most mathematically oriented programs created in the first round of awards: the Program in Non-linear Systems at Cornell University, and Multidisciplinary Training at the Interface of Biology, Mathematics and Physics at the University of Arizona.

Nonlinear Systems
"The subject of nonlinear systems is wonderfully broad," says Cornell program director Steven Strogatz, "with important applications in fields ranging from physics and mechanical engineering to medicine and finance." This breadth, he points out, is rarely conveyed in a traditional PhD program. "A mathematics student studying dynamical systems is unlikely to cross paths with an immunologist studying AIDS or an electrical engineer studying blackouts in the power grid---yet they are all investigating nonlinear phenomena."

The Cornell program has ten students, five just beginning their graduate work and five second- or third-year students who were already enrolled in Cornell PhD programs. Students are admitted to the program, which is administered by Cornell's Center for Applied Mathematics, through one of Cornell's graduate fields. More than fifty faculty, from six colleges at Cornell and several outside institutions, are involved in the program. Duncan Callaway, who is taking a year off from an NSF graduate fellowship to participate in the IGERT program, is in theoretical and applied mechanics, with microbiology and applied mathematics as minor areas of specialization. He has done two internships, one in the zoology department at Oxford University and the other in the theoretical biology and bio-physics group at Los Alamos National Laboratory, working at both places on theoretical aspects of HIV immunology.

The internships, he says, gave him "incredible opportunities to interact with immunologists and doctors studying HIV in a clinical setting" and strongly influenced the direction of his research: "I learned what's important in this field, what issues remain to be addressed, and how people are tackling problems." The IGERT fellowship, he tells SIAM News, "is an exceptional opportunity to work with the experts in any area of interest because you don't need to apply for any additional funding or rely on your host to provide it. Consequently, it isn't hard to work with whomever you please."

A summer internship---in a financial, industrial, laboratory, or clinical setting---is a requirement for all IGERT students at Cornell. First-year student Chris Maloney, a physics major from the University of Missouri, is leaning toward a Wall Street experience. "It's far from my career goals," he says, "but I'd like to get out and see how that side of the world operates . . . where the stuff gets applied in a totally different way."

Both Maloney and Callaway envision academic careers, although neither seems inclined to close the door on the "broad spectrum of opportunities" intended by the creators of the IGERT program. Maloney thinks that a position in a national lab could be extremely interesting, and Callaway mentions positions in a biotech company or in the pharmaceutical industry as possibilities for someone with his interests and experience.

In addition to completing the requirements for a PhD in their chosen fields, the IGERT students come together for an integrated two-semester course in nonlinear science (the mathematics of chaos, pattern formation, nonlinear PDEs, complex systems, stochastic methods, and computer simulation), to be taught for the first time this spring. For each topic, Strogatz says, the science will be studied alongside the mathematics. Thus, discussions of optical fibers will be part of the students' study of solitons; similarly, finance will be considered with the study of Brownian motion, fluid convection with pattern formation, and the propagation of nerve impulses with reaction-diffusion equations. Faculty from the varied disciplines will participate throughout the course.

As they move through the program, Strogatz says, the students are learning new scientific languages, "an essential skill for anyone hoping to work in cross-disciplinary settings." The weekly seminars that constitute the first semester of the integrated course are already succeeding in that respect, according to Callaway, who describes them as "a great opportunity to 'think outside the box,' to train yourself to speak other people's language." In a way, he says, "I think that this program is like a language course: We arrive with a certain set of basic skills and . . . the program then challenges us to introduce these skills to a field which traditionally works without them."

At the Biology/Mathematics/Physics Interface
Creating meaningful interactions and graduate training opportunities at this interface is a challenging task, says Michael Tabor, head of the Program in Applied Mathematics and director of the IGERT program at the University of Arizona. "When a fascinating problem in biology is modeled mathematically, the biological connections can sometimes take second place to the model," he explains. "At the same time, the biologist needs to recognize that quantitative methodology should involve far more than the use of standard statistics procedures or canned software to analyze experimental data."

For true interdisciplinary advances, he points out, research collaborators need to be immersed in the facts and methodologies of their common research problem. In particular, mathematicians and physicists must be exposed to the laboratory aspects of a biological problem. Accordingly, the students in the IGERT program at Arizona are involved in research and training activities with multidisciplinary faculty teams (more than twenty faculty from eight departments in the colleges of science and medicine). As at Cornell, students enter through the disciplinary department of their choice and complete the requirements for a PhD in that discipline.

The two key components of the IGERT program are a "multimode" biomathematics seminar and a biological physics laboratory course. Planning for the lab course (based on the experience of the university's Applied Mathematics Experimental Laboratory) is now under way; students can look forward to experiments invol-ving the technique of laser tweezing, electrophysiology, and self-organization processes in biology. The seminar, according to current organizer Joe Watkins, an applied mathematician, adapts to the interests and levels of the students. With beginning graduate students, one strategy is to find mentors---Arizona faculty or outside visitors---who can build multidisciplinary interactions in areas of the students' research interests. This strategy led to three minicourses in the current semester's seminar---on physiology, biophysics, and biochemistry.

More advanced students, Watkins explains, present their research ideas and vision in the seminar, inviting interaction with faculty and other graduate students. The students later make follow-up presentations to report on progress made "and often to celebrate a success." The most advanced students, for whom career possibilities are becoming a pressing consideration, benefit the most from outside seminar speakers. Alan Perelson of Los Alamos was one very successful visitor, Watkins says. He spent a lot of time with the students, discussing the issues that arise in collaborations between medical scientists and mathematicians, and, in particular, some of the decisions made in developing the models that led to the well-known "cocktail" used in the treatment of AIDS.

The biomathematics seminar, in the words of Dmitry Kondrashov, a third-year graduate student in the applied mathematics program, brings "disparate and largely entirely isolated research areas together-biology on any scale, from molecules to populations---unified by the common thread of mathematical mo-deling." Kondrashov, who works in protein biophysics, has been a regular parti-cipant in the seminar for more than a year. He finds it simultaneously enriching---touching on disciplines that he "never even wanted to hear about" and bringing together people from many departments---and frustrating, largely because of the inevitable need to begin with the basics for any problem presented to such a heterogeneous group. In the end, he pronounces the seminar "unconventional," sometimes reaching "extraordinary."

As an undergraduate premedicine/mathematics major, first-year student Tessa Osborne-Smith worked on a model of the auditory system, finding in the process that she wanted to dig deeper into both the biology and the advanced mathematics. "An interdisciplinary program seemed the obvious choice," she tells SIAM News.

Now enrolled in the seminar, she considers the presentation she gave during the physiology minicourse "a wonderful experience . . . because it allowed me to build on my basic knowledge of muscle structure and the vascular system, and it opened my mind to thinking of the systems in terms of mathematical modeling---presenting some of the questions that arise in the construction of a model."

Pharmaceutical sciences student Stacey Tannenbaum, whose concentration is in pharmacokinetics, has found the seminar a welcome "chance to step away from pharmacokinetics for a while and learn about something completely new and different. . . . In many cases, the other students were able to give me fresh insights that helped me take my work in new directions I would otherwise never have considered."

Looking to the future, Kondrashov ponders the "unusual situation" of a person whose research crosses disciplinary boundaries: "It is entirely unclear to me which traditional department could hire me."

Mathematics, physics, chemistry, biology---maybe none would be interested, he says, or maybe all. Although disciplinary divisions are far less rigid in government labs and in industry, he is not ready to give up the idea of an academic career. "If anything is certain," he concludes, "it is that my career will be untraditional, thanks to the applied math program and the IGERT program."

An academic career, "and/or working with conservation groups," are the career possibilities cited by second-year student Will Turner, from the ecology and evolutionary biology department. "It seems there's a schism between theoreti-cal/mathematical researchers and field/empirical researchers in ecology," he says. "I'd like to lie square in the middle of this continuum: Theory and observation/empiricism complement one another, each informing the other as to the next step to take."

Thinking mainly in terms of an academic career, Tannenbaum has found the students and faculty in the biomathematics seminars "an ideal audience for teaching practice: completely new to the topic and from varied backgrounds." And if she opts for an industrial career, "the collaboration with the other students and faculty in the biomathematics group will be greatly beneficial."

This program, Tannenbaum says in conclusion, "has been of great help to me as a student, a scientist, a teacher, and a researcher." It's a rare person who cannot benefit from an outside perspective, "and I feel that this is a major benefit of being part of this group."

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