Mathematics will aid Carnegie in defining needed Ph.D. qualities

Nils Barth, a third-year Ph.D. student in Mathematics, whose specialty is high-dimension geometry, teaches Math 133/Calculus.

There is more to educating doctoral students in mathematics than teaching them Zermelo-Frankel set theory, the Mayer-Vietoris sequence and Green’s functions for differential equations. That is why the Carnegie Foundation for the Advancement of Teaching has selected the Mathematics Department and 31 other leading graduate programs in chemistry, education, English and mathematics to participate in a five-year research and action project aimed at improving U.S. doctoral education.

The foundation’s focus for the project is to define the qualities a new Ph.D. should exhibit upon graduation.

“It’s somewhat broader than just asking how we can produce more and better research mathematicians,” said Kevin Corlette, Professor and Chairman of Mathe-

matics. “We also want to determine how we can produce research mathematicians who will be stewards of the field who contribute to its health at all different levels.”

The Mathematics Department’s Graduate Affairs Committee, co-chaired by Peter May, Professor in Mathematics and the College, and Paul Sally Jr., Professor in Mathematics and the College, already has met twice to discuss the project.

“The first year to year and a half will largely be devoted to internal deliberations about experiments we might want to carry out and a review of the graduate program from the ground up,” Corlette said. “We expect there will be certain experiments that we want to try, and Carnegie will provide some support for those experiments.”

One idea is to start a teaching seminar for graduate students to augment the training they receive during their second year. The faculty also will probably discuss how to ensure that graduate students receive a broad education in mathematics and how to improve the two-adviser system the department adopted for Ph.D. students more than a year ago.

Other possible issues to address include the steadily increasing time it takes students to complete a Ph.D. and how to respond to a shrinking academic job market in bad economic times.

The Carnegie program can be viewed as an extension of the National Science Foundation’s VIGRE, Vertical Integration of Research in Education, Corlette said. In fact, the Mathematics Department’s successful implementation of its own VIGRE grant was one reason Carnegie invited Chicago to participate in the foundation’s doctorate initiative.

The department, at least since the 1970s, has practiced vertical integration–integrating the activities of undergraduate students, graduate students, postdoctoral researchers and senior faculty members–May said. This is quite uncharacteristic of the nation’s other top mathematics departments, he added.

“We’re as successful in teaching at all levels as we are in doing research, and that’s not easily accomplished,” May said. “I don’t know any place that does it as well.”

The department actively shares its expertise through such community outreach efforts as the Young Scholars Program, Seminars for Elementary Specialists and Mathematics Educators, the Summer Seminar in Calculus, and the Seminar Program for High School Teachers.

“Also, the graduate program is much better integrated into the undergraduate program, both because of the way graduate students teach and the esprit de corps that develops with the undergraduates serving as tutors for classes taught by the graduate students,” May said. “It builds extraordinary cooperation between the two groups.”

This summer, the department’s Research Experience for Undergraduates Program will begin its fourth year. Funded by the VIGRE grant, last year’s program attracted participation from 45 students of the College.

The REU has had a noticeable impact on the department’s production of bachelor’s degrees, May said. Most of the Mathematics Department’s peers produce no more than 1 percent of their institutions’ graduates. This year, 80 students are concentrating in math or double concentrating in math and another field. They will comprise 8 percent of the graduating students.

“Last year it was 6 percent. The year before it was 5 percent. This, I think, is directly attributable to the REU,” May said.

The number of women enrolled in the graduate program also has nearly doubled in the last three years, even though the department has no female tenured faculty members. Twenty-seven of 100 graduate students in mathematics are women, for which May credits the department’s collegial atmosphere.