Program opens students’ eyes to research in math sciences

Program opens students’ eyes to research in math sciences

BY JADE BOYD
Rice News staff

When Carl Hammarsten signed up for Math 499 last year, he wasn’t sure what to expect. Even so, the Brown College senior would never have guessed how far he would come in one year: standing at a blackboard leading a research discussion for a dozen people, including two professors, a graduate student and a postdoctoral student.

Hammarsten, who seems to exude confidence at the board, follows the talk by reassuring a fellow undergraduate who wants to join the group. “We were all nervous about (leading a discussion) at first, but it’s really important,” he said. “There’s a real difference between learning something well enough to take a test on it and learning it well enough to teach it.”

The class, “Geometric Calculus of Variations,” is one of 11 seminar sections offered this fall under Rice’s Vertical Integration of Research and Education (VIGRE) program.

In its third year, the program directly involves at least 17 faculty, six postdoctoral instructors, 18 graduate students and about 50 undergraduates from the departments of Mathematics, Statistics and Computational and Applied Mathematics (CAAM). Funded with a five-year, $2.3 million grant from the National Science Foundation, VIGRE was intended to open up whole new dimensions of the mathematical sciences student experience at Rice, and by all accounts, it has been successful.

“Every science and engineering student at Rice passes through our three departments as freshmen and sophomores,” said Steven Cox, a professor of CAAM who participates in three VIGRE seminar sections. “Even though a good fraction of them are looking for a research internship, most of them never consider pursuing mathematics research. We’d like to change that by giving them a taste of what math research is really like.”

Within VIGRE, seminar sections are known as “PFUGs.” The acronym derives from the group composition of post-graduates, faculty, undergraduates and graduate students. Pronounced like the word fugue, the name captures the spirit of vertical integration that’s central to VIGRE, alluding to the musical name for a piece that is introduced by one voice and developed by others.

Almost all PFUGs are interdisciplinary. By their very nature, they strive to weave together intellectual paths from pure math, numerical methods, statistics and a particular area of science like finance, genetics or medical imaging. Furthermore, each PFUG is centrally focused on an active research question.

“This is not a lab exercise or an elaborate homework problem with a known answer,” said Michael Wolf, professor and chair of mathematics and the principal investigator on the VIGRE grant. “These are real problems, with unknown answers.

“In a traditional classroom setting, that’s a scary prospect, because the group might work all semester and not find an answer,” he said. “But it’s the process of trying to work collectively to solve a problem that we want students involved in.”

Another primary goal of VIGRE is to give graduate students and postdocs exposure to classroom teaching and firsthand experience in directing research groups. Toward that end, the majority of VIGRE funding goes toward the salaries of graduate and postgraduate instructors in each of the 11 sections. Significant funding is also available for undergraduates participating in VIGRE’s summer research programs.

“The VIGRE program gave me classroom teaching experience that helped me land a tenure-track faculty position,” said Ginger Davis, a 2005 statistics Ph.D. recipient who began her academic career this fall as an assistant professor of systems and information engineering at the University of Virginia.

“VIGRE taught me some valuable lessons about teaching and doing research with people who have different backgrounds,” said Davis, who taught a section of STAT 280 and participated in the computational finance PFUG last year. “On the teaching side, I learned how important it was to get feedback, and get it early. I learned not to assume that students had all the background they needed to start working on a problem.

“On the research side, I learned how valuable it was to have a breadth of knowledge and experience in a group. People shared different approaches and had ideas I would never have thought of.”

VIGRE faculty say a large measure of credit for VIGRE’s success goes to the original three department chairs from math, CAAM and statistics — Robin Forman, Bill Symes and Kathy Ensor, respectively — who played lead roles in landing the grant and who served as principal and co-principal investigators during the first two years of the program.

“Leadership was one of the keys to making this all happen,” Cox said. “I think VIGRE’s structural changes — taking research seminars for credit, the vertical PFUG mix — are here to stay.”

Cox said the program’s approach of exposing students to the process of research is also likely to outlast the grant. Cox is not surprised that PFUG participants, be they students or instructors, become personally invested in the group’s research. “Pride of ownership” is a term that’s been used to describe the sense of commitment members feel to PFUG, and Cox said that was part of VIGRE’s formula from the beginning.

“The thing that surprised me the most about VIGRE was how free-form it was,” Hammarsten said. “Up until now, math has always involved working on whatever I was assigned. With this, what I think of to work on is what I work on.”