The College of William and Mary has entered the vanguard of undergraduate computational mathematics instruction, fueled by a multiyear $800,000 grant from the National Science Foundation.
The NSF grant will fund the operations through 2012 of an interdisciplinary program called CSUMS— Computational Science Training for Undergraduates in the Mathematical Sciences. The goal of CSUMS is to increase undergraduate proficiency in computational mathematics, by development of new courses and by incorporation of computational mathematics examples into existing courses.
Chi-Kwong Li, Ferguson Professor of Mathematics, is director of the CSUMS program at William and Mary. He also is the principal investigator on the NSF grant and was department chair when the application was filed.
“At the NSF, they see the need that the current generation, the younger students, should be trained to have a good sense about computation in the mathematical sciences,” Li said. He stressed that CSUMS is not just for mathematicians and the William and Mary program includes students and faculty from applied science and computer science.
The nucleus of a computational mathematics initiative had been forming at the College for some time. Michael Lewis, an associate professor of mathematics, had spearheaded an NSF-funded initiative to establish a computing cluster in the department, a good start on the hardware infrastructure necessary to support a program.
"The main goal of the NSF is to support research in science and mathematics, but it’s also interested in keeping the curriculum in these disciplines as modern as possible,” said David Lutzer, Chancellor Professor of Mathematics and current chair of the department. “When we saw the NSF call for proposals, we asked if this was something we wanted to do. As it happens we had recently hired several people whose strong interests were on the computational side of mathematics.”
One such new hire is Sarah Day, an assistant professor of mathematics, who is teaching a senior seminar titled Computational Dynamics and Topology, one of the CSUMS training courses. At the other end of the undergraduate computational experience, Lewis is teaching a freshman seminar he says is “innocuously titled Mathematics and Computation,” but which takes first-year students to mathematics’s jumping-off point.
“The idea is to make the students aware of the whole other interesting set of questions that arise when you go to actually solve problems,” Lewis explained. “Mathematical analysis can tell if solutions exist. Finding those solutions is apt to be a much more difficult problem, a computational problem.”
Lutzer said CSUMS will facilitate the introduction of computational techniques at every level of the curriculum. “You can just ignore computing in freshman calculus if you want to. But you can also address computation issues that arise when calculus is used, if you want to,” he said. “Part of this project is because we want to.”
Virginia Torczon, associate professor of computer science, says that CSUMS will encourage interdisciplinary thinking among students in two departments. “We want computer science students to take more math courses to complement their computing curriculum and we want more students in mathematics to take classes in computer science to complement their research there,” she said. “We also want to incorporate projects within individual courses to involve more computers, to show the students that they can use computing as a tool.”
Li noted that CSUMS will have an intensive undergraduate research component in addition to the curricular restructuring. “New courses are only part of it. What we are doing now is to increase the sense—the sense and sensibility—of students about computational issues,” Li said. “Do we expect a freshman seminar to train students to be competent in computational math? No. But it will increase the sense that there are many problems related to computational issues.”