Adding up CSUMS

NSF-funded program advanced undergrad math research

by Alla Herman ’15

For the past five summers, while other students were hitting the beach, William & Mary math majors had been hitting the books and the labs to conduct computational mathematics research.

William & Mary’s Computational Science Training for Undergraduates in the Mathematical Sciences (CSUMS) program has come to an end after expiration of a five-year grant. The program, a collaboration among William & Mary’s mathematics, applied science and computer science departments, received funding from the National Science Foundation (NSF) for the period of 2007 to 2012 to support undergraduate math research. Though the NSF grant has ended, William & Mary continues to reap benefits brought by CSUMS.

The CSUMS program began at William & Mary in 2007, providing around six students every year with funding to participate in mentored computational research experiences.

CSUMS’s aim is to provide undergraduates with the opportunity to become familiar with the skills necessary for computational mathematics research. Faculty and CSUMS alumni both agree that the experience is excellent preparation for graduate school and careers that require advanced computational skills.

Exploring mathematical applications

Chi-Kwong Li, Ferguson Professor of Mathematics at William & Mary, said that CSUMS is unmatched in providing opportunities for students to grow in computational mathematics. Li says the opportunity to do work that builds towards a possible honors thesis and to explore the applications of a mathematical topic to other fields are the greatest assets to participants.

“It’s the application that’s important, whether it’s theoretical or applied math—it’s the total package,” Li explained. “Doing an honors thesis will ensure the best research experience. It’s not just doing research to do research—it’s about communicating with people, learning, gaining insight, and gaining experience in the field.”

Each CSUMS program was held on the William & Mary campus for an eight-week period over the summer, integrating classes with individualized mentoring periods as well as off-campus excursions and special lectures.

As courses were conducted in the summer, students had time to focus on their research and work with professors more closely, attending seminars and presentations. Students also participate in weekly lunch seminars where they took turns presenting their progress over the session. Students also went on field trips to companies and organizations to see how computational mathematics is put into action.

Li pointed out that many courses offered during the CSUMS program also are offered at William & Mary during the academic year. Not only do these classes allow previous CSUMS participants to expand on their knowledge from the summer, but they also attract more math majors to the CSUMS program for the following summer. Courses such as Math 345, Mathematical Models in Biology, and Math 410, Topics in Computational Mathematics, while counting towards the degree requirements for math majors, also provide valuable training for students thinking about applying for the CSUMS program. Li said Topics in Computational Mathematics in particular has been crucial to the recruitment process for CSUMS over the last five years.

“Many students go on to pursue careers in math after the CSUMS program, and since CSUMS began the enrollment in math courses has doubled,” he said.

A variety of topics—but all computational

CSUMS was initially aimed at math majors, although Li points out that at William & Mary many participants are computer science majors or are double majoring in a contrasting discipline. Professors participating in the program as instructors and mentors also had varying research interests, from neurophysiology to computational biology. These diverse topics allowed students with different interests to apply computational mathematics to their other areas of study.

Gexin Yu, assistant professor of mathematics, stressed the importance of the connection between professors in the CSUMS program. Yu said through CSUMS collaborations, faculty members have become aware of each other's strengths, making it easier to match students with mentors with similar research interests.

As of summer 2011, 27 CSUMS students chose to continue their research as the topic for their senior honors theses, said Yu. Also, 21 students published or submitted their research papers. Over half of the CSUMS participants who have graduated continued on to graduate school in math or science.

Yu explained that one of the main goals of the program is to provide students with more insight into the real-world applications possible with a mathematics degree. The professors involved in the program say there is a heavy emphasis on interdisciplinary studies due to the mix of interests among CSUMS faculty. This mix allows students to choose research topics a little bit out of their comfort zones and extend their mathematical prowess to other disciplines.

Many CSUMS alumni keep on researching

All alumni of CSUMS experienced were encouraged to continue their research, and many continued working with their mentors throughout the school year. Li said projects started over the summer during the program are often expanded on in the spring semester of students’ junior year.

Li states that since the inception of the CSUMS program, more students than ever have gone on to pursue successful careers in computational mathematics.

Allison Oldham ’13 researched graph theory with Yu during her time in the CSUMS program. She also did research with Rex Kincaid, another professor of mathematics, and Yu and Kincaid co-advised her on a project.

Oldham says the program opened up countless opportunities for her. One such opportunity was the ability to participate in the Joint Mathematics Conference in Boston.

“This was a great opportunity to meet other mathematics students and professors and also gave us a chance to be in an environment totally devoted to mathematics research,” said Oldham.

Oldham says CSUMS has provided her a major advantage in that it not only is a great addition to a graduate school application, but it also gave her the chance to experience research before being thrown into a more intense environment. She says CSUMS is the perfect place for students to gain research experience.

“Mathematics research and mathematics classwork are so different and it's so important to experience both,” said Oldham.

An impressive list of successes

CSUMS faculty point to some experiences of recent graduates who benefited from their CSUMS experiences. For example, Tanner Crowder ’08, a mathematics and physics double major, began his research on genetic codes and quantum computing through the CSUMS program. While a participant in the CSUMS program, Crowder was a speaker at the 2008 workshop, took additional courses in the spring semester after he completed the program, and completed an honors thesis in mathematics. Currently, Crowder is a research mathematician at the Naval Research Lab.

Another alumnus, Ashwin Rastogi ’09, also a mathematics and physics major, conducted research on linear preserver problems and quantum computing. He completed an honors thesis on an electroweak model in 2008. Rastogi presented his research at the International Workshop of Operator Theory and its Applications in July 2008, one of many opportunities the CSUMS program has been involved in. After graduation, Rastogi went on to a graduate program in physics at Harvard University.

This kind of success is not rare for CSUMS students, according to Li. The program also attracts more students to do honors theses, which Li believes has been the true impact of the program.

Yu added that the interest in the math program at William & Mary has skyrocketed since the CSUMS program began. He said the number of math majors went from around 20 per year at the beginning of the program to about 50 per year.

“There are more math majors and more students in math classes. A lot of students are afraid to be math majors, and we want to show that if you're interested, you should come to us,” said Yu.

According to Li, the experience is the most important thing he wanted students to get out of the program.

“I want to show that mathematics can be rewarding, and having students complete their own projects like this is the most rewarding thing for everyone involved.”