Expanding the Boundaries on Summer Undergraduate Research
Since 2015 there has been a dramatic increase in the number of undergraduates pursuing mathematics research on campus in the summer months.
A traditional view among mathematicians is that mathematics is not well suited to undergraduate research. Students generally need several years of coursework before they can understand the questions that are most interesting to mathematicians. However, there is growing demand for such experiences from undergraduates who are considering moving on to graduate study. Furthermore, research experiences can be key in helping students secure jobs and internships.
In response to this growing demand and the fact that a successful undergraduate research project can be a transformative experience, the department is developing programs that make these experiences more available. This began with an effort to expand the number of mathematics students who receive Summer Undergraduate Research Fellowships (SURF), a program under the university’s Undergraduate Research Office that awards students stipends to pursue full-time summer research on campus.
Recognizing the value of this program, the department started to directly fund math students pursuing SURFs, leveraging gifts from alumni, including Larry Jennings and David Simmons, in 2016. The size of this program grew from a previous norm of one or two mathematics SURFs each summer to a total of 14 mathematics SURFs in the summer of 2019 (see page 29 for details on the SURF projects from 2019).
Furthermore, the quality of these projects has improved as the faculty has become more engaged with students’ research. Almost half of the permanent faculty have advised at least one SURF project in one of the last three summers. “This is special in itself,” said Department Head Tom Bohman, who created an incentive program for faculty who mentor summer research. The department also introduced the David Simmons competition for undergraduate research in mathematics and appointed Irina Gheorghiciuc to the position of director of undergraduate research in mathematics. In this role she helps match students who have an interest in research with faculty mentors.
SURF projects rely on one-on-one advising and being able to provide close faculty contact has had a direct effect on students’ academic growth. One such student, senior Varun Gudibanda, worked with Assistant Professor Franziska Weber last summer on numerical analysis of liquid crystals to produce numerical schemes for the system and simulate the system in MATLAB. “My summer research helped me find confidence in my plans to attend graduate school and beyond,” said Gudibanda. He also worked on a numerical analysis project with Associate Teaching Professor Jason Howell in the summer of 2018 and now plans to obtain a Ph.D. in numerical analysis, with the goal of eventually providing numerical frameworks for exciting real-world problems such as Formula 1 race car aerodynamics.
As the SURF program grew and improved, it became clear that there was a need for a separate program focused exclusively on the mathematics of finance. Professor Bill Hrusa launched the Mathematical Finance Summer Undergraduate Research Program (MFSURP) in the summer of 2017.
Twelve students participated in the first MFSURP. This year, that number increased to a staggering 38 students.
MFSURP is an early research experience for first-years and sophomores to work on mathematical problems that are relevant to finance. Normally, students with an interest in finance look to secure an internship by their junior year. Having done research on a topic in finance has made a big difference for those students come internship recruiting season.
Following her first-year, current junior Lily Qiao and her partner Laura Li conducted research on portfolio optimization with order-size impact. They won the Young Researcher Award at the 2019 Simmons Competition.
“This is one of the most important topics in finance right now,” said Qiao.
Current financial theory assumes that the price of a security doesn’t depend on how many shares an investor buys. Qiao and Li developed simple models for order size impact and used them to explore the effect on the structure of optimal portfolios.
Qiao says that internship recruiters were impressed by her research, and she credits MFSURP with giving her the confidence to connect with people currently working in finance.
“I’m really grateful that Dr. Hrusa offers this undergraduate research experience,” added Qiao, who secured an internship with Bank of America for next summer over a year in advance.
For sophomore Minty Xia, she appreciates that MFSURP gives students a chance to work on the same problems that people in the industry are currently grappling with.
This summer, Xia’s group studied utility indifference pricing. In certain situations, a given security may have more than one price that is consistent with the basic theoretical framework. The idea of utility indifference pricing is to single out a price that is consistent with investors’ risk preferences. Xia’s group analyzed the limits of utility pricing to see how current models would behave when order sizes get large.
“We were doing things that we knew would be meaningful in a real-world context. That was the most meaningful part to me,” Xia said. She also believes the program has practical outcomes.
Xia will intern with the Bank of America next summer, an impressive feat for a sophomore. “Most of my interviewers asked about my research because they would say it’s really rare for a first-year student to have a research experience,” she said.
Most recently, the program added a weekly market watch seminar series, where students discuss what’s going on in current financial markets, which also gave Xia a leg up.
“Before going to my final interviews, I had to prepare for market knowledge. Having been through that experience during MFSURP was really helpful,” she said.
As it’s grown, MFSURP has attracted corporate sponsorship from Principal Financial and Goldman Sachs and also garners support from the CMU Provost’s Office.
These last four years have shown that not only are students highly motivated to pursue research but that it has a strong impact on their futures. The department continues to raise endowed funds to support the growing number of students undertaking summer research.
The Martin Fund for Undergraduate Research supports mathematics SURF students and the Steven Shreve Fund for Mathematics supports the MFSURP. Visit math.cmu.edu/giving for details.