Before last summer, Suneil Parimoo had never worked on partial differential equations. But that didn’t stop the University of Pennsylvania senior from spending eight weeks solving one such problem at a Math REU at the Florida Institute of Technology.

REU stands for Research Experiences for Undergraduates. Dozens of these highly selective programs, sponsored by the National Science Foundation, take place across the country, bringing together groups of students from a range of backgrounds and focusing on any areas of active study the NSF funds. Parimoo, of Bridgewater, N.J., a dual-degree candidate in mathematical economics in the School of Arts & Sciences and statistics in the Wharton School, sought out this type of collective problem solving.

“Before this, I had done some research but more on an individual level, and I think that’s my default work style. I tend to be a very individual thinker,” he said. “This gave me a good opportunity to collaborate with other researchers, which is important in academia.”

The problem he and 11 other undergrads (divided into three sub-groups, one of which included Penn junior Rashad Abdulla) aimed to solve isn’t easy to explain. Simply deciphering how Parimoo described the topic — “the evolution of interfaces of double degenerate, non-linear reaction-diffusion equations” — requires more than a little basic math knowledge.

But, despite his limited time studying partial differential equations, or PDEs, Parimoo can break it down nicely. Researchers use PDEs to formulate problems that have several variables, he said. His open problem involved time and space variables, and it focused on how the point in space called the interface evolves in time. He offered as a simple example the motion of a wave.  

“Picture a wave moving through the ocean. Ideally we would like to find the exact shape of this wave and precisely how it moves over time, but we cannot. Instead we look at the crest of the wave,” he said. How do changes to wind, air pressure and other factors alter the crest’s behavior? What happens when those forces compete?

“What we worked on was fully classifying for which parameters this crest moves forward, backward, remains stationary or even waits for a little before moving forward,” he said. “We also constructed numerical simulations for these different cases to help visualize the problem.”

Though the work is technically pure math, it has applications in fields like physics, biology and chemistry, looking at how heat in plasma radiates, for example, or how chemicals move through groundwater.

The REU was about more than spending two months just doing math. It included excursions to places like the Kennedy Space Center, seminars on topics like ethics and the relations between music and math, collaboration with Ph.D. students and the professor-mentor, plus practice presentations every couple weeks. The experience was good preparation for the two actual presentations Parimoo subsequently gave, at the 2015 Young Mathematicians Conference in August and at the 2016 Joint Mathematics Meeting, the largest math conference in the world, this past January.

Though Parimoo and his research partner haven’t fully solved their open problem yet (they had one or two cases left, which they hope to continue to work on), he highly recommends an REU to anyone who’s had even minimal exposure to research.

“The process of finding an REU begins freshman year,” he said. “If you’re interested in research and aren’t sure where to begin, an REU is a great platform to expose students to research at the academic level. At the same time, you’re not committing to an academic career, so it’s a good opportunity to explore your options and interests.”

It’s one that helped Parimoo become a better researcher and mathematician and one that will likely benefit both his short- and long-term goals. After graduation, he has a job working for a consulting firm that assists Fortune 500 companies with data analytics. Eventually, he said, he hopes to attend grad school to study economics, statistics or, fittingly, pure math.

Information about REUs and additional resources supporting undergraduate research is available via Penn’s Center for Undergraduate Research & Fellowships.