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Exploring Abstract Mathematics

Mathematics majors Kirsten Hutchison and Derek Pouliot spent ten summer weeks searching for unexplored based rings. What’s a based ring? “A collection of characters that can be added and multiplied,” says Hutchison.

Why study based rings? According to Pouliot, there’s still a lot to be discovered about them. “It’s something that hasn’t been the focus of a lot of research,” he says, “even at the graduate level.”

At the suggestion of their faculty mentor, Associate Professor Dmitri Nikshych, the pair applied for a received a Summer Undergraduate Research Fellowship (SURF) that enabled them to spend several hours each week working on computations.

In doing so, they disproved Kaplansky’s 1973 Conjecture. They also wrote a computer program that can search for based rings (since, as the dimensions grow larger, the computations become too tedious to work through by hand). While both admit it’s not the average summer job, they expect the experience will help them in their post-graduate endeavors. “It helped me discover new problem-solving skills,” says Derek, who plans to become an actuary.

“It was great experience in mathematical research,” says Kirsten, who plans to go on to graduate school for an advanced degree in applied mathematics. “It opened my eyes to how much we don’t know about math. This makes me interested in exploring what’s left to be discovered.”