Having fun with discrete mathematics

Mathematics isn’t all fun and games, but sometimes it is. This summer, two undergraduate researchers and three mathematics professors at Dordt University are experiencing the fun of mathematics firsthand as they work to develop strategies for games on graphs.

Elisa Benthem, a Colorado Springs, Colorado, native double majoring in mathematics and physics, was motivated to develop strategies for games on graphs partly because games are a great way to show how enjoyable mathematics can be.

“Plenty of people have one bad experience with math and decide that they’re ‘not a math person,’” she says. “This attitude makes me sad, because math can be so beautiful and fun.”

Benthem and Cooper Burkel are exploring discrete mathematics by working on a game they are calling Edge Distinguishing Game – or EDGe, for short. One benefit of discrete mathematics and graph theory is that it doesn’t require much background knowledge.

“I can draw a picture and easily describe to someone who has limited mathematics knowledge what project we’re trying to work on,” explains Professor of Mathematics Dr. Mike Janssen. “The problems are accessible. The questions we are working through are easy to understand, but hard to answer.”

“The specific game we are doing has never been done before, and the mathematical concept it is based on—the edge-distinguishing chromatic number—is relatively unstudied as well,” says Burkel, a mathematics and secondary education major from New Lenox, Illinois. “That really sealed the deal for me, because we are exploring something that is brand new to pretty much everyone.”

After reading papers and familiarizing themselves with games on graphs, Benthem and Burkel dove into the research. Janssen, Assistant Professor of Mathematics Dr. Marissa Chesser, and Assistant Professor of Mathematics Dr. Nate Benjamin keep tabs on the pair, frequently answering questions and brainstorming possible solutions to ongoing problems they encounter.

“In mathematics research, it can be easy to get stuck on something and feel like you’re not making any progress, which might feel demoralizing,” says Chesser. “Even though they are doing work on their own, they know that if they need ideas or want our opinion on something, they can come talk to us.”

Benthem appreciates how the research has helped her better understand what she is capable of. “Working on my own and with a peer has been useful in teaching me how to work independently and explore what I find interesting, and helping others to do the same,” she says. “Each of the three professors has different experiences within the field, and it’s been wonderful to learn from them and to collaborate.”

Burkel loves “exploring something that has never been done before.”

“Trying something new and being able to do so on a daily basis in my research is really fun,” he says. “Also, it is enjoyable to work individually with the professors and see their excitement for mathematics.”

Part of the reason Janssen, Chesser, and Benjamin embarked on this summer research opportunity was to help students like Benthem and Burkel to get early exposure to research opportunities.

“The goal is to provide sophomore students with experience in mathematics research so that they can understand what it is and then decide if it’s something they want to pursue in the future,” says Chesser.

“Then, by junior or senior year, they can go after nationally funded research opportunities such as REUs and feel like they not only understand what those opportunities entail but also have competitive applications in that they have previously worked in research,” adds Janssen.

The summer research project will culminate in on-campus presentations this summer and fall.

“If they get enough results, they might be able to write a paper to submit to a research journal,” adds Janssen.

Benthem and Burkel follow in the footsteps of other Dordt mathematics majors who have pursued research opportunities. 2024 graduate Anika Homan completed an undergraduate research project at Dordt in 2021 before going on to REU opportunities at Grand Valley State University in 2022 and The Ohio State University in 2023; she later earned a Goldwater Scholarship, received a prestigious National Science Foundation Graduate Research Fellowship, and was accepted to a Ph.D. program at University of Notre Dame.

Jocelyn Zonnefeld, 2024 graduate who also completed an undergraduate research project at Dordt, later participated in a prestigious REU program at Northwestern University; she has been accepted to a Ph.D. program at Tufts University.

“We’re experiencing momentum with students engaging in mathematics research,” says Janssen. “I hope students can picture themselves working in mathematics. We want to create a culture of undergraduate research here at Dordt, and I think that this summer research opportunity is one way we’re able to help build that.”

About Dordt University

As an institution of higher education committed to the Reformed Christian perspective, Dordt University equips students, faculty, alumni, and the broader community to work toward Christ-centered renewal in all aspects of contemporary life. Located in Sioux Center, Iowa, Dordt is a comprehensive university named to the best college lists by U.S. News and World Report, the Wall Street Journal, Times Higher Education, Forbes.com, Washington Monthly, and Princeton Review.