Centre students conducting research in graph theory on campus this summer
Centre’s campus is constantly buzzing with people doing exciting and innovative research, and summertime is no exception. Numerous students are currently spending time on campus studying and learning, including Ruohan Liu ’12 and YaYa Zhou ’13.
Liu and Zhou are both working with assistant professor of mathematics Lesley Wiglesworth on a graph theory project. Their goal is to determine an algorithm that will allow them to find a winning strategy in a computer game — specifically, to help the first player in a gold-grabbing game win first place.
“Graph theory is a relatively new discipline,” Liu says. “It has many applications, depending on the project.”
For their study, Liu, Zhou and Wiglesworth are using a type of graph known as a caterpillar tree — a graph in which at least two vertices are connected by one central path and are a specific distance away from that path.
“We consider each vertex — which you would know as a point — to have some gold in it,” Zhou explains. “Two players take turns picking up the gold. At the end of the game, the player who gets the most gold wins. We want to determine a way for the first player to win by using graph theory.”
Though the concept of the study may seem difficult to grasp, Liu found that he already knew everything he needed to know for the project.
“There was almost no jargon we had to know before doing this research — we brought in terms like ‘caterpillar’ and ‘vertices’ and ideas we had used in class,” he says.
The graph theory class Liu and Zhou took with Wiglesworth last year is what gave the two students the opportunity to do research with the professor this summer. So far, they all agree that the project has been demanding but rewarding.
“[Professor Wiglesworth’s graph theory class] was a challenge for me, so I was glad to be chosen and am so happy to get to do this research,” Zhou says. “It’s giving me a chance to think about whether I’d like to continue research or not.”
Wiglesworth appreciates that this kind of research allows her students to go further in-depth with their studies than they might be able to in a class.
“Summer research allows my students to think like mathematicians, not just as math students,” she says. “We are trying to find solutions to a mathematics problem that no one has solved. That’s exciting!”
But the collaborative aspect of the project has been one of the most rewarding parts of the experience for Liu, Zhou and Wiglesworth.
“I enjoy getting to know my students more informally,” Wiglesworth says. “It’s also exciting to watch their reaction when we discover something that no one else knows.”
Zhou also appreciates the benefits of being on a research team and what she has gained from being at Centre for the summer.
“Working with each other, sharing ideas, learning how to communicate with others and figuring out how to balance your time are all important,” she says. “You kind of push yourself. It’s a good chance to get experience for future work.”
Liu and Zhou will present the findings of their project at a campus research symposium next week. Though they may not find the algorithm they’re searching for before school begins again, all three involved agree that the study has been a great experience.
“This is my first time doing something meaningful in the summer,” Liu says. “It’s a lot more difficult than I ever could have imagined, but I like doing this research. It’s required more devotion than anything else I’ve done in college so far.”