Calculated fun

Learning advanced mathematics concepts isn’t necessarily fun and games — except in Instructor Jeff Ibbotson’s MAT690: Selected Topics in Mathematics course, where games are the point. In it, students explore how game theory — the study of strategic interactions whose outcome for each participant depends on choices of all involved — is an effective way to apply mathematical calculations to strategic thinking.

“Game theory allows students to see applications of mathematics in a different way because the concept is based on the idea of agents playing a game against one another or as part of a group,” Ibbotson says. “Games like the Prisoner’s Dilemma have aspects of conflict and cooperation, and can apply to situations in politics and economics.” Two of his students applied the game theory model of cooperation to show how hermit crabs trade shells, writing and illustrating a picture book to explain their findings.

Ibbotson aspires to teach mathematics beyond theorems and formulas, and attract a broad range of students, some who enjoy math and others who feel they should give math another try. Maybe because Ibbotson didn’t always know mathematics would be his route to happiness.

“When I was in college, I was a physics major and I wound up completing a physics program,” he says. “I took English classes, but eventually the style of arguments got to me. I was like I want something where there’s a provable answer. Not that I didn’t enjoy arguing, I do. … but it was when I was in real analysis that I fell in love with the mathematics of infinity.”

Drawing on his vast interests in art, religion and history, he uses spherical paintings on a globe to illustrate six-point perspective or passes around a graspable dodecahedron to help students visualize complex ideas. In another course he developed,

MAT40H: History of Mathematics, students study numbering systems from ancient Egypt, Babylon, China, India and other non-Western cultures — and have an opportunity to build their own. “They invent their own symbols and the stories behind the symbols,” Ibbotson says.

Ibbotson has been able to share his fondness for physics in an integrated studies course about the intersection of mathematics and sound. Using content based on his research into distribution theory and partial differential equations, students use trigonometric functions like sine and cosine to model complex sound waves (which correspond to musical concepts like pitch and volume). An avid Marvel and DC comic book fan, Ibbotson hasn’t integrated comics into his math courses, but he plans to.

In everything he teaches, Ibbotson strives to impart that learning mathematics is an effective way to learn to think, especially around the Harkness table. “That pedagogy feels right to me,” he says. “We want students engaged as soon as possible in doing mathematics. We have all sorts of problems that can go in various directions and sometimes the students find original ways to solve them. We celebrate that.”