Nathan Carter, associate professor of mathematical sciences at Bentley University, is a winner of the Mathematical Association of America (MAA) Beckenbach Book Prize for Visual Group Theory (Mathematical Association of America, 2009). A $2,500 prize will be presented on January 5, 2012, at the 2012 Joint Mathematics Meetings in Boston.

The Beckenbach Book Prize is awarded to an author of a distinguished, innovative book published by the MAA, but not awarded  on a regularly scheduled basis.  It is given only when a book is judged to be truly outstanding. Carter receives the award along with American University’s Dan Kalman (Uncommon Mathematical Excursions: Polynomia and Related Realms).

“Knowing those who have received this award in the past, I am surprised and honored to join their company,” Carter says. “I'm grateful to the MAA for this honor, and for supporting me by publishing the book.”

Visual Group Theory covers a typical undergraduate course in group theory from a thoroughly visual perspective, versus the majority of textbooks that take a technical approach.

“Mathematics is a technical subject, so the precise (but sometimes difficult) notation used to write and convey it is both necessary and useful,” Carter notes. “However, it shouldn't be the only medium we use to communicate mathematical ideas. Just as there are graphs and plots in calculus and statistics to help us get some concrete intuition for abstract ideas, we can do the same  in higher-level mathematics as well.”

According to Carter, group theory is a subject in which visualization is possible but rarely used due to the degree of difficulty of creating diagrams by hand.

“The software I wrote and the subsequent book fill the need for visual media in the subject of group theory, a topic almost all students majoring in pure mathematics spend one or two semesters studying,” Carter says.