If given the choice offered to Neo in The Matrix, Gary Gordon, professor of mathematics, would likely choose the blue pill. He appreciates a finely constructed matrix, thank you very much.
Gordon’s upcoming book, tentatively titled Matroids: A Geometric Approach, examines matrices, networks, and their points of connection. Written in collaboration with Professor Jennifer McNulty of the University of Montana, the textbook offers undergraduates a depth of understanding in the practical aspects of matroids normally reserved for graduate students.
“When you study matrices, that subject is called linear algebra, one of the most useful areas of math, as it can be applied to a lot of real-world problems,” Gordon says. “For example, if you’re running an airline and need to schedule certain planes in certain places, constraints exist, and your goal is to maximize your profits. You can arrange this problem as an enormous linear program. The airline makes money based on efficient solutions. They don’t make money on planes flying empty or sitting in the wrong place. Matroids help find a common mathematical framework for networks on one hand and matrices on the other.”
Working on such practical problems in mathematics led Gordon to establish Lafayette as a site for Research Experiences for Undergraduates (REU), an elite program funded by the National Science Foundation. Gordon, the principal investigator behind the research, and other Lafayette faculty work with two to four Lafayette students and eight students from other colleges. Together, they explore unsolved problems in mathematics and work toward solutions that yield practical results. Each year, the handpicked REU team publishes several papers covering everything from combinatorics to gaming theory.
“I went into math because the feeling of figuring out a difficult problem was the best feeling in the world,” Gordon says. REU and his book are his ways to develop that same excitement in students. For this reason, he chose to focus much of his attention in Matroids on student exercises, enlisting math major Bidur Dahal ’12 (Kaski, Nepal) to work through them. “He absorbed the spirit of the book and likes it,” says Gordon.
That student feedback is important for Matroids, as it broaches a subject not normally discussed at the undergraduate level. Gordon thinks the book will make an impact.
“As an undergraduate, you’ve taken courses in abstract algebra and real analysis. Maybe some geometry. Maybe some combinatorics. This text combines ideas from all those courses; it’s a capstone.” Despite this, Gordon adds that the breezy style of the text keeps the subject approachable. “There’s heavy math in it, but it should be enjoyable.”
Reaching students matters to Gordon. To add to his 2005 Marquis Distinguished Teaching Award, he shared the 2010 Excellence in Diversity Education Award with his wife, Liz McMahon, professor of mathematics. Given to faculty or administrators whose commitment and service to diversity on campus promotes awareness and a positive learning environment for all students, the award celebrates, in part, their work with the Posse Scholars program. Posse encourages multiculturalism on campus by identifying and providing scholarships to academically worthy high school students who would not otherwise attend college.
“I’ve found this to be an amazing experience,” says Gordon of his experience as a mentor to Posse scholars. “I get to see things in these students that other faculty don’t see. These students have so much drive and motivation, they don’t want to waste a second. That’s inspiring to me.”