by Carolyn Arnold
Over in the Bannow Science Center, three math research students are studying tetrahedra and other geometric figures. To the casual observer, this means they are drawing complex, (but colorful) shapes on a blackboard and discussing their geometric properties.
In another classroom, three different students and their faculty mentor are puzzling over a function. Some try to figure it out on a computer, others work it out on paper.
Meanwhile, a third group of students and their professor are in Beijing, China, learning from experts around the world about Nielsen fixed point theory, a topological study of stability and how stability points change under small perturbations.
Clearly, math is an exciting adventure of the mind for this group of students. This summer, students from around the country came to Fairfield to research original mathematics concepts as part of Fairfield’s first Research Experiences for Undergraduates (REU) program in mathematics and computational science.
The REU was made possible thanks to a three-year $296,569 grant from the prestigious National Science Foundation awarded to Dr. Shawn Rafalski, assistant professor of mathematics.
Through the program, talented undergraduates are provided on-campus housing and stipends. Students apply for the specific mathematical research project closest to their interests and, once accepted, work in small groups in close consultation with a Fairfield faculty mentor.
Dr. Rafalski, the program director, was pleased with the caliber of applicants. “We had over 300 applications, and they were of an extraordinarily high quality,” he said. In all, there are nine students in the program, two – Jacqueline Brimley ’13 and Brian Haswell ’12 – are from Fairfield.
Jacqueline Brimley ’13 applied to the program to see what her professional career would be like if she pursued mathematical research. “A math degree provides many occupational avenues, and I hope that by the end of the summer I’ll have a better indication of whether I would enjoy taking the graduate school and research path,” she said.
The students working with Dr. Rafalski on three-dimensional hyperbolic geometry include Brian Haswell ’12 (Fairfield), Kelli Burkhardt ’12 (University of Texas), and Tom Crawford ’12 (Williams College). The research focus of this group was on the geometric properties of objects like pyramids and cubes in spaces that obey different rules than those from standard Euclidean geometry.
Like the rest of the students in the program, Haswell has always enjoyed math. “I was one of those people who sighed with relief when I’d go from the reading section of standardized tests to the math section,” he joked.
Dr. Christopher Bernhardt, professor of mathematics, and his students, Whitney Radil ’13 (College of St. Benedict), Adriana Johnson ’12 (Bard College), and Zach Gaslowitz ’13 (Harvey Mudd College) studied one-dimensional combinatorial dynamics.
And the REU funds made it possible for Dr. Christopher Staecker, assistant professor of mathematics, and his team – Fairfield’s Jacqueline Brimley, Matthew Griisser ’12 (Georgia Tech), and Allison Miller ’12 (Pomona College) – to travel to China for the “International conference on Nielsen fixed point theory and related topics.” The conference is held every two to three years and this year was the first time that undergraduate students attended. Dr. Staecker also presented his own research at the conference.
While in China, the group went on a one-day excursion to the Great Wall of China and the Temple of Heaven. “I think being dropped into a country I’ve never been to before only made me that much more receptive to everything I was exposed to, including different aspects of math,” Brimley concluded.
Original research is something that will be very attractive to future employers and graduate schools. Brimley said, “The whole program goads us into becoming a mini-expert in a specific facet of mathematics, and it is empowering to have a professor truly valuing your ideas and perspectives.”
Dr. Rafalski said, “It’s not always easy, but very often it’s fun and a worthwhile challenge. I’ve found that my students have digested their research topic so well toward the program’s conclusion that they often are posing questions that stump me, which I love because it keeps me on my research toes.”
At the end of the REU program, each research group will prepare a written report on their work and present the results to all of the program participants. Some will be asked to present the results of their work at conferences, including the National Joint Meeting of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA) in Boston.
The students and teachers have made lasting friendships and networks with the inaugural group. Brimley said, “I am really enjoying the Fairfield REU. At Fairfield, I am constantly interacting with the same group of people in my math classes, as we are all math majors following the same mapped-out curriculum. This has given me an opportunity to meet and interact with new people who are equally as interested in this scientific area.”
Despite the hard work, the program has been a one-of-a-kind experience. “Doing mathematical research is a very creative process,” Dr. Rafalski said. “No artist would ever tell you that it was easy to create something. Creativity requires the courage to try new things, the judgment to realize when something you try isn’t working the way you thought it would, and the perseverance to push through difficulty. Mathematics research is the same way, and conveying this awareness to the students is one of the program goals.”