What goes on in the mind of a mathematician? For Dr. Shawn Rafalski, Assistant Professor of Mathematics, it could be time-traveling rock-and-roll bands or billion-year-old intelligent computers, some of the themes of the fiction he has written in his spare time since high school. Or it could be 3-dimensional geometric topology, the topic of a research project he led with 3 undergraduate students during the Williams College Summer REU Program SMALL in 2008. For both fiction and figures, imagination is key.
“One of my favorite quotes is from the Russian poet Alexander Pushkin: ‘Inspiration is needed in geometry, just as much as in poetry.’ This is how I think about doing original mathematics,” says Rafalski. “The mathematician has all of the necessary ‘language,’ that is, the numbers and the mathematical concepts, at hand — just as the poet has all the necessary words. It just takes the right creative insight to put everything in place. No one would say that the poet thinks linearly in the creative process — and mathematicians are no different.”
Unleashing the minds of undergraduate students to the possibilities of producing original mathematics will be the task at hand during Fairfield University’s first Research Experiences for Undergraduates (REU) Program in Mathematics and Computational Science, slated for the summer of 2011.
Awarded a 3-year, $296,569 grant from the National Science Foundation (NSF) for the program, Rafalski hopes to extend his positive and pivotal experience at Williams to other faculty and students here at Fairfield. “Williams’ REU program was the first real opportunity I had to guide undergraduate research, and it turned out to be the most rewarding professional, personal, and pedagogical experience of my career,” he says.
The Path to Fairfield
While Rafalski began his own academic career in pursuit of becoming a novelist, “several fantastic and inspiring mathematics professors” at Eastern Michigan University where he attended as an undergrad tapped his mind and helped him discover a different way to apply his imagination. Then after receiving his mathematics Ph.D. in 2007 from the University of Illinois at Chicago, he was hired as a Visiting Assistant Professor at Williams College where he found his true calling as a teacher. “It is highly rewarding to inspire people to want to learn,” he says.
Rafalski’s passion for teaching and research was palpable during the interviewing process at Fairfield.
“When we hired Shawn, we were looking specifically for someone who would be a departmental leader in the area of undergraduate research,” says Dr. Matthew Coleman, Chair of the Department of Mathematics at Fairfield. “The Department was won over by Shawn’s energy and enthusiasm, and his involvement in the very successful REU program at Williams College. Although he hit the ground running when he got here, we had no idea that he would have the wherewithal to put together an NSF REU proposal so quickly, and we were thrilled when we found out that the proposal would be funded.”
To Rafalski, the word “research” means asking questions. “When you ask a question that someone already knows the answer to,” he says, “that’s great, because it means you probably asked a good question. But don’t stop there. Ask another and another, and eventually you might ask a question that no one has answered yet. That’s when you start advancing the body of knowledge – in any field.”
Coleman points to a strong national trend toward mathematics research with undergraduates, and the advantages a smaller school like Fairfield has. Here, the REU program will give students an opportunity to work very closely with a faculty member, something not usually available at larger schools.
In addition to select Fairfield students, college students from institutions with limited access to faculty-sponsored scholarly activity will be encouraged to apply for this intensive 8-week summer program. Nine talented students in total will be provided on-campus housing and student stipends. In close consultation with a Fairfield faculty mentor, each will be engaged in original mathematics and computing research on a topic from the mentor’s field of expertise.
REU Program Objectives
For the 12 mathematicians and computer scientists at Fairfield who have committed to the University’s REU program for the next 3 summers, Rafalski hopes their involvement will be as affirming as his was at Williams. “There’s a deep connection between pedagogy and research,” he says. “They are essentially two sides of one coin, and I have found that the effective development of each is integral to maintaining balance in an academic career.”
For the students, Rafalski hopes that the cohort experience will be lifetime lasting. At Williams he attended a reunion in celebration of the 20th anniversary of their REU program, where he met students from the first cohort to the previous year’s. “You can just feel that their shared experiences had created a lifelong bond,” he recalls.
Fairfield’s summer research cohort will also be important in engendering an awareness of one’s place in scientific endeavor. “We hope the students come to realize that, even if their work seems isolated and specific, it fits into a broader context that advances the field of mathematics as a whole,” Rafalski says.
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