all adds up
By David J. Craig
Tiffany Caufield had planned for years to become a high school teacher. But last year the SED sophomore realized that her heart was in research.
“Just as I was finishing up my required math courses, I found myself getting really excited by them,” says Caufield (CAS’04), who switched her major to mathematics last November and now plans to become a professor. “I would have been so depressed if I wasn’t doing math anymore.”
Today, Caufield is among a growing number of undergraduates nationwide participating in independent math research that a few years ago was considered appropriate only for students at the graduate level and beyond. But increasingly educators are encouraging undergraduates to become involved in math research in order to expose them to the creative and imaginative aspects of the discipline.
Several of BU’s brightest math students, including Caufield, will
showcase their research on Saturday, March 22, at the first Research by
Undergraduates in Mathematics Boston University Symposium (RUMBUS). Students
from 24 colleges and 6 local high schools are expected to attend the symposium,
which will include a poster session presenting the independent projects
of about a dozen undergraduates from BU, Holy Cross, SUNY-Genesco, Fairfield
University, and the University of Scranton. The researchers also will
give a brief talk about their work.
In addition to Caufield, who helped organize RUMBUS, BU participants include Cecilia Busuioc (CAS’03, GRS’03), Pradeep Mouli (CAS’05), Tiffany Psemeneki (CAS’04), Yakov Shapiro (CAS’03), and Melissa Vellela (CAS’03). The symposium is sponsored by the CAS math department’s Undergraduate Mathematics Association.
“I want to foster an exchange of ideas among the students and also to help them learn to talk about their work, which is something that is generally not taught enough in the classroom,” says event coordinator Emma Previato, a CAS professor of mathematics, who hopes to make RUMBUS an annual event. Another objective of the symposium, she says, is to inspire high school students to pursue advanced studies in math.
For Shapiro, a senior who assisted a BU postdoctoral math researcher two years ago and already is involved in his own graduate-level research, discussing his work with his undergraduate peers is particularly challenging because it is so advanced and specialized. The research he will present at the symposium involves complex dynamical systems — specifically, describing the patterns that form when quadratic functions are applied to complex numbers repeatedly. “I often feel that my research is too complicated to explain because it’s so abstract, but I like talking about it, and it’s very satisfying to help someone understand what it’s all about,” says Shapiro, who intends to become a theoretical physicist. “You then feel that it has something to do with reality.”
Caufield recently developed an algorithm to map the path of a particle
bouncing endlessly within a closed elliptical curve. She says that listening
to students describe their research often gives her ideas for her own.
“You always hear about theories that apply to your work that you’re
weren’t familiar with,” she says. “It’s energizing,
and that’s how new math is born.”
In addition, the symposium will include a keynote presentation, entitled Soap Bubbles and Mathematics, by Frank Morgan, a Williams College mathematics professor. An internationally recognized expert in geometric measure theory, minimal surfaces, and calculus of variations, Morgan is expected to focus on the mathematical principles involved in how bubbles attach to one another.
“Dr. Morgan is a wonderful speaker who is extremely passionate about encouraging people to learn how to communicate about mathematics,” says Previato. “Audience members at any mathematical level, from freshman calculus to faculty, will enjoy his presentation.”
For more information, visit http://math.bu.edu/people/RUMBUS03.