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What Kristen Mazur ’08 (Fayetteville, N.Y.) enjoyed the most about her Research Experiences for Undergraduates (REU) project this summer at Lafayette is that it combined two of her prime interests.
“I really liked the idea of combining math and biology,” says Mazur, a math major. “I think it is fascinating that we can combine two seemingly incompatible topics, differential equations and biology, and learn even more about each.”
Lafayette’s REU Program is an intensive, eight-week summer research experience in which undergraduate students from colleges and universities throughout the country investigate unsolved problems in mathematics. Student participants work in small groups directed by individual faculty members.
Mazur and three other students – Jonathan Adler of Worcester Polytechnic Institute, Lynne Erickson of Ursinus College and Thomas Tyrrell of Boston University – were led by L. Thomas Hill, professor of mathematics. Mazur served as research assistant on the project.
The group investigated the asymptotic behavior of solutions of two systems of delay differential equations. An asymptote is a straight line which is being approched by a curving line. The two lines can intersect but never make contact. According to Hill, delay differential equations are used to model a system whose evolution depends not just on the current state of the system, but also on past states.
“The particular equations we examined are used to model vertically transmitted diseases,” he explains. “The parameters in these equations correspond to birth and removal rates for susceptible and infected individuals. It is a measure of the frequency with which those who are infected pass the disease to their offspring, and a measure of how easily the disease is contracted by others who have contact with infected people. While we used the biological interpretations of our systems to guide some of our explorations, our primary focus was on the mathematical analysis of the systems and not on the underlying biological phenomena.”
Mazur reports that she liked the dynamics of her group. Since everyone had slightly different backgrounds, she says that one person’s weakness was another’s strength.
“We were able to bounce ideas off one another and come up with some really neat things,” Mazur adds. “It was nice to be able to spend a summer with people who are just as interested in math as I am. Math jokes are accepted and even encouraged. It was a nice change of pace.”
Hill appreciates Mazur’s organizational skills, and her thorough and careful work on the REU project.
“However, her greatest strength was that she was not easily discouraged,” he adds. “Results did not come quickly and easily, and there was no guarantee that any worthwhile results would be obtained, but Kristen stuck with the project and made very significant contributions to our group’s work.”
Likewise, Mazur appreciated Hill’s guidance.
“He was really interested in the project and seemed excited to work on it and reach our goals,” She says. “Also, he always treated us as equals. I felt like I was working with a team of five instead of with a professor and three other students. I really liked that.”
The teamwork aspect among students from different academic institutions and backgrounds is the hallmark of the REU program. In addition to their research work, the students attended a week-long research conference, heard presentations by guest speakers, and gave formal presentations on their own work both to the students in Lafayette’s REU program and to a group of REU students at Rutgers University.
“Lafayette is the perfect environment for REU projects,” Mazur says. “The professors get really into the project and really take the time to get to know all of the students on the project. That really makes everyone feel welcome and comfortable and creates an enjoyable atmosphere for the summer.”
Many students who have participated in Lafayette’s REU program have published papers in professional journals and presented talks on their summer research at national mathematics conferences. The students who worked on Hill’s project plan to present their results at the annual Joint Meetings of the American Mathematical Society and the Mathematical Association of America in New Orleans in January 2007.