A Summer of Computational Mathematics at FSU

January 1, 2005

Student participants in the 2004 Research Experiences for Undergraduates Program in Computational Mathematics at Florida State University.

Steven L. Blumsack and Susan Greenwalt

Tallahassee, Florida, July 2004. World-class meteorologist T.N. Krishnamurti was at the front of the seminar room, explaining the importance of mathematics in the forecasting of hurricanes. No one could have known just how timely these ideas would prove to be for Florida, Haiti, Grenada, and other places in the paths of the devastating hurricanes of August-September 2004.

Making up the majority of the audience at the seminar were 16 university students---participants in the eight-week Research Experiences for Undergraduates (REU) program at Florida State University in the area of computational mathematics. At the time of Krishnamurti's talk, the students were thoroughly immersed in a variety of research projects. The projects integrated phenomena in the physical sciences, mathematical concepts, and computational tools in very much the same way that hurricane models are developed.

One key to the success of the program, which was sponsored by the National Science Foundation and the Department of Defense, was the involvement of postdoctoral fellows in mentoring the students. The postdocs' schedules permitted them to have frequent contact with the students, providing the students with a smooth transition from the initial short courses and workshops to quasi-independent research experiences.

Some of the students worked on projects in which their mentors had already developed the basic software necessary to initiate the complex research. These students adapted the computer programs to research challenges posed by their mentors.

In other cases, the students developed models and the necessary computer programs from the ground up. One such student, Hila Hashemi (University of California, Berkeley), studied the effects of the roughness of a thin long tube on the flow of a fluid by finding approximate solutions of an appropriate set of differential equations. She captured the essence of the REU program in her final report, writing that she had fulfilled her objective of having a "research experience on computational science and applied mathematics, including defining a problem, formulating solution strategies, implementing the strategies, and analyzing the results."

To develop a model for the optimal pacing in biking, Brian Pike (North Carolina State University) and Satesha Augustin (University of the Virgin Islands) began by researching the literature. After developing simple models and scenarios, they progressed to models that included cooperation among teammates and cycling over hilly terrain. As part of their research, they developed software for determining the optimal values of parameters in a system of differential equations.

Christopher Rogan (Princeton University) developed a neural network model of composite materials, with a genetic algorithm to determine the set of parameters that best described the composites. Eric Schmidt (Colorado State University-Pueblo) used real data and applied statistical methods to study the maximum and minimum temperatures for the month of January during an El Nino event.

Tobin Isaac (Rice University) and John Gemmer (Millersville University) studied the shape changes in falling drops. The material they were investigating had both viscous and elastic properties. Their numerical results agreed with existing experimental observations.

The students described their experiences in individual interviews with an outside evaluator. In the words of a few of them,

"During this summer's REU I feel that I gained an incredible amount of confidence in my ability to apply mathematics to real world problems."

"It helped me be more familiar with the process of doing applied math research and gave more insight into the possibility of going to graduate school."

"This program gave me a chance to do research that was not available at my college and allowed me to easily explore the possibilities of graduate school and more advanced work in math and science."

Additional information about the 2004 program (the participating students, their mentors, and projects) and the 2005 program (description of projects and application information) can be found at http://www.cespr.fsu.edu/people/myh/reu.html.

Steven Blumsack is an associate professor of mathematics and Susan Greenwalt is the REU program coordinator at Florida State University.

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