Students Apply Math Research to Real-World Problems

Posted: June 21, 2010 at 1:00 am, Last Updated: June 18, 2010 at 3:02 pm

Philip Naudus, who recently graduated, presented his research at a national conference.

By Catherine Ferraro

Who would have thought that majoring in math would lead to studying the causes of aneurysms or analyzing the interaction of light and gravity using galaxies? In fact, this is exactly the type of research two Mason undergraduates have been conducting for the past year.

As part of Mason’s Undergraduate Research in Computational Mathematics (URCM) program, Avis Foster, a senior applied mathematics major, and Philip Naudus, a recent graduate with a double major in applied mathematics and physics, had the opportunity to work with professors in the Mathematical Sciences and Computational Data Sciences Departments on cutting-edge research.

Each year, Mason’s URCM program awards up to 10 undergraduate research assistantships for students majoring in mathematics. Students receive stipends for full-time research in the summer and part-time research during the academic year.

The program is funded by the National Science Foundation under its Computational Science Training for Undergraduates in Mathematical Sciences initiative.

Interested in applying research to real-world situations, Foster was inspired by a lecture given by Padhu Seshaiyer, associate professor of mathematical sciences, about his own research on aneurysms. The decision to pursue this topic was also a personal one for Foster – her uncle died because of an aneurysm.

Avis Foster plans to continue her research during her senior year at Mason.

Foster’s project titled “Numerical Modeling and Analysis of Fluid Structure Interaction in Biological Systems” analyzed how aneurysms were formed and examined how the arterial wall interacts with blood on one side and cerebral spinal fluid on the other to the point that the wall breaks.

“I decided to pursue this area of research because I am most interested in how mathematics can be used to help people in the real world,” says Foster. “With the passing of my uncle, the idea that my research could someday be used by doctors to help them understand and prevent aneurysms is a very rewarding feeling.”

For the past year, Foster’s research has focused on running different numerical methods to determine the status of the arterial wall and then continuing to add components that would make the model more complex and realistic.

Naudus’ topic was one that is more traditionally related to mathematics. For his project, he did computer modeling of gravitational lensing systems, which occurs during the interaction of light and gravity. Expanding on Albert Einstein’s theory of general relativity, Naudus examined the positions of two galaxies, one in the distance and the other in the foreground, and how light bends around the closest galaxy.

“Gravitational lensing is something that occurs on an astronomical scale, so it doesn’t really affect people as they go about their day-to-day lives,” Naudus explains.

“However, the theory of general relativity has significant implications to modern technology. As we continue to do further research on this theory, it is my hope that engineers can use this knowledge to apply to future technologies.”

As part of the URCM program, Foster and Naudus, along with Franz Hamilton, Josh Snyder, Marlene Ouyaro and James O’Beirne, traveled to San Francisco in January to present their research at the 2010 Joint Mathematics Meeting of the American Mathematical Society and the Mathematical Association of America. Nearly 6,000 mathematicians, exhibitors and students attended.

Each student gave a 10-minute presentation to research professionals in the field and then attended the Undergraduate Poster Session with nearly 250 other students. After the judging, Foster took home a first-place prize for her research.

Both Foster and Naudus plan to continue research on their particular topics in the fall. Foster, who will be a senior, hopes to pursue a graduate degree in mathematics research after she graduates. Naudus will continue researching the theory of general relativity in a joint master’s and PhD program in physics at Rutgers University.

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