Student participation rejuvenates math colloquium

The first Spokane Regional Mathematics Colloquium of the school year, on Oct. 5, showcased advanced math research done by Gonzaga and Whitworth University students over the summer.

The colloquium featured two presenters from Gonzaga and two from Whitworth. It was not a competition – just a gathering of math faculty from local universities who were treated to slide shows on a wide variety of math-related topics.

Whitworth student Shane Shetler started the slide shows off with "A Brief Introduction to Ramsey Theory." He began his presentation by showing the audience a pentagram. Then he colored some of the lines connecting the points of the pentagram red and some blue. When he tried to do the same thing with a hexagon, some of the triangles had the same color on all three edges. This gave him the "Ramsey number."

"It's easier to see it than to read a description," Shetler said.

Professor Vesta Coufal, the Gonzaga contact for the colloquium, said that the meetings are mainly meant to bring math faculty members together, but occasionally, the colloquium will also accommodate students.

"Traditionally, it has been a chance for math faculty to talk with other math faculty," she said. "This is still the case, though lately there has been more of an effort by some speakers to give talks about interesting mathematics, targeted at undergraduates."

Gonzaga student Erika Helgeson provided an interesting blend of math and biology with her presentation, "Modeling Genetic and Environmental Influences on Resource Allocation Traits of Arabidopsis lyrata." Arabidopsis lyrata is a plant that has evolved in different ways to adapt to different environments. Helgeson used mathematical formulas and graphs to map the ways that the plant's genes develop differently in North Carolina and Norway– a "resource-rich" and "resource-poor" environment, respectively.

Helgeson, who did research for the project at the University of North Carolina Greensboro, said that implications include furthering our understanding of crop productivity and plant responses to environmental change.

Marshall Hurson, a junior at Gonzaga, gave his presentation on the genetic algorithm, or "Searching for an Optimal Book Embedding." A computer science major, Hurson's mission was to find a way to solve NP-complete problems, problems where the solution is so complex that the time it takes to calculate it is infinite.

"It might take 4 billion years to find a solution to one of these problems," Hurson said.

Hurson was able to explain how to solve these problems while staying within the 10 minutes allotted to each presenter. He did this by turning some aspects of a problem, such as finding out what the quickest route for a traveling salesman to take to reach multiple cities is into chromosomes, and then mating those chromosomes with a computer program.

Coufal said that the current incarnation of the colloquium can trace its history back quite a way.

"It has been going on for many decades and started, as I understand it, with math faculty in the region getting together once a month to talk about teaching and school issues, and about interesting math that they were working on or had encountered," she said. "It was very informal. It is more formal now."

The last student presenter was Sarah Whittemore from Whitworth, who whittled the complex phenomenon of stress-induced insomnia down to a series of graphs and charts.

Though she admitted that the biology behind sleep is "a riddle wrapped in a mystery inside an enigma," her "Mathematical Modeling of Stress-Induced Insomnia" showed that insomnia is not a result of a person's sleeping functions performing poorly, but rather a result of their "waking up" functions performing too well.

Whittemore also drew the biggest laugh of the night from the audience of about 30 professors and students when she gave examples of stressors that could cause insomnia, which included "a college student freaking out about a presentation."

While Whittemore, Helgeson and Hurson all linked their research back to real-world situations, Shetler was content to explain why he did his work on Ramsey theory, as only a participant in the Mathematics Colloquium could.