Math research projects range from worm movements to sports predictions

In a petri dish, they're barely visible to the naked eye, appearing more like sand grains than living creatures. Under a microscope, the 1 mm long roundworms look and move around just like typical worms.

For Jeff Kopsick, a biology major and a mathematics minor, the tiny organisms provided an opportunity to combine interests in both disciplines for a mathematics research project this summer. Kopsick wondered what could be learned about the movements of the worms by putting them in a maze filled with liquids of varying viscosities. And would it even be possible to build a maze small enough to test any mathematical theories?

Kopsick's roundworm locomotion study was just one of 14 projects student math researchers tackled this summer at JMU. Other projects involved predicting the success of National Basketball Association teams in playoff series, exploring how a multi-legged robot could change speeds and creating a matrix population model for Monarch butterflies. The student researchers received stipends for their work, some funded by the National Science Foundation and others funded internally.

Kopsick, a junior, learned that he could build a microscopic maze with a 3D printer in the math department's newly established Maker Lab, thus enabling him to further study the worm movements. He came up with the idea during classes and presentations last year, but he wasn't sure how to go about starting a research project. One thing he was certain about was that faculty would listen to his idea. "The nature of the university is just, you have that door open. There's no, 'Hey, I don't want you. ' It's, 'Let's hear what you have to say. Oh, maybe this could work,'" said Kopsick, who plans to write a journal article about his project.

His advisor, Dr. Eva Strawbridge, said she helped make the project feasible, but Kopsick made it work. "He's very independent. It was his design. He was the one who was doing the talking to the dean when the dean came to visit and he was the one who completely handled a visit from the president."

Added Kopsick, "Working in this lab has just been a great opportunity and I'm very thankful for being able to learn so many different skills, whether it be an intro to programming or an intro to fluid mechanics."

In addition to the 3D printer, Kopsick used a custom microscope built at JMU and a rheometer, a device used to measure a liquid's viscosity. Both devices are housed in the math department's Wiggling Organism Research and Modeling (WORM) Lab.

Strawbridge, an assistant professor of mathematics and statistics, said Kopsick's research has mathematical significance. "When you put objects in a fluid, it's not just an object interacting with another object, it's the object interacting with this fluid which then interacts with the object. You have a lot of interactions going on and the way Jeff has designed the environment, we can start to model the fluid interaction."

While Kopsick concentrated on microscopic worms, John Ellis spent his summer formulating a model to predict the success of teams consisting of larger-than-average humans, a.k.a NBA teams.

Ellis, a senior math major who will graduate in December, worked with statistics from the 2002-2003 season through the 2011-2012 season. To run the model, he would choose one of the 10 seasons as a test. The model would then determine, based on statistics from the other nine seasons, the results of each round of the playoffs in the test season. Best of all, Ellis said, was that the model's accuracy remained consistent, picking winners correctly about 85 percent of the time, whether he picked an early season from the dataset or a late season.

While the model is not set up to predict what will happen in the upcoming season, Ellis said he could work with the numbers to do that. However, the accuracy might not be as good.

An avid basketball fan, Ellis said one of the most rewarding aspects of the project was working in a subject area he enjoyed. "I was rewarded with something I really wanted to do," he said.

Emily Hunt, a junior majoring in math and Spanish, did her research in Mexico, where she used periodic population matrices to model the life cycle of the eastern Monarch butterfly. While some researchers have sounded the alarm that butterfly migration is at risk, Hunt came to a different conclusion. Her preliminary research results showed that the monarch butterfly is not currently at risk of extinction.

Hunt is continuing the project by working with a biologist to refine some of her parameter estimates in order to make her mathematical model as accurate as possible.

"Summer research opens unexpected paths, and allows students to discover something new," Hunt said. "It allows a student the opportunity to make new connections and become involved in something completely different from anything they may have experienced before."

Lisha White, a sophomore engineering major, came to a similar conclusion while working as part of a four-person team that researched how to build a multi-legged robot that could change speeds. "I was with people that I wouldn't normally talk to because we all have different majors and we are in different class years," she said. Two of the team members, Mikias Kidane and Luis Parada, are senior math majors and the other member of the team was sophomore chemistry major Jojo Yirrah.

White said the topic was challenging and rewarding. "We were looking at math that some of us have never seen before and trying to apply it to our previous knowledge," she said. "I think students should pursue summer research because it gives a taste of what research in your field is like. It is what you learn in class applied to life. I also realized that I would love to do this type of research for a career."