Several students at a St. Mary’s College of Maryland summer program spent the last six weeks trying to untangle some aspects of knot theory, a high-level math concept that developed out of shoelaces, tangled holiday lights and electronic networks.

The key questions in knot theory, according to David Kung, associate professor of mathematics, is to tell mathematically whether one tangled loop of rope could be moved into the form of another. Sounds simple enough, in theory, but with even just three pieces of rope the number of combinations quickly can become overwhelming.

The students ran various simulations on the college’s computers to test their skills and hypothesis related to knot theory.

“It’s faster” with computers, Isabel Juarez of Chicago said. However, when the students tried to run some more complex tests, even the college’s computer processors did not have enough power.

Juarez said a big part of the study still relied on the students discussing and thinking about aspects of math theory.

The students were part of a college mathematics camp that finished up last week, during which students also looked at game theory and graph theory, elements known as pure math, according to David Kung, associate professor of mathematics.

Kung said about 170 college students from across the country applied for the Emerging Scholars Program Research Experience for Undergraduates, which only had 12 available spots.

Most of the students were rising sophomores; this type of college research program that is usually geared toward juniors and seniors, Kung said. The idea of opening it up to younger students was to hook them on the possibilities of a career in mathematics or science, he said, and the program included some information on continueing their educations through graduate schools.

“We think it’s a really valuable experience,” Kung said.

“We study pure math because it’s beautiful and it presents exciting intellectual challenges,” Kung wrote in an email. “At the same time, mathematics has a long history of being amazingly and unexpectedly useful. We were studying knots long before chemists needed our work to understand how proteins fold.”

Such theories are often the work of senior undergraduates or future career mathematicians doing gradate work. These 12 got a chance for an in-depth study of the topics with assistance from professors at St. Mary’s College.

“This definitely opened my eyes to the kind of math I want to keep learning,” Nora Stack of College Park said. She was one of four St. Mary’s College of Maryland students in the six-week program.

Why study math theories such as the ones the students tackled over the last six weeks? Stack said that it is interesting and can lead into other types of sciences. There are other reasons, too, she said.

“It’s the unknown, it’s the mystery,” Stack said.

The students stayed on campus for a month and a half in a campus dormitory. During their downtime between math sessions the students explored the campus, played games and generally hung out and got to know one another, they said.

The National Science Foundation funds hundreds of such programs, called research experience for undergraduates; this is the first of its kind at St. Mary’s College, Kung said. “These students will go off to regional conferences and their home institutions and present their work,” Kung said.

The program was funded through a $287,000 grant from the foundation, which provided pay for the professors involved, covered all of the students’ expenses and even gave them stipends for their time. The grant will cover the program for two more summers, he said.

Emerging scholars programs like the camp at St. Mary’s College are aimed at different populations of students that historically have not performed up to their potential, Kung said. They are often held during summers by colleges to help level the playing fields in different disciplines.

“Like many others, for us that includes economically disadvantaged students, first-generation college students, as well as African-American and Latino/a students,” he wrote in an email. “In mathematics, it also includes women.”

Along with Kung, professors Alex Meadows, Sandy Ganzell and Alan Jamieson acted as research mentors for the program, while Susan Goldstine was the seminar leader.

jyeatman@somdnews.com