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Sophomore Ekaterina Jager (Tashkent, Uzbekistan) is using complex mathematical formulas to determine success rates in network systems.
A participant in Lafayette’s EXCEL Scholars program, she is working under the guidance of Gary Gordon, professor of mathematics. In EXCEL, students work closely with faculty on research while earning a stipend.
“Our research deals with the concept of probability,” explains Gordon. “It has applications in industries such as water or power utilities where one central information location is important.
“Imagine a computer network with one server, where each machine communicates only with the server, not necessarily with the other computers. If each computer serves as a node in that network, the edges of the network may be susceptible to failure. For example, if we have 50 computers to set up and 52 connecting wires, we can use mathematics to determine the best configuration and estimate probability of failures and successes in that network.”
Jager, a double major in electrical & computer engineering and math & economics, explains the mathematical theory behind the research.
“We are investigating a given number of vertices and edges and attempting to determine the best way to connect them. Also, in directed networks, given the geometry of the network, [we’re determining] the best way to assign directions for each edge.”
“At this point, we have some conjectures that are based on cases we generated by hand as well as more complicated cases generated by a computer program I wrote. We are trying to prove some of the conjectures, which is quite challenging,” she says.
Jager says Gordon gives very good advice and ideas while guiding her through the project, and provides specific cases as background. “At the same time, he gives me freedom to explore some aspects of the problem,” she adds.
Jager explains that this research is broadening her mathematical horizons by providing an opportunity to solve problems beyond the classroom.
“I am very interested in mathematics, especially in studying problems that have not been solved yet,” she says. “This experience is quite different from solving a problem that has the answer in the back of the book. I am very confident that the knowledge and experience I acquire while working on tough problems will be very relevant to my future plans.
“It’s great that Lafayette gives so many opportunities to undergraduate students to conduct research. It is a meaningful experience that helps students decide what they want to do in life.”
Treasurer of Society of Women Engineers, Jager is a member of the Math Problem Solving Group, International Students Association, Investment Club, and Hispanic Society. She has also participated in Latin and swing dancing.