Jess & Mildred Fisher College of Science & Mathematics

Department of Mathematics

Undergraduate Student Research

2013 Regional Undergraduate Mathematics Research Conference

March 30, 2013
Department of Mathematics
Towson University

The Undergraduate Mathematics Research Conference at Towson was a one-day meeting designed to promote undergraduate research in mathematics by showcasing completed original research, selected expository presentations, as well as research projects in progress. If you are an undergraduate student or a high-school student who has participated in an original research project, you were invited to give a presentation about your research. The web page Advice for Presenters offered information about the length of the talk, the physical facilities, and some links to website for helpful hints in preparing your presentation.

In addition to student presentations, the conference featured two invited faculty talks, a short tutorial on LaTeX, and information sessions on mathematical modeling and career opportunities in government, industry, and academia.

The first invited talk was given by Dr. Bruce Torrence, Professor of Mathematics at Randolph-Macon College.

The Mathematics of Lights Out

The game Lights Out, by Tiger Electronics, is a five-by-five array of lighted buttons, each of which can be either on or off. The game starts with a random collection of buttons that are lit. Your task is push buttons until you turn off all the lights. It sounds easy, but here's the rub: each time a button is pushed, its state changes, and so do the states of its vertically and horizontally aligned neighbors.

Lights Out has inspired an impressive body of mathematical literature. In this presentation, we'll begin with an overview of the mathematics behind the game. In particular, we'll learn how to use linear algebra to solve Lights Out games, not just on 5 x 5 boards, but on rectangular boards of all sizes. (See full abstract.)

The second invited talk was by Dr. Gisela Bardossy, Professor at the Merrick School of Business at the University of Baltimore.

The Mathematics of YouTube:
Where Exactly on the Internet is the Gangnam Style Video?

Digital information is constantly poured into the cloud: webpages, images, videos, likes, comments. But do you know exactly where in the cloud is all that information physically stored? Do you know how many copies of those webpages, images, videos are stored? Who decides that and how? More copies of the information ensure accessibility and better service, but also higher storage cost and power consumption. There is a natural trade-off between quality of service and cost. (See full abstract.)

Also, a workshop on mathematical modeling was given by Dr. Sommer Gentry, a mathematician working at the U.S. Naval Academy and at Johns Hopkins University School of Medicine.

Mathematics That Makes More Kidney Donors

Did you know that operations research can increase the number of kidneys available for patients who need a transplant? Patients in kidney failure often have loved ones willing to donate one of their own healthy kidneys, but at least one third of these offers must be declined because of a blood type or other incompatibility. A kidney paired donation matches one patient and his incompatible donor with another patient and donor in the same situation for an organ exchange. Patient-donor pairs can be represented as the vertices of a graph, with an edge between two vertices if a paired donation is possible. Then, a maximum matching on that graph is an arrangement in which the largest number of people can receive a transplant. You will learn how to rescue patients in need of a transplant by creating and solving an integer programming model.

Support for this conference was provided by National Science Foundation grant DMS-0846477 through the Regional Undergraduate Mathematics Conferences program of the Mathematical Association of America. Additional support is provided by the Department of Mathematics at Towson University, and the Mathematics Club at TU.


2013 Undergraduate Mathematics Research Conference
Conference Poster




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