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.