Yes, it is possible for undergraduates to do research in mathematics and several of our students are doing so! On April 8, the School of Science held its first Undergraduate Research Day with presentations by more than forty undergraduates including four from the Mathematics Department. The four students each worked independently under the supervision of a faculty member on a project in which the mathematical background was accessible to a typical undergraduate, but that involved a topic of current interest in the mathematics research community.
Tim Engle, under the supervision of Professor Fabio Milner, worked on the mathematical modeling of crystal precipitation in photographic film, a project that involved modeling the Ostwald ripening process by differential equations and then solving them numerically.
In his project, Ilya Gluhovsky tried to find best approximations to a matrix from a class of "good" matrices like normal matrices or nilpotent matrices. Gluhovsky was supported by a National Science Foundation Research Experiences for Undergraduates grant and was supervised by Professor Carl Cowen. Elad Harel, also working with Professor Cowen, studied the numerical range of a matrix, devised an effective algorithm to plot the numerical range, and wrote a MATLAB program to do so. Gluhovsky also presented his work at the San Francisco meeting of the American Mathematical Society, and Harel expects to present his work at a meeting of the International Linear Algebra Society later this summer.
Richard Verhaagen studied quasigeometric series under the direction of Professor David Cruz-Uribe. Quasigeometric series are positive infinite series for which the sum of terms in a tail is no more than a multiple of the previous term. Verhaagen found some necessary and some sufficient conditions for a series to be quasigeometric.
While the projects of these undergraduates were smaller in scope and depth than a Ph.D. thesis or a research project by a professional mathematician, the students who participated have a better understanding of research in mathematics and an appreciation that it is possible for new mathematics to be discovered.