Updated for 2013
Dr. Tetyana Berezovski
Mathematical Knowledge for Teaching in the content of Geometry and Linear Algebra.
My fields of research are combinatorics and graph theory. In very general terms, combinatorics deals with enumeration of the number of ways to perform a mathematical task (such as choosing a delegation of three people to represent a group of 15 people), and graph theory is concerned with diagrams you make by connecting dots with lines. Since these areas are relatively accessible to undergraduates, they are often sources of undergrad-level research problems, but not all the projects I have directed have been purely combinatorial, because the choice of topic is in large part driven by the student’s needs and interests. I have directed projects each of the last five summers. In ’06, I directed two summer scholar projects: The role of invariance in mathematics (which, among other things, investigated the use of an invariant in a number of combinatorial problems) and Generalized Möbius Inversion (which is abstract combinatorics). In Summer ’07, I directed a project in another area of combinatorics, Pólya-de Bruijn Theory, which deals with enumeration questions in which not all the ways of performing a task count as different. (For example, consider painting the faces of a cube using k colors. Rotating the cube will make some colorings coincide with others.) I directed a project centered on probability theory in ’08, on stochastic processes and the Black-Scholes formula in ’09, and on problem solving in ’10. For more details on these projects, please see the one-page summaries prepared by the students.
