Faculty interested in undergraduate research
Feryal Alayont
Contact information: [email protected]
Office: MAK A-2-160
Research areas: Discrete mathematics, graph theory
Current projects: Edge covers of graphs: During the last two summers, I have worked with nine students on edge covers of graphs. An edge cover of a graph is a collection of edges for which every vertex in the graph is an endpoint of at least one edge. Each student worked with a different family of graphs to find edge cover sequences to add to the Online Encyclopedia of Integer Sequences. These students gave presentations at local colleges, and at regional, national and international conferences. The students’ backgrounds ranged from not having taken a proof course to having taken a course in Galois theory, so any background is welcome for this project.
Definite integrals using the bracket method: Given a definite integral abf(x) dx, if there is an antiderivative of f(x), we know how to evaluate the integral. But what if we have 0ex2dx? How do we evaluate the integral? This integral is related to the statistically ubiquitous normal distribution. The value of the integral is 2which can be found by looking up in a table of integrals. However, these tables sometimes contain incorrect values. A new heuristic method to evaluate these definite integrals is the bracket method, invented by I. Gonzalez in his doctoral thesis in physics. In this project, we will learn about this method and apply it to verify integral values in the Tables of Integrals by I. S. Gradshteyn and I. M. Ryzhik. Calculus 2 is the minimum background for this project.
Other discrete topics: I have also supervised projects in the past on rook polynomials, prime and coprime labelings, and I like any project where we count things or where there are numbers. I have worked with a total of 84 students on independent projects over the past 18 years.
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