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: An edge cover of a graph is a subset of the edges that includes all vertices. I am interested in enumerating edge covers of various families of graphs to find new sequences or new interpretations of sequences in the On-Line Encyclopedia of Integer Sequences. Students from all backgrounds are welcome to join this project.
Interlace polynomials of graphs: The interlace polynomial of a graph is a polynomial calculated recursively using a vertex deletion and edge switching process at each step. One we reach a collection of vertices by themselves, we assign x^n to the result. This process mysteriously gives a polynomial with real roots for certain types of graphs. I am interested in finding which graphs result in with real roots or other slightly nice cases.
Definite integrals using the bracket method: A new heuristic method to evaluate definite integrals from 0 to ∞ is the bracket method, invented by I. Gonzalez in his doctoral thesis in physics. The method involves four different rules that assign values to integrals using solutions of a linear system. In this project, students will learn about this method and apply it to verify accuracy of 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 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 more than 95 students on independent projects over the past 19 years.
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