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 subgraph 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.
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.
I am interested in running a MTH 496 course in Fall 2026 on any of the topics above.
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