My area of research is computational number theory, particularly the study of invariants over cubic fields. My other interests include mathematical logic, games, and the philosophy of mathematics. Faculty-student research is mainly dependent on the interests of students. Faculty-students projects from 2006-2007 include:
- A study of mathematical physics in the internal combustion engine. This study included an examination of the mathematics of how car engines work.
- The properties of sudoku and shidoku completed games, both in themselves and as matrices under standard matrix operations. In particular, a study of the properties of two of these games under matrix addition was examined, along with the beginnings of a study of their properties under matrix multiplication.
- The design of a mathematics summer camp for late middle-school to early high school students. This project consisted of a study of the way mathematics is taught in secondary education. Also designed were several long-term projects for the students.
- A study of the Collatz problem. This study takes the reverse approach of treating the Collatz problem as a tree with a single root, and looking at the behavior of the tree as it branches out.