- Linear algebra, including numerical linear algebra
- PDE-based image processing.
- The use of technology in teaching mathematics (see, for example, the applets I've written and used for teaching Calculus and Linear Algebra).

**Current research projects**

- Adaptive TV image restoration using exact solution theory.
- Comparing implicit vs. explicit time-marching in doing anisotropic diffusion
(TV Regularization is a model case of anisotropic diffusion).
- Developing a TV-minimizing median filter: basically,
combine the effectiveness of TV Regularization with the
speed of a median filter.
- Unifying TV image restoration and PDE-driven image restoration.
- Local variance-based adaptive TV regularization.
- Numerical considerations in TV regularization.
- Numerical methods for TV regularization.

- I'm currently combing through books dealing with the history and evolution of math in the hopes of putting together a presentation of some of the basic and common mathematical discoveries that would be interesting to non-math people.