As a physicist and computational scientist, my knowledge of applied mathematics incorporates many topics in discrete systems: logical grammar (if p then q); techniques of proofs; recursion relations, difference equations & their solutions; matrices operations; counting, combinatorics & probability; set theory and graph theory. My Ph.D. thesis had an exact, constrained enumeration as its springboard into statistical calculations. In order to simplify the resulting complex statistics, I reduced the problem to a graph for which I developed a kinetic model. I simulated kinetics on the graph and solved the eigenvalue problem associated with a matrix chosen to approximate the graph. To this day, I reduce high dimensional problems to low dimensional ones to provide solutions for real-world problems. I'm competent to teach both theory and practice of discrete mathematics.