Teaching  Mathematics is essentially about problem-solving.  My role in the classroom is to equip students with the tools used to approach these problems by explaining and modeling their use.  However, simply knowing about proper techniques is not sufficient for finding a solution; students must be proficient at properly applying these methods, often in creative ways.  This proficiency and creativity can only be developed through individual practice.  One of my professors once told me that the path of mathematical learning runs from the hand to the brain. (This was his response to me not turning in my homework.)

Although I believe the time students spend in class is important, I often tell them that the time they spend outside of class working on problems is much more important. I feel that my role in this process is close to that of a coach: I don′t do the work for them, but instead provide them with insight into proper techniques. I currently hold extended office hours on Tuesday afternoon when students come to work on problems together.  I like and encourage this arrangement because it allows me to provide immediate guidance, and allows a wonderful opportunity for students to learn from each other. I′m not there to answer all the questions, but rather to help students learn how to ask the right questions of themselves as they work.

Research  My primary area of research is graph theory. Graphs are mathematical objects used to model relationships, and are most often represented by a collection of points connected by lines. Though graphs can be applied to practically any discipline, I am a pure mathematician at heart and am interested in graph problems for their own sake. My primary interest is in graph coloring. Coloring requires that elements of the graph be partitioned in such a way that certain requirements are met. An easy way to consider such problems is by coloring the elements of the graphs different colors, hence, the name.

A well-known graph coloring result can be stated as follows: every political map (historical or fictional) can be colored with four colors so that no two territories sharing a border have the same color.  A proof of this fact, known as the four-color theorem, eluded mathematicians for over a hundred years. The first correct proof was given by Appel and Haken in 1976 and required the use of a computer program to check over a thousand small cases (sparking considerable debate on the nature of mathematical proof in the process). I like the fact that many graph coloring problems can be stated rather easily, yet their solutions are frequently non-trivial.

In addition to graph coloring problems, I have dabbled a little bit in additive number theory.  I am also interested in Ramsey graph theory, ergodic Ramsey theory, and proofs utilizing the probabilistic method.

Outside The Classroom

I live in Midtown with my wife Megan, a 2004 Rhodes alumna, and our orange tabby cat, Sigma.  We are both active members of our church, Second Presbyterian. I am currently finishing my doctoral dissertation at The University of Memphis under the guidance of my advisor, Jeno Lehel.  I was a rower at one point in my life, and am trying to spend more time on an erg this year. I′m an avid gamer, often to the chagrin of my wife; I don′t have a favorite genre, but games with zombies are usually considered favorably. My wife and I enjoy watching quirky comedies: one of our favorite movies is Hot Fuzz, and our current favorite television shows are 30 Rock and Flight of the Conchords. Another favorite activity is walking to the Memphis Zoo, where our guilty pleasure is watching the sea lion show. We are excitedly awaiting the arrival of our first child in January.