Teaching Experience

University of Kentucky:
• MA 330, History of Math, Spring 2009. Course website.
• MA 330, History of Math, Graduation Writing Requirement Section, Spring 2009. Course Website
• MA 714, Topological Methods in Combinatorics, Fall 2008. Course Website
• MA 515, Linear Programming and Combinatorial Optimization, Fall 2008. Course Website
• Math 330, History of Math, Spring 2008. Course website.
• Math 322, Matrix Algebra and its Applications, Fall 2007. Syllabus.

Washington University:
• Math 309, Matrix Algebra, Fall 2005.
• Math 220, Finite Mathematics, Summer 2004.

University of Missouri-St. Louis:
• Math 1100, Section E01, Basic Calculus, Summer 2004.
  

Talk List :

2009
• "On the stable Kneser graphs," Summer 2009, Algebra, Geometry, and Combinatorics Seminar, San Francisco State University.
• "Cones and Affine Varieties," Parts I, II and III, Spring 2009, Algebra Seminar, University of Kentucky.
• "Enumerating Integer Points In Lattice Simplices,"Spring 2009, Graduate Student Colloquium, University of Kentucky.
• "Nowhere Harmonic Colorings of graphs," Spring 2009, AMS Western Sectional Meeting, San Francisco State University. Joint with Matthias Beck.
• "On the stable Kneser graphs," Spring 2009, Discrete CATS Seminar, University of Kentucky.
• "The Complex of Non-Crossing Diagonals in a Polygon," Spring 2008, AMS Southeastern Sectional Meeting, North Carolina State University. Joint with Richard Ehrenborg.
• "On the stable Kneser graphs," Spring 2009, Ulam Centennial Conference, University of Florida.

2008
• "The Geometry of Voting," Fall 2008, Undergraduate Math Club, University of Kentucky.
• "Morphism Complexes, Graph Coloring, and Characteristic Classes, Part 2 of 2" Fall 2008, Topology and Geometry Seminar, University of Kentucky.
• "Morphism Complexes, Graph Coloring, and Characteristic Classes, Part 1 of 2" Fall 2008, Topology and Geometry Seminar, University of Kentucky.
• "The Complex of Non-Crossing Diagonals in a Polygon," Spring 2008, Algebra, Geometry, and Combinatorics Seminar, San Francisco State University. Joint with Richard Ehrenborg.
• "The Complex of Non-Crossing Diagonals in a Polygon," Spring 2008, Discrete CATS Seminar, University of Kentucky. Joint with Richard Ehrenborg.
• "Discrete Hodge Theory," Spring 2008, Graduate Student Colloquium, University of Kentucky.

2007
• "Topological Approaches to Evasiveness," Fall 2007, Topology and Geometry Seminar, University of Kentucky. A discussion of Karp's Evasiveness Conjecture.
• "The Topological Tverberg Conjecture," Fall 2007, Discrete CATS Seminar, University of Kentucky. A discussion of the Topological Tverberg Conjecture and numerical index theory.
• "Graph Homomorphism Complexes," Fall 2007, Graduate Student Colloquium, University of Kentucky. A discussion of graph HOM-complexes and related conjectures.
• "h*-vectors of Lattice Polytopes," Fall 2007, Indiana University Combinatorics Seminar. An overview of recent work regarding Ehrhart h^*-vectors. Some of this is joint work with M. Develin.
• "h*-vectors of Lattice Polytopes," Fall 2007, AMS Southeastern Sectional Meeting, Middle Tennessee State University. An overview of recent work regarding Ehrhart h^*-vectors. Some of this is joint work with M. Develin.
• "Some open questions about f-vectors of polytopes," Spring 2007, OT Seminar, Washington University.

2006
• "Ehrhart h^*-vectors of lattice polytopes," Fall 2006, OT Seminar, Washington University. An overview of recent work regarding Ehrhart h^*-vectors. Some of this is joint work with M. Develin.
• "Ehrhart Theory and Reflexive Polytopes," Fall 2006, University of Kansas Combinatorics Seminar. An introduction to Ehrhart theory and h^* -vectors for reflexive polytopes.
• "Roots of Ehrhart Polynomials," Spring 2006, AMS Summer Research Conference -- Integer Points in Polyhedra, Snowbird, Utah. A discussion of a bound on the zeros of Ehrhart polynomials.
• "Norm Bounds for Ehrhart Polynomial Roots," Spring 2006, Graduate Student Combinatorics Conference, UW-Madison. A discussion of a bound on the zeros of Ehrhart polynomials.
• "Oh, what a change of basis can do!," Spring 2006, Missouri MAA Section, Spring 2006 Meeting, UM-Columbia. A discussion of a bound on the zeros of Ehrhart polynomials.
• "The Frobenius Coin Exchange Problem," Fall 2006, Undergraduate Math Club, Washington University. An introduction to the coin exchange problem and quasi-polynomials.
• "Brion's Theorem and Lattice Polytopes," Spring 2006, Undergraduate Math Club, Washington University. An introduction to the topic in the title.
• "Pick's Theorem," Fall 2006, Math Circles, Washington University.
• "The Pigeon-hole principle: a powerful idea with a funny name," Spring 2006, Math Circles, Washington University. Some applications of the pigeonhole principle.
• "Lattice Points in Lattice Polytopes," Spring 2006, Math Circles, Washington University. An introduction to Brion's theorem.

2005
• "Roots and Coefficients of Ehrhart Polynomials," Fall 2005, Major Oral Presentation, Washington University. A discussion of work by Beck, De Loera, Develin, Pfeifle, and Stanley regarding the title of the talk.
• "The Combinatorial Laplacian on Simplicial Complexes," Fall 2005, Spectral Graph Theory Course, Washington University. An introduction to the combinatorial Laplacian and some results obtained with it.
• "Monomial Ideals, Simplicial Complexes, and Stanley Reisner Rings I," Fall 2005, Combinatorial Commutative Algebra Seminar, Washington University. The first of three lectures based on the first chapter of the book Combinatorial Commutative Algebra by Miller and Sturmfels.
• "Monomial Ideals, Simplicial Complexes, and Stanley Reisner Rings II," Fall 2005, Combinatorial Commutative Algebra Seminar, Washington University.
• "Monomial Ideals, Simplicial Complexes, and Stanley Reisner Rings III," Fall 2005, Combinatorial Commutative Algebra Seminar, Washington University.
• "Graph Homomorphism Complexes," Spring 2005, Graduate Student Seminar, Washington University. A discussion of graph HOM-complexes and related conjectures.
• "The Erdos-DeBruijn theorem and points in the plane," Spring 2005, Undergraduate Math Club, Washington University. An introduction to the topic in the title.
• "How to Use a Generating Function," Fall 2005, Math Circles, Washington University. A proof of the closed formula for the Fibonacci numbers obtained with generating functions.
• "Using Matrices to Count Paths in Graphs," Spring 2005, Math Circles, Washington University. An introduction to interpreting matrix multiplication in graph theoretic contexts.
• "Stanley's Twelvefold Way to Counting," Spring 2005, Math Circles, Washington University. An overview of Stanley's Twelvefold Way, as found in his Enumerative Combinatorics, Vol. 1.
• "Matchings in Bipartite Graphs," Spring 2005, Math Circles, Washington University. An introduction to Hall's marriage theorem.
• "Integer Lattice Points in and on Circles in R^2," Spring 2005, Math Circles, Washington University. Some interesting results about bounding lattice points in circles.

2004
• "Topological Obstructions to Graph Colorings," Fall 2004, Minor Oral Presentation, Washington University. A discussion of various simplicial complexes associated to graph coloring problems with special emphasis on the box complex.
• "The Irrationality of Pi and e," Fall 2004, Undergraduate Math Club, Washington University. A proof of the irrationality of Pi and e.
• "Some Bounds in the Game of Sprouts," Spring 2004, Undergraduate Math Club, Washington University. A discussion of maximum and minimum lengths for Sprouts.
• "The Erdos-DeBruijn theorem and points in the plane," Fall 2004, Math Circles, Washington University. An introduction to the topic in the title.
• "The Golden Ratio and Fibonacci Numbers," Fall 2004, Math Circles, Washington University. An introduction to the topic in the title.
• "The Game of Sprouts," Spring 2004, Math Circles, Washington University. An introduction to the topic in the title and recreational mathematics.

2003
• "Euler's Formula for Planar Graphs," Fall 2003, Undergraduate Math Club, Washington University. An introduction to and proof of Euler's formula.
• "What is Graph Theory?", Fall 2003, Math Circles, Washington University. A broad overview of basic problems in graph theory.
• "K(G,1) Spaces and the Origins of Homological Algebra," Fall 2003, Washington University Graduate Student Seminar. An overview of K(G,1) spaces and their properties.
• "An introduction to Group Theory via R^2," Spring 2003, Math Circles, Washington University. The introduction of the group axioms as motivated by the group of affine transformations of R^2.

2002
• "The Bridges of Konigsberg problem," Fall 2002, Undergraduate Math Club, Washington University. A discussion of necessary and sufficient conditions for a graph to possess an Euler cycle.