Eric Gottlieb

Teaching 

I love teaching mathematics at all levels. I favor the traditional lecture style of pedagogy, though I encourage my students to participate in classroom discussion. I enjoy teaching math-phobic students and math majors equally. It is just as important to me that students learn to appreciate the beauty and power of mathematics as it is that they learn the content we are studying.

Courses

Courses I have taught many times include Linear Methods, Calculus I, Calculus II, Combinatorics, and Abstract Algebra I and II. Courses that I have taught less frequently include Applied Calculus, Differential Equations, Excursions in Mathematics, Introduction to Applied Statistics, Introduction to Contemplative Practices, Linear Algebra, Transition to Advanced Mathematics, Mathematical Probability and Statistics I and II, Discrete Structures for Computer Science, Automata Theory, and Senior Seminar. I have taught Mathematical Programming and GRE Preparation as reading courses. One semester, I taught a section of Applied Calculus in Spanish, and I taught Calculus II in Spanish twice during the year I spent in Chile. I have supervised senior projects on a wide variety of subjects and internships at several Memphis-area organizations.

Research 

I am trained as an enumerative and algebraic combinatorialist. Combinatorialists study finite sets. Enumerative combinatorialists use mappings between finite sets to establish relationships about their sizes. Algebraic combinatorialists study finite sets that carry algebraic structure and look for mappings that supply information about size while respecting algebraic structure. I am particularly interested in partially ordered sets.

I have also published in graph theory, voting theory, and Ramsey theory. I am currently studying partial orders in the context of fair division and have an interest in combinatorial game theory. I enjoy practical problems that can be approached through the lens of mathematical programming.

Outside the Classroom 

I am a native Floridian, as is my wife, Rebecca Terrell. I enjoy the company of the many excellent people I have had the good fortune to befriend. I have an interest in Buddhist practices, especially as taught by Thich Nhat Hanh. I often commute by bike or on foot. In previous lives I worked as a geologistand as a commercial salmon fisherman.

SELECTED PUBLICATIONS

Erdős-Szekeres results for set partitions, Integers 15 (2015). (with M. Sheard)

The h, k-equal partition lattice is contractible when h ≥ k, Order (2013).

Elections with partially ordered preferences, Public Choice (2012). (with M. Ackerman, S.-Y. Choi, P. Coughlin, and J. Wood)

Inclusion-exclusion and the topology of partially ordered sets, in Resources for Teaching Discrete Mathematics, MAA Notes #74 (2008).

La formula de Euler: poliedros, grafos planares, y topologia. Revista del Instituto de Matematica y Fisica, Año 7, No. 11, 1-12.

Color-induced subgraphs of Grünbaum colorings of triangulations of the sphere. Australasian Journal of Combinatorics 30, 183-192. (with K. Shelton)

An EL-shelling of the nondecreasing partition lattice. Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium 162, 119-127.

On the homology of the h, k-equal Dowling lattice. SIAM Journal of Discrete Mathematics 17, 50-71.

Using integer programming to guide college admissions decisions: A preliminary report. The Journal of Computing in Small Colleges 17, 257-265.

Cohomology of Dowling Lattices and Lie Superalgebras. Advances in Applied Mathematics 24, 301-336. (with M. Wachs)