Topics in Discrete Mathematics: Topological Methods in Combinatorics, MA 714, Fall 2008

Course Materials:

• Course Syllabus
• Some Applications of Laplace Eigenvalues of Graphs, by Bojan Mohar. We will be reading through parts of this paper for the second half of the course.

In-class talks

• Nov 17th: Prof. Serge Ochanine - Quasi-toric Varieties
• Nov 24th: Beth Kirby - Toric Varieties
• Dec 1st: Matt Zeckner - Asymptotic Clique Numbers
• Dec 3rd: Jay Hineman - Infinite Dimensional Analogues of Topological Fixed-Point Theorems
• Dec 8th & 10th: David Cook - Cohen-Macaulay Complexes and Reisner's Theorem

Summer Suggestions

• For MA 714, I will assume the following "loose" prerequisites from topology:
  • 1) Know what a topological space is and continuous maps are;
  • 2) Know what a homotopy between continuous maps is;
  • 3) Know the following basic examples: R^n, n-dimensional spheres; and
  • 4) Know what the quotient topology is.
• None of these are particularly hard ideas in and of themselves; they basically constitute 5 or 6 sections of the standard book by Munkres that has been used recently in MA 551/651. I don't expect anyone to be an expert, I really am more interested that people be familiar with the ideas.

Resources for mathematics word processing: LaTeX: Latex is a fantastic system for writing mathematics. While it might appear more complicated than Open Office or Microsoft Word (as it is a document preparation system rather than a word processor), writing in Latex goes as quickly as with common word processing programs once you learn the basics. Further, nothing else even comes close to the quality of a document prepared with Latex.

• www.latex-project.org
• A nice introduction to the LaTeX structure and commands can be found here
• A large list of commands for LaTeX symbols can be found here. Section 1.2 of this document, on page 8, collects commonly requested symbols. If you are just starting out, I'd look there to see if your question can be answered.