Syllabus

Math 535, September 1 2010

Meeting times and location
11:00 am - 12:00 pm, Cupples I room 216

Web page: http://www.math.wustl.edu/~russw/math535/

Introduction
Math 535 will be an introduction to geometric and topological methods in combinatorics. Topics include: posets and lattices, including their order complexes; Moebius inversion; hyperplane arrangements and geometric lattices; graph complexes; shellable and Cohen-Macaulay complexes; discrete Morse theory; and additional topics as time and student interest directs.

Prerequisites
The prerequisites are knowledge of topology including basic homology theory, and of algebra on the level of e.g. Math 430.

My contact info:

     Russ Woodroofe

     Cupples I 114

     Office hours: Tues 1 - 3 pm
                     + by appt

     russw at math,wustl,edu

Textbook
I will not follow any one textbook throughout the course. Some good references which I will draw material from are:

Michelle Wachs, Poset topology: tools and applications, arXiv:math/0602226.
Anders Björner, Topological methods, available at his webpage.
Jakob Jonsson, Simplicial complexes of graphs, downloadable from Springer.
Dmitry Kozlov, Combinatorial algebraic topology, downloadable from Springer.
Jiří Matoušek, Using the Borsuk-Ulam Theorem, downloadable from Springer.
Richard Stanley, Combinatorics and commutative algebra. You'll have to go to the library for this one.

For general background on homology, etc, I recommend:
Allen Hatcher, Algebraic topology, available at his website.

I will update the schedule periodically with a record of the topics covered.

Grading
Your grade will be based on occasional homeworks, at the rate of around 1 / month.

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