MATH 262
Topics in Combinatorial Mathematics
Winter, 2007
Lecturer: Professor Fan Chung Graham
Time: T Th 10-11:20 am
Place: 5402 APM
In this course, we plan to cover basic and advanced methods in combinatorics.
These methods all share a similar flavor in linear algebra.
We will examine their applications
in extremal graph theory, including, in particular, Tur'an theorems and Ramsey theory.
A tentative list of topics is the following:
-
Space of polynomials
- Dimension of graphs
- Intersection theorems of set systems
-
The inclusion matrices with applications
-
Combinatorial Nullstellensatz
-
Partially ordered sets
-
Geometric representation of graphs
-
Eigenvalues of graphs with applications
Recommended books:
-
The main book:
Linear Algebra Methods in Combinatorics, by L. Babai and P. Frankl,
Department of Computer Scinece, University of Chicago, preliminary version, 1992.
-
Supplementary books:
Some related lecture notes by Oleg Pikhurko.
Midterm
|Final
|Reading
|Notes
|Problems
Back