Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
A good background in undergraduate algebra such as Algebra I (18.701) and Algebra II (18.702).
Homework will be due about once every two weeks. A paper of 6-12 pages related to algebraic combinatorics is due on the last class.
A tentative description of the first part of the course is as follows:
|1||Selection of Topics from Linear Algebra
Odd Subsets with Even Intersections
Partitioning the Edges of the Complete Graph Kn into Complete Bipartite Subgraphs
The Nonuniform Fisher Inequality
Odd Neighborhood Covers
The Shannon Capacity of the 5-cycle
|2||A Taste of Algebraic Number Theory: Circulant Hadamard Matrices|
|3||Commutative Algebra and the f-vectors of Simplicial Complexes|
|4||Exterior Algebra and the f-vectors of Simplicial Complexes|