Applied Extremal Combinatorics

18.325 Topics in Applied Mathematics

This class meets MW2:30-4:00 in room 24-115.

A * following the link means that scribe notes are now available for that lecture. Note that many of these notes a still a little bit rough. This is the fault of the instructor rather than the note takers.

Course Announcement, with description of curriculum.
(9/9/96) Lecture 1 - Introduction to the Laplacian*
(9/11/96) Rough summary of the second lecture
(9/16/96) Lecture 3 was on the Koebe embedding theorem and spectral partitioning of planar graphs.*
(9/18/96) Lecture 4 - using Linear Programming to approximate sparsest cut
(9/23/96) Institute holliday - no class.
(9/25/96) Lecture 5 - why the Linear Programming relaxation is only a log approximation.*
(9/30/96) Lecture 6 - The log gap continued, and an introduction to expanders.*
(10/2/96) Lecture 7 - Gabber and Galil's construction of expanders.
(10/7/96) Lecture 8 - Introduction to error-correcting codes, part 1. *
(10/9/96) Lecture 9 - Introduction to error-correcting codes, part 2.
(10/14/96) Columbus day - no class
(10/16/96) FOCS - no class
(10/21/96) Lecture 10 - Using expander graphs to construct error-correcting codes
(10/23/96) Lecture 11 - Linear-time encodable and decodable error-correcting codes
(10/28/96) Lecture 12 - An introduction to derandomization.*
(10/30/96) Lecture 13 - Public coins = Private coins in interactive proofs of graph non-isomorphism.*
(11/4/96) Lecture 14 - Testing Isomorphism of graphs with distinct eigenvalues.*
(11/6/96) Lecture 15 - Testing Isomorphism of graphs with bounded eigenvalue multiplicity.
(11/11/96) Veteran's day, no class.
(11/13/96) Lecture 16 - Strongly Regular Graphs*
(11/18/96) Lecture 17 - Polynomial systems and extremal point sets, and extremal set theory*.
(11/20/96) Lecture 18 - A counterexample to Borsuk's conjecture.*
(11/25/96) Lecture 19 - Spherical codes and designs.
(11/27/96) Lecture 20 - Testing isomorphism of SRGs, and building expanders from ECCs.*
(12/2/96) Lecture 21 - The Linear Programming bound, part 1.*
(12/4/96) Lecture 22 - The Linear Programming bound, part 2.
(12/9/96) Lecture 23 - Lovasz's theta function.
(12/11/96) Lecture 24 - Last class, summary.

Daniel A. Spielman <spielman@math.mit.edu>

Last modified: Wed Mar 5 16:12:47 1997 junk string