Math 8440 Combinatorics - Fall 2006

Prerequisites: Ideally Math 300, 3420, 6420, actually only math maturity is needed.
 
Topics: Math 8440 is a graduate course in Combinatorics. We will cover major results
 and methods of extremal combinatorics and some applications in theoretical computer
 science. Topics includes classical Results of extremal set theory (2-coloring
 hypergraphs, Sunflowers and Delta systems, theorems of Erdos-Ko-Rado, Kruskal-
 Katona, Sperner, Dilworth, Ramsey, and Turan), linear algebra methods (Fisher’s
 inequality, Ray-Chaudhuri--Wilson Theorem, disproof of Borsuk's conjecture), and
 probabilistic methods (first and Second moment method, deletion method, Local
 Lemma, entropy, randomized algorithm).
 
Lectures: T Th 5:30-6:45 pm, Sparks Hall 308.

Textbook: Extremal Combinatorics, by S. Jukna, Springer-Verlag 2001

http://lovelace.thi.informatik.uni-frankfurt.de/~jukna/EC_Book/

Instructor: Dr. Yi Zhao

Email: yzhao6@gsu.edu,

788 COE, (404) 651-0683

Hours: T Th 1:30 – 2:30 pm or by appointment

Participation You should read materials before they are discussed in class. You are expected to participate in the discussion every lecture. After four (4) or more absences, you may be withdrawn from the class with a WF.

Homework: collected every other Tuesday. Working on homework problems is necessary for learning. You may discuss homework problems with others including me. But you must write solutions in your own words. No late homework will be accepted.

Exam: one take-home final.

Grades: homework (60%), final exam (30%), participation (10%).

Remark: This course syllabus provides a general plan for the course-- deviations may be necessary.

Academic honesty: Academic honesty is expected from every student. Violation of this policy will result, at a minimum, in a grade of F and an academic dishonesty form filed with the Dean: http://www2.gsu.edu/~wwwdos/codeofconduct_conpol.html

Disruptive Behavior will be handled under Section 401.08 of the Faculty Handbook

http://www.gsu.edu/~wwwsen/minutes/2002-2003/disrupt.html