Course: MCS 591, Advanced topics in combinatorial theory: Call no: 39527 Time: MWF 1200-1250pm Place: 427 SEO
Professor: Dhruv Mubayi Office: 620 SEO Tel:
3-8036 E-mail: mubayi@uic.edu Course Web Page:
http://www.math.uic.edu/~mubayi/591/591Spring2017.html
Office Hours: M,W 11-12
Course Description: This course is a general introduction to discrete structures, which include graphs, partially ordered sets, hypergraphs, codes and designs. We will cover a very broad array of topics, focusing on enumerative questions and results. The emphasis will be on methods, and we will showcase these mainly via algebraic, probabilistic and analytic techniques. Since combinatorics plays such an important role in a variety of areas of mathematics, statistics, and computer science, the course should provide something useful to students in all these areas.
Prerequisites: Undergraduate mathematics (algebra, analysis, probability, combinatorics) and the mathematical maturity of a graduate student.
Text and outline: We will try and cover roughly the first half of the book "A course in Combinatorics, Van Lint and Wilson" and after that we will study basic discrete Fourier analysis, and the modern enumerative techniques that use hypergraph containers, and their applications to problems in discrete geometry (planar point sets), additive number theory (counting sum-free sets) and logic (0-1 laws).
Grade: Your grade will be based on homework, and perhaps some class presentations.
Homework 1, Due Wednesday January 25
Homework 2, Due Friday February 3
Homework 3, Due Friday February 17
Homework 4, Due Friday March 3
Homework 5, Due Friday March 17
Homework 6, Due Friday April 28