Course: MCS 584, Enumerative Combinatorics:
Call no: 43425
Time: MWF 1000-1050 am
Place: 308 Lincoln Hall

Professor: Dhruv Mubayi
Office: 620 SEO
Tel: 3-8036
E-mail: mubayi@uic.edu
Course Web Page: http://www.math.uic.edu/~mubayi/584/Fall19/584Fall19.html

Office Hours: TBD

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 is on methods, and we will showcase these 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 beginning graduate student.

Text and outline: We will start by covering 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 modern enumerative techniques that use the polynomial method and hypergraph containers, and their applications to problems in discrete geometry (planar point sets), additive number theory (counting sum-free sets, arithmetic progression in finite fields) and logic (0-1 laws).

Grade: Your grade will be based on homework (about every two weeks), and perhaps some class presentations.

Homework 1, Due Friday September 13

Homework 2, Due Friday September 27

Homework 3, Due Friday October 11

Homework 4, Due Friday October 25

Homework 5, Due Friday November 8: 13A, 13D, 13F, 14C, 14F (there are hints in the book that you may use)

Homework 6, Due Friday November 22