Combinatorics II – Spring 2015
Instructor: Shubhangi Saraf
Timing: MW 1:40 pm - 3:00 pm
Office hours: Monday 3:00 pm– 4:00 pm (Hill 426, Busch Campus)
Text: There is no text, but there are several books that we will be referring to, and many of them will be on library reserve.
Some of the relevant books include: The Probabilistic Method (Alon & Spencer), Extremal Combinatorics (Stasys Jukna), Linear Algebra Methods in Combinatorics (Babai & Frankl)
Prerequisites: 16:642:582 or permission of instructor
Description: This is the second part of a two-semester course surveying basic topics in combinatorics.
Topics for the full year should include most of:
• Enumeration (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics)
• Matching theory, polyhedral and fractional issues
• Partially ordered sets and lattices, Mobius functions
• Theory of finite sets, hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities
• Probabilistic methods
• Algebraic and Fourier methods • Entropy methods
Grade: The grade will be based on problem sets. There will be about 4 -5 problem sets assigned over the course of the semester. There will be no exams.
Homework 1 (due Feb 25)
Homework 2 (due March 25)
Homework 3 (due April 13)
Homework 4 (due May 4)