Combinatorics II – Spring 2015

642:583

Instructor: Shubhangi Saraf

Email:   shubhangi.saraf@rutgers.edu

Timing:  MW 1:40 pm - 3:00 pm 

Location:  Hill-425

Office hours:  Monday 3:00 pm– 4:00 pm (Hill 426, Busch Campus)

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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)