Math 579: Combinatorics (Spring 2024) 
Lecture Schedule

Instructor: Christopher O'Neill
E-mail: cdoneill@sdsu.edu

Below is a list of the topics we intend to cover, along with a rough schedule.  Actual schedule is subject to change without notice.  Last updated January 11, 2024.  


1/17 - 1/19
Overview of Syllabus
Introduction to Combinatorics
Review Mathematical Induction (Section 2.1-2.2)

1/22 - 1/26
Elementary Counting Methods (Section 3.1-3.3)
Permutations and Binomial Coefficients

1/29 - 2/2
The Pigeon-Hole Principle (Section 1.1-1.2)
Inclusion-Exclusion and the Sieve Formula (Section 7.1)

2/5 - 2/9
Combinatorial Proofs (Section 4.2)

2/12 - 2/16
The Binomial Theorem (Section 4.1)

*2/19 - 2/23
Compositions (Section 5.1)
Integer Partitions (Section 5.3)

2/26 - 3/1
Set Partitions (Section 5.2)

3/4 - 3/8
Catalan Numbers

3/11 - 3/15
Mapping Catalan-Land

3/18 - 3/22
Exam Review
Midterm Exam: Thursday, March 21

*3/25 - 3/29
Directed and Undirected Graphs (Section 9.1-9.3)
Graph Isomorphisms (Section 9.4)

4/1 - 4/5
Spring Break: No Classes

4/8 - 4/12
Trees (Section 10.1)
Adjacency and Incidence Matrices (Section 10.3)
Counting Spanning Trees (Section 10.4)

4/15 - 4/19
Bipartite Graphs (Section 11.1-11.2)
Coloring and Matching (Section 11.3-11.4)

*4/22 - 4/26
Planar Graphs (Section 12.1)
Dual Graphs (Section 12.2)

*4/29 - 5/2
The Sensitivity Conjecture
Review for Final Exam