Math 579: Combinatorics (Spring 2023)
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 19, 2023.


1/18 - 1/20
Overview of Syllabus
Introduction to Combinatorics
Review Mathematical Induction (Sections 2.1 - 2.2)


1/23 - 1/27
Elementary Counting Methods (Sections 3.1 - 3.3)
Permutations and Binomial Coefficients


1/30 - 2/3
The Pigeon-Hole Principle (Sections 1.1 - 1.2)
Inclusion-Exclusion and the Sieve Formula (Section 7.1)


2/6 - 2/10
Combinatorial Proofs (Section 4.2)


2/13 - 2/17
The Binomial Theorem (Section 4.1)


*2/20 - 2/24
Compositions (Section 5.1)
Integer Partitions (Section 5.3)


2/27 - 3/3
Set Partitions (Section 5.2)


3/6 - 3/10
Catalan Numbers


3/13 - 3/17
Exam Review
Midterm Exam: Thursday, March 16


3/20 - 3/24
Mapping Catalan-Land
Guest Lecture: Gordon Kirby


3/27 - 3/31
Spring Break: No Classes


*4/3 - 4/7
Directed and Undirected Graphs (Sections 9.1 - 9.3)
Graph Isomorphisms (Section 9.4)


4/10 - 4/14
Trees (Section 10.1)
Adjacency and Incidence Matrices (Section 10.3)
Counting Spanning Trees (Section 10.4)


4/17 - 4/21
Bipartite Graphs (Sections 11.1 - 11.2)
Coloring and Matching (Sections 11.3 - 11.4)


*4/24 - 4/28
Planar Graphs (Section 12.1)
Dual Graphs (Section 12.2)


*5/1 - 5/4
The Sensitivity Conjecture
Review for Final Exam