Fall 2015 Math 431: Structures and Methods of Combinatorics
Lecture: TTh 11:10am–12:25pm, Blocker 121
Instructor: Christopher O’Neill
Office: Blocker 513G
E-mail: coneill@math.tamu.edu
Below is a list of the topics we intend to cover, along with a rough time outline. Actual
schedule is subject to change without notice. Last updated August 9th, 2015.
Week
9/1 – 9/3
9/8 – 9/10
9/15 – 9/17
9/22 – 9/24
9/29 – 10/1
10/6 – 10/8
10/13 – 10/15
10/20 – 10/22
10/27 – 10/29
11/3 – 11/5
11/10 – 11/12
11/17 – 11/19
11/24
11/26
12/1 – 12/3
12/8
12/11
Topic
Introduction to Combinatorics
Review: The Pigeon-Hole Principle
Review: Mathematical Induction
Permutations
Words and Alphabets
Binomial Coefficients
The Binomial Theorem
The Multinomial Theorem
Inclusion-Exclusion and the Sieve Formula
Compositions
Set Partitions
Integer Partitions
Review
Exam 1
Directed and Undirected Graphs
Hamiltonian Cycles
Graph Isomorphisms
Trees
Minimum Weight Spanning Trees
Adjacency and Incidence Matrices
Counting Spanning Trees
Bipartite Graphs
Coloring and Matching
Planar Graphs
Polyhedra and Dual Graphs
Ramsey Theory
Review
Exam 2
Partially Ordered Sets
The Möbius Function
Lattices
Recurrence Relations
Ordinary Generating Functions
Exponential Generating Functions
Applications of Generating Functions
Thanksgiving Holiday (no class)
Extra Topics
Review
Exam 3
1
Chapters
1.1–1.2
2.1–2.2
3.1
3.2
3.3
4.1
4.2
7.1
5.1
5.2
5.3
9.1–9.3
9.2
9.4
10.1
10.2
10.3
10.4
11.1–11.2
11.3–11.4
12.1
12.2
13.1–13.2
16.1
16.2
16.3
8.1
8.2