Math 218

Combinatorics

General Information Schedule Homework

Schedule

We will cover parts of the material from Chapters 1-13 of the book, along with a few additional topics if time permits. The following is a sketch of the topics we covered on each day.

Class Number Date Sections in Text Brief Description
1 Monday, 1/23 - Introduction, Divisibility
2 Wednesday, 1/25 2.1 Divisibility, Induction
3 Friday, 1/27 2.1 Induction
4 Monday, 1/30 2.2 Division with Remainder, Strong Induction
5 Wednesday, 2/1 2.2 Greatest Common Divisors, The Euclidean Algorithm
6 Friday, 2/3 - Functions, Injections, Surjections, and Bijections
7 Monday, 2/6 1.1 Pigeonhole Principle
8 Wednesday, 2/8 1.1 Applications of the Pigeonhole Principle
9 Friday, 2/10 3.1, 3.2 Fundamental Counting Principles
10 Monday, 2/13 3.1, 3.2 Counting Sequences and Functions
11 Wednesday, 2/15 3.3 Combinations, Counting Problems
12 Friday, 2/17 - First Exam
13 Monday, 2/20 4.1 Pascal's Triangle, The Binomial Theorem
14 Wednesday, 2/22 4.1 Properties of Binomial Coefficients
15 Friday, 2/24 5.1 Compositions
16 Monday, 2/27 5.2 Set Partitions, Stirling Numbers of the Second Kind, Surjections
17 Wednesday, 2/29 5.2, 7.1 Stirling Numbers, Inclusion-Exclusion
18 Friday, 3/2 7.1, 7.2 Inclusion-Exclusion, Surjections, Derangements
19 Monday, 3/5 6.1 Permutations, Cycle Notation
20 Wednesday, 3/7 6.1 Counting Permutations by Cycle Structure, Stirling Numbers of the First Kind
21 Friday, 3/9 6.1 Connections Between Stirling Numbers, Countably Infinite Sets
22 Monday, 3/12 - Uncountable Sets, Equivalence Relations
23 Wednesday, 3/14 - Equivalence Relations and Equivalence Classes
24 Friday, 3/16 - Second Exam
- - - Spring Break
25 Monday, 4/2 - Class Canceled
26 Wednesday, 4/4 9.1 Graphs, Directed Graphs, Walks, Trails, and Paths
27 Friday, 4/6 9.1 Degree of a Vertex, Cycles
28 Monday, 4/9 10.1 Trees, Leaves, Forests
29 Wednesday, 4/11 10.1 Equivalent Characterizations of Trees, Cayley's Formula
30 Friday, 4/13 10.1, 10.2 Cayley's Formula, Kruskal's Algorithm
31 Monday, 4/16 10.2, 11.1 Kruskal's Algorithm, Vertex Coloring
32 Wednesday, 4/18 11.2 Bipartite Graphs
33 Friday, 4/20 11.3 Matchings
34 Monday, 4/23 11.3 Augmenting Paths, Stable Matchings
35 Wednesday, 4/25 12.1 Planar Graphs
36 Friday, 4/27 12.1, 12.3 Coloring Planar Graphs
37 Monday, 4/30 - Third Exam
38 Wednesday, 5/2 13.1 Ramsey Theory
39 Friday, 5/4 13.1 Ramsey Theory
40 Monday, 5/7 15.2 Probabilistic Method, Lower Bounds on Ramsey Numbers
41 Wednesday, 5/9 8.1 Generating Functions
42 Friday, 5/11 8.1 Generating Functions and Recurrence Relations