Math 218

Combinatorics and Graph Theory

General Information Schedule Homework

Schedule

The following is a sketch of the topics covered in each class.

Class Number Date Sections in Notes Brief Description
1 Monday, 2/1 1.1 - 1.2 Introduction, Sets, Cardinality
2 Tuesday, 2/2 1.3 - 1.4 Relations, Equivalence Relations, Functions
3 Thursday, 2/4 1.5 - 2.1 Divisibility, Induction
4 Friday, 2/5 2.2 - 2.3 Strong Induction, Well-Ordering, Division with Remainder
5 Monday, 2/8 3.1 The Euclidean Algorithm, Greatest Common Divisors
6 Tuesday, 2/9 4.1 - 4.2 Injective and Surjective Functions, The Bijection Principle
7 Thursday, 2/11 4.3 The Pigeonhole Principle
8 Friday, 2/12 4.4 Countable and Uncountable Sets
9 Monday, 2/15 5.1 Counting Permutations and Functions, Recognizing Overcount, Quotient Rule
10 Tuesday, 2/16 5.1 - 5.2 Counting Problems, Pascal's Triangle
11 Thursday, 2/18 5.2 The Binomial Theorem, Properties of Binomial Coefficients
12 Friday, 2/19 - First Exam
13 Monday, 2/22 5.3 Compositions, Set Partitions, Stirling Numbers of the Second Kind
14 Tuesday, 2/23 5.4 Inclusion-Exclusion
15 Thursday, 2/25 6.1 Graphs, Representations, Subgraphs
16 Friday, 2/26 6.2 Walks, Trails, and Path, Connected Components, Cycles
17 Monday, 3/1 6.2 - 6.3 Cycles, Trees, Forests
18 Tuesday, 3/2 6.3 Equivalent Characterizations of Trees, Cayley's Formula
19 Thursday, 3/4 6.3 - 6.4 Prufer Codes and Cayley's Formula, Minimum Weight Spanning Trees
20 Friday, 3/5 6.4 - 6.5 Kruskal's Algorithm, Vertex Coloring, Chromatic Number
21 Monday, 3/8 6.5 Bipartite Graphs, Maximum Number of Edges in Bipartite Graphs
22 Tuesday, 3/9 - Second Exam
23 Thursday, 3/11 6.6 Matchings, Augmenting Paths
24 Friday, 3/12 6.6 Stable Matchings
25 Monday, 3/15 6.7 Planar Graphs
26 Tuesday, 3/16 6.7 Coloring Planar Graphs, Regular Polyhedra
27 Thursday, 3/18 6.8 Ramsey's Theorem
28 Friday, 3/19 6.8 Bounds on Ramsey Numbers, Probabilistic Method