| Class Number |
Date |
Sections in Text |
Brief Description |
| 1 |
Monday, 1/20 |
- |
Introduction, Combinatorial Problems, Sets |
| 2 |
Wednesday, 1/22 |
- |
Set Operations, Cardinality, Relations |
| 3 |
Friday, 1/24 |
- |
Equivalence Relations |
| 4 |
Monday, 1/27 |
- |
Functions, Divisibility |
| 5 |
Wednesday, 1/29 |
2.1 |
Divisibility, Induction |
| 6 |
Friday, 1/31 |
2.2 |
Strong Induction, GCDs |
| 7 |
Monday, 2/3 |
1.1 |
Counting with Functions, Pigeonhole Principle |
| 8 |
Wednesday, 2/5 |
1.1 |
Applications of the Pigeonhole Principle |
| 9 |
Friday, 2/7 |
3.1 - 3.2 |
Monotonic Subsequences, Counting Permutations |
| 10 |
Monday, 2/10 |
3.1 - 3.3 |
Recognizing Overcount, Quotient Rule, Counting Functions and Combinations |
| 11 |
Wednesday, 2/12 |
3.1 - 3.3 |
Examples of Counting Problems |
| 12 |
Friday, 2/14 |
- |
First Exam |
| 13 |
Monday, 2/17 |
4.1 |
Pascal's Triangle, The Binomial Theorem |
| 14 |
Wednesday, 2/19 |
4.1 |
Properties of Binomial Coefficients |
| 15 |
Friday, 2/21 |
4.2, 5.1 |
Multinomial Theorem, Compositions |
| 16 |
Monday, 2/24 |
5.1 - 5.2 |
Compositions, Set Partitions, Stirling Numbers of the Second Kind |
| 17 |
Wednesday, 2/26 |
5.2, 7.1 |
Counting Surjections, Inclusion-Exclusion |
| 18 |
Friday, 2/28 |
7.1 - 7.2 |
Inclusion-Exclusion |
| 19 |
Monday, 3/3 |
7.2, 6.1 |
Derangements, Permutations |
| 20 |
Wednesday, 3/5 |
6.1 |
Permutations, Cycle Notation, Stirling Numbers of the First Kind |
| 21 |
Friday, 3/7 |
6.1 |
Counting Permutations By Cycle Structure, Inversions in Permutations |
| 22 |
Monday, 3/10 |
6.1 |
Polynomial Coefficients, Connections Between Stirling Numbers |
| 23 |
Wednesday, 3/12 |
- |
Countable and Uncountable Sets |
| 24 |
Friday, 3/14 |
- |
Second Exam |
| - |
- |
- |
Spring Break |
| 25 |
Monday, 3/31 |
9.1 |
Graphs, Representations, Subgraphs |
| 26 |
Wednesday, 4/2 |
9.1, 9.4 |
Isomorphisms, Walks, Trails, and Paths |
| 27 |
Friday, 4/4 |
9.1 |
Connected Components, Cycles |
| 28 |
Monday, 4/7 |
10.1 |
Trees, Leaves, Forests |
| 29 |
Wednesday, 4/9 |
10.1 |
Equivalent Characterizations of Trees, Cayley's Formula |
| 30 |
Friday, 4/11 |
10.1 - 10.2 |
Prufer Codes and Cayley's Formula, Minimum Weight Spanning Trees |
| 31 |
Monday, 4/14 |
10.2 |
Kruskal's Algorithm |
| 32 |
Wednesday, 4/16 |
11.1 - 11.2 |
Vertex Coloring, Bipartite Graphs |
| 33 |
Friday, 4/18 |
11.2 - 11.3 |
Maximum Number of Edges in Bipartite and Triangle-Free Graphs, Matchings |
| 34 |
Monday, 4/21 |
11.3 |
Maximal and Maximum Matchings, Augmenting Paths |
| 35 |
Wednesday, 4/23 |
11.3 |
Hall's Theorem, Stable Matchings |
| 36 |
Friday, 4/25 |
- |
Stable Matchings |
| 37 |
Monday, 4/28 |
- |
Third Exam |
| 38 |
Wednesday, 4/30 |
12.1 |
Planar Graphs |
| 39 |
Friday, 5/2 |
12.2 - 12.3 |
Coloring Planar Graphs, Regular Polyhedra |
| 40 |
Monday, 5/5 |
13.1 |
Ramsey's Theorem |
| 41 |
Wednesday, 5/7 |
13.1 |
Upper Bounds on Ramsey Numbers |
| 42 |
Friday, 5/9 |
15.2 |
Lower Bounds on Ramsey Numbers, Probabilistic Method |