| 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 |