| Class Number |
Date |
Sections in Text |
Brief Description |
| 1 |
Friday, 8/26 |
- |
Introduction, Examples of Combinatorial Problems |
| 2 |
Monday, 8/29 |
2.1 |
Divisibility, Induction |
| 3 |
Wednesday, 8/31 |
2.1 |
Induction, Division with Remainder |
| 4 |
Friday, 9/2 |
2.2 |
Strong Induction, Primes, Greatest Common Divisors |
| 5 |
Monday, 9/5 |
- |
Greatest Common Divisors, The Euclidean Algorithm |
| 6 |
Wednesday, 9/7 |
- |
The Fundamental Theorem of Arithmetic |
| 7 |
Friday, 9/9 |
1.1 |
The Pigeonhole Principle, Injections, Surjections |
| 8 |
Monday, 9/12 |
1.1, 1.2 |
Applications of the Pigeonhole Principle |
| 9 |
Wednesday, 9/14 |
1.2 |
More Pigeonhole Applications |
| - |
Friday, 9/16 |
- |
Class Canceled |
| 10 |
Monday, 9/19 |
3.1, 3.2, 3.3 |
Elementary Counting Problems, Permutations, Combinations |
| 11 |
Wednesday, 9/21 |
3.1, 3.2, 3.3 |
Counting Problems |
| 12 |
Friday, 9/23 |
4.1 |
Binomial Theorem, Properties of Binomial Coefficients |
| 13 |
Monday, 9/26 |
- |
First Exam |
| 14 |
Wednesday, 9/28 |
4.1 |
Binomial Coefficient Identities |
| 15 |
Friday, 9/30 |
4.1, 4.2, 5.1 |
Sums of Binomial Coefficients, Multinomial Theorem, Compositions |
| 16 |
Monday, 10/3 |
5.1, 5.2 |
Compositions and Set Partitions |
| 17 |
Wednesday, 10/5 |
5.2, 5.3 |
Stirling Numbers of the Second Kind, Integer Partitions |
| 18 |
Friday, 10/7 |
5.3, 6.1 |
Integer Partitions, Permutations |
| 19 |
Monday, 10/10 |
6.1 |
Permutations, Stirling Numbers of the First Kind |
| 20 |
Wednesday, 10/12 |
6.1 |
Stirling Numbers of the First Kind, Inversions in Permutations |
| 21 |
Friday, 10/14 |
7.1, 7.2 |
The Sieve Formula (Inclusion-Exclusion), Surjections, Derangements |
| - |
Monday, 10/17 |
- |
Fall Break |
| - |
Wednesday, 10/19 |
- |
Fall Break |
| - |
Friday, 10/21 |
- |
Fall Break |
| 22 |
Monday, 10/24 |
7.1, 7.2 |
Counting Primes, Euler Phi-Function |
| 23 |
Wednesday, 10/26 |
- |
Equivalence Relations |
| 24 |
Friday, 10/28 |
9.1 |
Equivalence Relations, Fundamental Definitions of Graph Theory |
| 25 |
Monday, 10/31 |
9.1, 9.2 |
Cycles, Eulerian Trails |
| 26 |
Wednesday, 11/2 |
- |
Second Exam |
| 27 |
Friday, 11/4 |
9.1, 9.2 |
Eulerian Trails, Hamiltonian Cycles |
| 28 |
Monday, 11/7 |
10.1 |
Trees |
| 29 |
Wednesday, 11/9 |
10.1 |
Equivalent Characterizations of Trees, Cayley's Formula |
| 30 |
Friday, 11/11 |
10.1, 10.2 |
Cayley's Formula, Kruskal's Algorithm |
| 31 |
Monday, 11/14 |
11.1, 11.2 |
Vertex Coloring, Bipartite Graphs |
| 32 |
Wednesday, 11/16 |
11.3 |
Matchings in Bipartite Graphs |
| 33 |
Friday, 11/18 |
11.3 |
Augmenting Paths, Stable Marriages |
| 34 |
Monday, 11/21 |
12.1 |
Planar Graphs |
| 35 |
Wednesday, 11/23 |
12.2 |
Planar Graphs, Convex Regular Polehydra |
| - |
Friday, 11/25 |
- |
Thanksgiving Break |
| 36 |
Monday, 11/28 |
12.3, 13.1 |
Coloring Planar Graphs, Coloring Maps, Ramsey Theory |
| 37 |
Wednesday, 11/30 |
- |
Third Exam |
| 38 |
Friday, 12/2 |
13.1 |
Ramsey Theory |
| 39 |
Monday, 12/5 |
15.2 |
Probabilistic Method, Lower Bounds on Ramsey Numbers |
| 40 |
Wednesday, 12/7 |
8.1 |
Generating Functions |
| 41 |
Friday, 12/9 |
8.1 |
Generating Functions and Recurrence Relations |