| Class Number |
Date |
Sections in Notes |
Brief Description |
| 1 |
Friday, 8/26 |
1.1 |
Introduction, Overview of Combinatorics and Number Theory, Sets |
| 2 |
Monday, 8/29 |
1.1 - 1.2 |
Set Operations, Cardinality |
| 3 |
Wednesday, 8/31 |
1.3 |
Relations and Equivalence Relations |
| 4 |
Friday, 9/2 |
1.4 - 1.5 |
Functions, Divisibility |
| 5 |
Monday, 9/5 |
2.1 |
Induction |
| 6 |
Wednesday, 9/7 |
2.2 - 2.3 |
Strong Induction, Well-Ordering, Division with Remainder |
| 7 |
Friday, 9/9 |
2.3 - 3.1 |
Division with Remainder, The Euclidean Algorithm |
| 8 |
Monday, 9/12 |
3.1 - 3.2 |
Greatest Common Divisors, Primes |
| 9 |
Wednesday, 9/14 |
3.2 - 3.3 |
Relatively Prime Numbers, Determining the Set of Divisors of a Number |
| 10 |
Friday, 9/16 |
3.3 - 3.4 |
Counting the Number of Divisors, The Fundamental Theorem of Arithmetic |
| 11 |
Monday, 9/19 |
3.4 - 4.1 |
Consequences of the Fundamental Theorem, Injective and Surjective Functions |
| 12 |
Wednesday, 9/21 |
- |
First Exam |
| 13 |
Friday, 9/23 |
4.1 - 4.3 |
Inverses of Functions, The Bijection and Pigeonhole Principles |
| 14 |
Monday, 9/26 |
4.3 |
Applications of the Pigeonhole Principle |
| 15 |
Wednesday, 9/28 |
4.3 - 4.4 |
Monotonic Subsequences, Countable Sets |
| 16 |
Friday, 9/30 |
4.4 - 5.1 |
Uncountable Sets, Counting Permutations and Functions |
| 17 |
Monday, 10/3 |
5.1 |
Recognizing Overcount, Quotient Rule, Counting Subsets of a Given Size |
| 18 |
Wednesday, 10/5 |
5.1 |
Examples of Counting Problems |
| 19 |
Friday, 10/7 |
5.2 |
Pascal's Triangle, The Binomial Theorem |
| 20 |
Monday, 10/10 |
5.2 |
Properties of Binomial Coefficients, Multinomial Theorem |
| 21 |
Wednesday, 10/12 |
5.3 |
Compositions, Set Partitions, Stirling Numbers of the Second Kind |
| 22 |
Friday, 10/14 |
5.3 - 5.4 |
Counting Surjections, Inclusion-Exclusion |
| - |
- |
- |
Fall Break |
| 23 |
Monday, 10/24 |
5.4 |
Inclusion-Exclusion, Derangements |
| 24 |
Wednesday, 10/26 |
- |
Second Exam |
| 25 |
Friday, 10/28 |
5.5 |
Permutations, Cycle Notation, Stirling Numbers of the First Kind |
| 26 |
Monday, 10/31 |
5.5 |
Inversions in Permutations, Polynomials |
| 27 |
Wednesday, 11/2 |
5.5 - 6.1 |
Relationships Between Stirling Numbers, Congruences |
| 28 |
Friday, 11/4 |
6.1 |
Modular Arithmetic |
| 29 |
Monday, 11/7 |
6.1 - 6.2 |
Solving Linear Congruences, Modular Powers |
| 30 |
Wednesday, 11/9 |
6.2 |
Fermat's Little Theorem, Wilson's Theorem |
| 31 |
Friday, 11/11 |
6.3 |
The Euler Phi Function |
| 32 |
Monday, 11/14 |
6.3 |
Euler's Theorem |
| 33 |
Wednesday, 11/16 |
6.3 - 6.4 |
More Properties of Euler's Function, Chinese Remainder Theorem |
| 34 |
Friday, 11/18 |
6.4 - 6.5 |
Chinese Remainder Theorem, Primality Testing |
| 35 |
Monday, 11/21 |
6.6 |
Cryptography |
| 36 |
Wednesday, 11/23 |
6.6 |
Public-Key Cryptography, RSA |
| - |
Friday, 11/25 |
- |
Thanksgiving Break |
| 37 |
Monday, 11/28 |
7.1 |
Growth Rates, Stirling's Approxmiation to n! |
| 38 |
Wednesday, 11/30 |
- |
Third Exam |
| 39 |
Friday, 12/2 |
7.2 - 7.3 |
Average Number of Divisors, Prime Counting Function \pi(n) |
| 40 |
Monday, 12/5 |
7.3 |
2n choose n: Bounds and Prime Factorization |
| 41 |
Wednesday, 12/7 |
7.3 |
Bounds on \pi(n) |
| 42 |
Friday, 12/9 |
- |
Ramsey's Theorem |