| Class Number |
Date |
Sections in Notes |
Brief Description |
| 1 |
Wednesday, 1/22 |
1.1 |
Introduction, Overview of Combinatorics and Number Theory, Sets |
| 2 |
Friday, 1/24 |
1.1 - 1.2 |
Set Operations, Cardinality |
| 3 |
Monday, 1/27 |
1.3 |
Relations, Equivalence Relations |
| 4 |
Wednesday, 1/29 |
1.4 - 1.5 |
Functions, Divisibility |
| 5 |
Friday, 1/31 |
2.1 |
Induction |
| 6 |
Monday, 2/3 |
2.2 - 2.3 |
Strong Induction, Well-Ordering, Division with Remainder |
| 7 |
Wednesday, 2/5 |
2.3 - 3.1 |
Division with Remainder, The Euclidean Algorithm |
| 8 |
Friday, 2/7 |
3.1 - 3.2 |
Greatest Common Divisors, Primes |
| 9 |
Monday, 2/10 |
3.2 - 3.3 |
Relatively Prime Numbers, Determining the Set Div(a) |
| 10 |
Wednesday, 2/12 |
3.3 - 3.4 |
Counting the Number of Divisors, The Fundamental Theorem of Arithmetic |
| 11 |
Friday, 2/14 |
3.4 - 4.1 |
Consequences of the Fundamental Theorem, Injective and Surjective Functions |
| 12 |
Monday, 2/17 |
- |
First Exam |
| 13 |
Wednesday, 2/19 |
4.2 - 4.3 |
The Bijection and Pigeonhole Principles |
| 14 |
Friday, 2/21 |
4.3 |
Applications of the Pigeonhole Principle |
| 15 |
Monday, 2/24 |
4.3 - 4.4 |
Monotonic Subsequences, Countable Sets |
| 16 |
Wednesday, 2/26 |
4.4 - 5.1 |
Uncountable Sets, Counting Permutations and Functions |
| 17 |
Friday, 2/28 |
5.1 |
Recognizing Overcount, Quotient Rule, Counting Subsets of a Given Size |
| 18 |
Monday, 3/2 |
5.1 |
Examples of Counting Problems |
| 19 |
Wednesday, 3/4 |
5.2 |
Pascal's Triangle, The Binomial Theorem |
| 20 |
Friday, 3/6 |
5.2 |
Properties of Binomial Coefficients, Multinomial Theorem |
| 21 |
Monday, 3/9 |
5.3 |
Compositions, Set Partitions, Stirling Numbers of the Second Kind |
| 22 |
Wednesday, 3/11 |
5.3 - 5.4 |
Counting Surjections, Inclusion-Exclusion |
| 23 |
Friday, 3/13 |
5.4 |
Inclusion-Exclusion, Derangements |
| - |
- |
- |
Spring Break |
| 24 |
Monday, 3/30 |
5.5 |
Permutations, Cycle Notation, Stirling Numbers of the First Kind |
| 25 |
Wednesday, 4/1 |
5.6 |
Polynomials, Relationship Between Stirling Numbers |
-
| 26 |
Friday, 4/3 |
6.1 |
Congruences, Modular Arithmetic |
| 27 |
Monday, 4/6 |
6.1 |
Solving Linear Congruences |
| 28 |
Wednesday, 4/8 |
6.2 |
Modular Powers, Fermat's Little Theorem |
| 29 |
Friday, 4/10 |
6.2 |
Wilson's Theorem, Classifying When -1 is a Square Modulo p |
| 30 |
Monday, 4/13 |
- |
Second Exam |
| 31 |
Wednesday, 4/15 |
6.3 |
The Euler Phi Function |
| 32 |
Friday, 4/17 |
6.3 |
Phi Function is Multiplicative, Euler's Theorem |
| 33 |
Monday, 4/20 |
6.4 |
Chinese Remainder Theorem |
| 34 |
Wednesday, 4/22 |
6.5 |
Primality Testing |
| 35 |
Friday, 4/24 |
6.6 |
Cryptography |
| 36 |
Monday, 4/27 |
6.6 |
Public-Key Cryptography, RSA |
| 37 |
Wednesday, 4/29 |
7.1 |
Growth Rates, Stirling's Approxmiation to n! |
| 38 |
Friday, 5/1 |
7.2 |
Average Number of Divisors |
| 39 |
Monday, 5/4 |
7.3 |
Prime Counting Function \pi(n), Prime Factorization of 2n choose n |
| 40 |
Wednesday, 5/6 |
7.3 |
Bounds on \pi(n) |