| Class Number |
Date |
Sections in Notes |
Brief Description |
| 1 |
Monday, 1/24 |
1.1 |
Introduction, Overview of Elementary Number Theory, Sets |
| 2 |
Wednesday, 1/26 |
1.1 - 1.2 |
Set Operations, Cardinality |
| 3 |
Friday, 1/28 |
1.3 |
Relations, Equivalence Relations |
| 4 |
Monday, 1/31 |
1.4 - 1.5 |
Functions, Divisibility |
| 5 |
Wednesday, 2/2 |
2.1 |
Induction |
| 6 |
Friday, 2/4 |
2.2 - 2.3 |
Strong Induction, Division with Remainder |
| - |
Monday, 2/7 |
- |
No Class |
| 7 |
Wednesday, 2/9 |
2.3 |
Well-Ordering, Division with Remainder |
| 8 |
Friday, 2/11 |
3.1 |
Greatest Common Divisors, The Euclidean Algorithm |
| 9 |
Monday, 2/14 |
3.2 |
Primes, Relatively Prime Numbers |
| 10 |
Wednesday, 2/16 |
3.3 |
Determining Div(a) and its Cardinality |
| 11 |
Friday, 2/18 |
3.4 |
The Fundamental Theorem of Arithmetic |
| 12 |
Monday, 2/21 |
- |
First Exam |
| 13 |
Wednesday, 2/23 |
4.1 - 4.2 |
Injective, Surjective, and Bijective Functions, The Bijection Principle |
| 14 |
Friday, 2/25 |
4.3 |
Counting Permutations and Functions, Recognizing Overcount |
| 15 |
Monday, 2/28 |
4.3 |
Counting Subsets of a Given Size, Examples of Counting Problems |
| 16 |
Wednesday, 3/2 |
4.3 - 4.4 |
Counting Problems, Pascal's Triangle, The Binomial Theorem |
| 17 |
Friday, 3/4 |
4.4 |
Properties of Binomial Coefficients |
| 18 |
Monday, 3/7 |
4.4 - 4.5 |
Properties of Binomial Coefficients, Inclusion-Exclusion |
| 19 |
Wednesday, 3/9 |
4.5 - 4.6 |
Inclusion-Exclusion, Countable Sets |
| 20 |
Friday, 3/11 |
4.6 |
Countable and Uncountable Sets |
| 21 |
Monday, 3/14 |
5.1 |
Congruences, Modular Arithmetic |
| 22 |
Wednesday, 3/16 |
5.1 |
Solving Linear Congruences |
| 23 |
Friday, 3/18 |
5.2 |
Modular Powers, Fermat's Little Theorem |
| - |
- |
- |
Spring Break |
| 24 |
Monday, 4/4 |
5.2 - 5.3 |
Wilson's Theorem, The Euler Phi Function |
| 25 |
Wednesday, 4/6 |
- |
Second Exam |
| 26 |
Friday, 4/8 |
5.3 |
Computing the Euler Phi Function |
| 27 |
Monday, 4/11 |
5.3 |
Euler's Theorem, More Properties of Phi |
| 28 |
Wednesday, 4/13 |
5.4 |
Systems of Congruences |
| 29 |
Friday, 4/15 |
5.5 |
Quadratic Residues, Classifying when -1 is a Square Modulo p |
| 30 |
Monday, 4/18 |
5.5 |
Euler's Criterion |
| 31 |
Wednesday, 4/20 |
5.5 |
Fast Exponentiation Modulo m, The Legendre Symbol, Quadratic Reciprocity Overview |
| 32 |
Friday, 4/22 |
5.6 - 5.7 |
Primality Testing, Cryptography |
| 33 |
Monday, 4/25 |
5.7 |
Public-Key Cryptography, RSA |
| - |
Wednesday, 4/27 |
- |
No Class |
| 34 |
Friday, 4/29 |
- |
Third Exam |
| 35 |
Monday, 5/2 |
6.1 |
Growth Rates, Stirling's Approximation to n! |
| 36 |
Wednesday, 5/4 |
6.2 |
Average Number of Divisors |
| 37 |
Friday, 5/6 |
6.3 |
Prime Counting Function \pi(n), Bounds on 2n choose n |
| 38 |
Monday, 5/9 |
6.3 |
Prime Factorization of 2n choose n, Bounds on \pi(n) |
| 39 |
Wednesday, 5/11 |
6.3 |
Bounds on \pi(n) |
| 40 |
Friday, 5/13 |
- |
Recap, Non-elementary Number Theory |