| Week |
Lectures |
Sections in Text |
Brief Description |
| 1 |
M 9/12 |
1.1, 1.2 |
Introduction, Division and Euclidean Algorithms |
|
W 9/14 |
1.2, 1.3 |
Bezout's Identity, Least Common Multiples |
|
F 9/16 |
1.4 |
Linear Diophantine Equations |
| 2 |
M 9/19 |
2.1 |
Prime Numbers |
|
W 9/21 |
2.2 |
Prime Distributions |
|
F 9/23 |
2.4, 2.3 |
Primality Testing |
| 3 |
M 9/26 |
3.1 |
Modular Arithmetic |
|
W 9/28 |
3.2, 3.3 |
Linear Congruences, Chinese Remainder Theorem |
|
F 9/30 |
3.3, 3.4 |
Simultaneous Congruences |
| 4 |
M 10/3 |
4.1 |
The Arithmetic of ${\mathbb Z}_p$ |
|
W 10/5 |
4.1, 4.2 |
Pseudoprimes |
|
F 10/7 |
4.2 |
Carmichael Numbers |
| 5 |
M 10/10 |
5.1, 5.2 |
Euler's Function |
|
W 10/12 |
5.3 |
Applications of Euler's Function |
|
F 10/14 |
|
Cryptography |
| 6 |
M 10/17 |
6.1, 6.2 |
The Group of Units and Primitive Roots |
|
W 10/19 |
6.3 |
Primitive Roots for Composite Moduli |
|
F 10/21 |
6.4, 6.5 |
The Existence of Primitive Roots |
| 7 |
M 10/24 |
6.6, 7.1 |
Applications of Primitive Roots, Quadratic Congruences |
|
W 10/26 |
7.2, 7.3 |
Quadratic Residues, The Legendre Symbol |
|
F 10/28 |
7.4 |
Quadratic Reciprocity |