Please read as far ahead as possible before lectures. Also, do as many of the problems in the book as you can; there are usually solutions in the back of the book.
This directory contains a quick summary of each lecture
along with relevant handouts.
| Date | Topic | Reading |
|---|---|---|
| Monday, March 26 | Introduction, Prime Factorization (part 1) | Section 1.1 |
| Wednesday, March 28 | Prime Factorization (part 2) | Section 1.1 |
| Friday, March 30 | The Sequence of Prime Numbers | Section 1.2 |
| Monday, April 2 | The Riemann Hypothesis | Section 1.2 and Mazur-Stein (tba) |
| Wednesday, April 4 | Integers Modulo n | Section 2.1 |
| Friday, April 6 | The Chinese Remainder Theorem | Section 2.2 |
| Monday, April 9 | Quickly Computing Powers | Section 2.3 |
| Wednesday, April 11 | Primality Testing | Section 2.4 |
| Friday, April 13 | Primitive Roots | Section 2.5 |
| Monday, April 16 | Diffie-Hellman Cryptosystem | Section 3.1 |
| Wednesday, April 18 | RSA Cryptosystem | Section 3.2 |
| Friday, April 20 | Attacks on RSA | Section 3.3 |
| Monday, April 23 | Midterm Review | Chapters 1-3 |
| Wednesday, April 25 | In Class Midterm | |
| Friday, April 27 | Quadratic Reciprocity | Section 4.1 |
| Monday, April 30 | Proof of Quadratic Reciprocity | Sections 4.2-4.3 |
| Wednesday, May 2 | Quadratic Reciprocity | Section 4.5 |
| Friday, May 4 | (project draft 1 due) Finish QR proof; start continued fractions | Section 5.1 |
| Monday, May 7 | Infinite Continued Fractions | Section 5.2 |
| Wednesday, May 9 | Quadratic Irrationals | Section 5.4 |
| Friday, May 11 | Recognizing Rationals from their Decimal Expansion | Section 5.5 |
| Monday, May 14 | Sums of Two Squares | Section 5.6 |
| Wednesday, May 16 | Elliptic Curves | Section 6.1 |
| Friday, May 18 | (project draft 2 due) The Group Law | Section 6.2 |
| Monday, May 21 | Lenstra's Integer factorization algorithm (part 1) | Section 6.3 |
| Wednesday, May 23 | Lenstra's Integer factorization algorithm (part 2) | Section 6.3 |
| Friday, May 25 | An Elliptic Curve Cryptosystem | Section 6.4 |
| Monday, May 28 | no class -- Memorial Day | |
| Wednesday, May 30 | The Birch and Swinnerton Conjecture (part 1) | Section 6.5 |
| Friday, June 1 | (final projects due) The Birch and Swinnerton Conjecture (part 2) | Section 6.5 |