To compile LaTeX versions of lecture notes, use macros.tex and header.tex.
| Date | Title | Notes | Reading |
| Tue 9/4 | Course Overview, Induction | pdf, tex | Gallian Ch. 0 |
| Thu 9/6 | The Integers | pdf, tex | Gallian Ch. 0 |
| Problem Set 0 (due 9/14) | pdf, tex | ||
| Tue 9/11 | Modular Arithmetic, Relations, Algorithms | pdf, tex | |
| Thu 9/13 | Measuring Complexity, The Euclidean Algorithm | pdf, tex | |
| Problem Set 1 (due 9/21) | pdf, tex | ||
| Tue 9/18 | Extended Euclid, Primality & Factoring, Intro to Groups | pdf, tex | Gallian Ch. 2 |
| Thu 9/20 | More Groups and Basic Properties | pdf, tex | Gallian Ch. 1,2 |
| Problem Set 2 (due 9/28) | pdf, tex | ||
| Tue 9/25 | Subgroups, Cyclic Groups | pdf, tex | Gallian Ch. 3,4 |
| Thu 9/27 | Cyclic Groups & Cryptography | pdf, tex | Gallian Ch. 4 |
| Practice Quiz I | |||
| Tue 10/2 | Permutation Groups | pdf, tex | Gallian Ch. 5 |
| Thu 10/4 | Quiz I | ||
| Problem Set 3 (due 10/12) | pdf, tex | ||
| Tue 10/9 | Isomorphisms and Cosets | pdf, tex | Gallian Ch. 6-7 |
| Thu 10/11 | Cosets | pdf, tex | Gallian Ch. 7 |
| Problem Set 4 (due 10/19) | pdf, tex | ||
| Tue 10/16 | Direct Products | pdf, tex | Gallian Ch. 8, 11 |
| Thu 10/18 | Normal Subgroups & Factor Groups | pdf, tex | Gallian Ch. 9 |
| Problem Set 5 (due 10/26) | pdf, tex | ||
| Tue 10/23 | Homomorphisms, Isometries | pdf, tex | Gallian Chs. 10, 27 |
Thu 10/25 |
Group Theory & Crystallography | Gallian Ch. 28 | |
| Problem Set 6 (due 11/2) | pdf, tex | ||
| Tue 10/30 | Rings | pdf, tex | Gallian Chs. 12, 13 |
| Thu 11/1 | Properties of Rings | pdf, tex | |
| Problem Set 7 (due 11/10) | pdf, tex | ||
| Tue 11/6 | EthiCS Module led by Kate Vredenburgh: |
Effective Altruism, Strangers Drowning, Mathematician's Apology |
|
| Thu 11/8 | Ideals and Factor Rings | pdf, tex | Gallian Ch. 14 |
| Practice Quiz II | pdf, tex | ||
| Tue 11/13 | Ring Homomorphisms | pdf, tex | Gallian Ch. 15 |
| Thu 11/15 | Quiz II | ||
| Problem Set 8 (due 11/30) | pdf, tex | ||
| Tue 11/20 | Polynomial Rings | pdf, tex | Gallian Ch. 16 |
| Thu 11/22 | No Class - Thanksgiving | ||
| Tue 11/27 | Factorization & Ideals in Polynomial Rings, Field Extensions | pdf, tex | Gallian Chs. 16-17 |
| Thu 11/29 | Vector Spaces | pdf, tex | Gallian Ch. 19 |
| Problem Set 9 (due Monday 12/10) | pdf, tex | ||
| Tue 12/4 | Error-Correcting Codes | pdf, tex | |
| Thu 12/6 | Conclusions | pdf, tex | |
| Final Exam Practice | pdf, tex | ||
| Thu 12/13 | Review Session I (7-9pm, MD 223) | ||
| Sun 12/16 | Review Session II (7-9pm, MD 223) | ||
| Wed 12/19 | Final Exam (9am-12pm, Harvard Hall 102) |