This is the homepage for Math 145-02, Abstract Algebra, taught by Prof. Moon Duchin. Note that section 01 is taught by Prof. Montserrat Teixidor and follows a different schedule and assignments!
Syllabus/course info sheet: here.
Here is a rough layout of topic timing. Obviously, real timing may vary from this plan. As you can see, it roughly follows the book, but the symbol * means that there is substantial extra material planned besides what you can find in the text.
| date | topic | text | |
| 1 | Tue Sep 3 | Intro to course; intro to proofs; intro to groups | |
| 2 | Thu Sep 5 | Ch 1 – the cyclic groups Z/nZ (cf Math 63) | 1 |
| 3 | Tue Sep 10 | Ch 2 – injection, surjection, bijection, permutation (Math 61) | 2 |
| 4 | Thu Sep 12 | Ch 1-2 wrapup | 1-2 |
| 5 | Tue Sep 17 | What is a group? discrete groups Z^d, Z[i], SLnZ, Fn, plus continuous versions | 3.1* |
| 6 | Thu Sep 19 | generators and relations; Cayley graphs; subgroups | 3.2* |
| 7 | Tue Sep 24 | examplepalooza: isometry (eg, dihedral) groups, fundamental groups, and more | 3.3* |
| 8 | Thu Sep 26 | homomorphism and isomorphism | 3.4,3.7 |
| 9 | Tue Oct 1 | cyclic, abelian, nilpotent groups | 3.5* |
| 10 | Thu Oct 3 | symmetric groups; permutations as matrices | 3.6* |
| 11 | Tue Oct 8 | cosets | 3.8 |
| 12 | Thu Oct 10 | normality and the magic of quotient groups | 3.8 |
| Tue Oct 15 | TUFTS MONDAY | ||
| Thu Oct 17 | Midterm 1: Groups | ||
| 13 | Tue Oct 22 | What is a ring? Z/pZ, matrices, R[x] | |
| 14 | Thu Oct 24 | polynomials and their roots | 4.1 |
| 15 | Tue Oct 29 | factorization and extensions | 4.2 |
| 16 | Thu Oct 31 | arithmetic in R[x]/I | 4.3 |
| 17 | Tue Nov 5 | more generalities on rings, ideals, fields, vec sps, modules | 5.1 |
| 18 | Thu Nov 7 | ring homomorphisms | 5.2 |
| 19 | Tue Nov 12 | PIDs and quotients | 5.3 |
| 20 | Thu Nov 14 | quotient fields | 5.4 |
| 21 | Tue Nov 19 | Chapters 4-5 review | |
| Thu Nov 21 | Midterm 2: Polynomials, Rings, Fields | * | |
| 22 | Tue Nov 26 | topics: free groups and quotients, free groups and paradoxes | * |
| Thu Nov 28 | THANKSGIVING | ||
| 23 | Tue Dec 3 | worksheet on free groups | * |
| 24 | Thu Dec 5 | wrap-up of Banach-Tarski paradox | |
| Mon Dec 16 | Final Exam: Cumulative |