| SES # | TOPICS | KEY DATES |
|---|---|---|
| Group representations | ||
| 1 | Todd-Coxeter algorithm | Problem set 1 out |
| 2 | Sylow theorems | |
| 3 | Group representations | |
| 4 | Unitary representations | Problem set 1 due |
| 5 | Characters | Problem set 2 out |
| 6 | The regular representation | |
| 7 | Characters (cont.) | |
| Rings: basic definitions | ||
| 8 | Rings, homomorphisms | Problem set 2 due Problem set 3 out |
| 9 | Ideals, quotient rings, correspondence theorem | |
| 10 | Maximal ideals, prime ideals, fractions | |
| Rings: factorization | ||
| 11 | Gauss' Lemma | Problem set 3 due Problem set 4 out |
| 12 | Criteria for irreducibility | |
| 13 | First quiz | |
| 14 | Unique factorization | |
| Rings: abstract constructions | ||
| 15 | Relations in a ring | Problem set 4 due Problem set 5 out |
| 16 | Adjoining elements | |
| Quadratic imaginary integers | ||
| 17 | Gauss primes | |
| 18 | Quadratic integers | Problem set 5 due |
| 19 | Ideal factorization | Problem set 6 out one day before Ses #19 |
| 20 | Ideal classes | |
| Linear algebra over a ring | ||
| 21 | Free modules | Problem set 6 due |
| 22 | Integer matrices | Problem set 7 out |
| 23 | Generators and relations | |
| 24 | Structure of abelian groups | |
| 25 | Second quiz | |
| Fields: field extensions | ||
| 26 | Algebraic elements, degree | Problem set 7 due |
| 27 | Ruler and compass | |
| 28 | Symbolic adjunction | Problem set 8 out |
| 29 | Finite fields | |
| 30 | Function fields | Problem set 8 due |
| Fields: Galois theory | ||
| 31 | The main theorem | Problem set 9 out |
| 32 | Cubic equations | |
| 33 | Symmetric functions | |
| 34 | Splitting fields, cyclotomic extensions | Problem set 9 due Problem set 10 out |
| 35 | Primitive elements | |
| 36 | Proof of the main theorem | |
| 37 | Third quiz | |
| 38 | Quartic equations | |
| 39 | Quintic equations | Problem set 10 due |