| SES # | TOPICS | KEY DATES |
|---|---|---|
| Group Representations | ||
| 1 | Group representations | |
| 2 | Unitary representations | Problem set 1 out |
| 3 | Characters | |
| 4 | One-dimensional characters | |
| 5 | The regular representation |
Problem set 1 due Problem set 2 out |
| 6 | Characters (cont.) | |
| Rings: Basic Definitions | ||
| 7 | Rings, ring homomorphisms | Problem set 2 due |
| 8 | Ideals, quotient rings, correspondence theorem | |
| 9 | Maximal ideals, prime ideals, fractions | Problem set 3 out |
| Rings: Factoring | ||
| 10 | Gauss' Lemma | |
| 11 | Unique factorization | |
| 12 | Factoring integer polynomials | Problem set 3 due |
| 13 | First quiz | |
| Quadratic Imaginary Integers | ||
| 14 | Gauss primes | Problem set 4 out |
| 15 | Quadratic integers | |
| 16 | Ideal factorization | |
| 17 | Prime ideals |
Problem set 4 due Problem set 5 out |
| 18 | Ideal classes | |
| Linear Algebra over a Ring | ||
| 19 | Integer matrices | |
| 20 | Free modules | |
| 21 | Presenting modules | Problem set 5 due |
| 22 | Hilbert Basis Theorem | Problem set 6 out |
| 23 | Structure of abelian groups | |
| 24 | Linear Operators | |
| 25 | Second quiz | |
| Fields: Field Extensions | ||
| 26 | Algebraic elements, degree | |
| 27 | Ruler and compass | Problem set 6 due |
| 28 | Adjoining elements | |
| 29 | Finite fields | Problem set 7 out |
| 30 | Primitive elements | |
| Fields: Galois Theory | ||
| 31 | Symmetric functions, discriminant |
Problem set 7 due Problem set 8 out |
| 32 | Splitting fields, the Galois group | |
| 33 | Fixed fields, Galois extensions | |
| 34 | The main theorem |
Problem set 8 due Problem set 9 out |
| 35 | Cubic and quartic equations | |
| 36 | Quartic equations (cont.) | |
| 37 | Third quiz | |
| 38 | Roots of unity, Kummer extensions | |
| 39 | Quintic equations | Problem set 9 due |