| 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 |