| Group representations |
| 1 |
Todd-Coxeter algorithm |
Chapter 6, sections 7, 8, 9 |
Chapter 6, 8.2, 8.3, 9.2a, b |
| 2 |
Sylow theorems |
Chapter 6, sections 3, 4 |
Chapter 6, 4.1, 4.2, 4.5, 4.6 |
| 3 |
Group representations |
Chapter 9, sections 1, 4 |
Chapter 9, 1.2, 1.5a, 1.7, 1.8, 4.4 |
| 4 |
Unitary representations |
Chapter 9, sections 2, 3, 4 |
Chapter 9, 2.1, 2.3, 4.1, 4.5 |
| 5 |
Characters |
Chapter 9, section 5 |
Chapter 9, 4.6, 5.2, 5.3, 5.4, 5.6 |
| 6 |
The regular representation |
Chapter 9, sections 6, 7 |
Chapter 9, 6.1, 6.2, 6.5 |
| 7 |
Characters (cont.) |
Chapter 9, sections 8, 9 |
Chapter 9, 7.2, 8.1, 9.3 |
| Rings: basic definitions |
| 8 |
Rings, homomorphisms |
Chapter 10, sections 1, 2, 3 |
Chapter 1.2, 1.3, 1.4, 2.1, 2.2a,b, 3.15, 3.17 |
| 9 |
Ideals, quotient rings, correspondence theorem |
Chapter 10, sections 3, 4 |
Chapter 10, 3.16, 3.18, 4.6, 4.7 |
| 10 |
Maximal ideals, prime ideals, fractions |
Chapter 10, sections 6, 7 |
Chapter 10, 6.2, 6.3, 6.5, 7.1, 7.2, 7.12a |
| Rings: factorization |
| 11 |
Gauss' Lemma |
Chapter 11, section 3 |
Chapter 11, 2.2b, 3.4, 3.8, 3.10a |
| 12 |
Criteria for irreducibility |
Chapter 11, section 4 |
Chapter 11, 4.1a,c, 4.2, 4.4, 4.6 |
| 13 |
First quiz |
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| 14 |
Unique factorization |
Chapter 11, sections 1, 2 |
Chapter 11, 1.1, 1.5, 1.6, 2.4 |
| Rings: abstract constructions |
| 15 |
Relations in a ring |
Chapter 10, section 4 |
Chapter 10, 4.1, 4.2, 3.34 |
| 16 |
Adjoining elements |
Chapter 10, section 5 |
Chapter 10, 5.1, 5.2, 5.4, 5.7, 5.8 |
| Quadratic imaginary integers |
| 17 |
Gauss primes |
Chapter 11, section 5 |
Chapter 11, 5.1, 5.2, 5.4, 5.5, 5.7 |
| 18 |
Quadratic integers |
Chapter 11, sections 6, 7 |
Chapter 11, 6.1, 6.2, 6.3 |
| 19 |
Ideal factorization |
Chapter 11, section 8 |
Chapter 11, 7.7c,d, 8.1, 8.6 |
| 20 |
Ideal classes |
Chapter 11, sections 9, 10 |
Chapter 11, 9.1a, 9.2, 9.7, 10.3 |
| Linear algebra over a ring |
| 21 |
Free modules |
Chapter 12, sections 1, 2 |
Chapter 12, 1.3, 1.6, 2.1, 2.3, 2.6 |
| 22 |
Integer matrices |
Chapter 12, sections 3, 4 |
Chapter 12, 3.1a,c, 4.1, 4.3, 4.5 |
| 23 |
Generators and relations |
Chapter 12, section 5 |
Chapter 12, 4.7, 5.1, 5.2, 5.4 |
| 24 |
Structure of abelian groups |
Chapter 12, section 6 |
Chapter 12, 6.1, 6.2, 6.3a,b, 6.4 |
| 25 |
Second quiz |
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| Fields: field extensions |
| 26 |
Algebraic elements, degree |
Chapter 13, sections 1, 2 |
Chapter 13, 1.3, 2.3, 3.1, 3.3b,c, 3.7a,b, 3.8, 3.12 |
| 27 |
Ruler and compass |
Chapter 13, section 4 |
Chapter 4.1, 4.2, 4.8 |
| 28 |
Symbolic adjunction |
Chapter 13, section 5 |
Chapter 13, 5.1, 5.2, 5.3, 5.4 |
| 29 |
Finite fields |
Chapter 13, section 6 |
Chapter 13, 6.2, 6.4, 6.5, 6.8a, 6.15 |
| 30 |
Function fields |
Chapter 13, section 7 |
Chapter 13, 4.5a,b,e,f |
| Fields: Galois theory |
| 31 |
The main theorem |
Chapter 14, section 1 |
Chapter 14, 1.1, 1.5, 1.7, 1.9, 1.12 |
| 32 |
Cubic equations |
Chapter 14, section 2 |
Chapter 14, 2.1, 2.2a,b,e, 2.3, 2.6 |
| 33 |
Symmetric functions |
Chapter 14, section 3 |
Chapter 14, 3.1, 3.3a,c,e, 3.5, 3.7 |
| 34 |
Splitting fields, cyclotomic extensions |
Chapter 14, sections 5, 8 |
Chapter 14, 8.1, 8.4 |
| 35 |
Primitive elements |
Chapter 14, sections 4, 5 |
Chapter 14, 4.1, 4.3a,d, 5.11 |
| 36 |
Proof of the main theorem |
Chapter 14, sections 4, 5 |
Chapter 14, 4.1, 4.3a,d, 5.11 |
| 37 |
Third quiz |
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| 38 |
Quartic equations |
Chapter 14, section 6 |
Chapter 14, 6.1, 6.3, 6.4, 6.31 |
| 39 |
Quintic equations |
Chapter 14, section 9 |
Chapter 14, 9.1, 9.6a, 9.8 |