| 1 |
Sylow Theorems |
Chapter 6, Sections 3, 4 |
Chapter 6, 4.1, 4.2, 4.5, 4.6 |
| 2 |
Proofs of the Sylow Theorems |
Chapter 6, Sections 4, 5 |
Chapter 6, 4.3, 4.6, 5.1 |
| Group Representations |
| 3 |
Group Representations and Definitions |
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 |
| 6 |
Characters (cont.) |
Chapter 9, Section 5 |
Chapter 9, 5.6, 5.8a, 8.2 |
| 7 |
The Regular Representation and Schur's Lemma |
Chapter 9, Sections 6, 9 |
Chapter 9, 6.1, 6.2, 6.5, 7.2, 9.3 |
| Rings: Basic Definitions |
| 8 |
Rings |
Chapter 10, Sections 1, 2 |
Chapter 1.2, 1.3, 1.4, 1.7, 2.1, 2.2a, b |
| 9 |
Homomorphisms |
Chapter 10, Section 3 |
Chapter 10, 3.15, 3.16, 3.18 |
| 10 |
Fractions |
Chapter 10, Section 6 |
Chapter 10, 6.2, 6.3, 6.5 |
| 11 |
First Quiz |
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| Rings: Factorization |
| 12 |
Unique Factorization |
Chapter 11, Sections 1, 2 |
Chapter 11, 1.1, 1.5, 1.6, 2.4 |
| 13 |
Gauss' Lemma |
Chapter 11, Section 3 |
Chapter 11, 2.2b, 3.4, 3.10, 3.11a |
| 14 |
Explicit Factorization |
Chapter 11, Section 4 |
Chapter 11, 4.1a, c, 4.2, 4.4, 4.6 |
| 15 |
Maximal Ideals |
Chapter 4, Section 7 |
Chapter 10, 7.1, 7.2, 7.9 |
| Quadratic Imaginary Integers |
| 16 |
Gauss Primes |
Chapter 11, Section 5 |
Chapter 11, 5.1, 5.2, 5.4 , 5.5, 5.7 |
| 17 |
Quadratic Integers |
Chapter 11, Sections 6, 7 |
Chapter 11, 6.1, 6.2, 6.3 |
| 18 |
Ideal Factorization |
Chapter 11, Section 8 |
Chapter 11, 7.7c, d, 8.1, 8.6 |
| 19 |
Ideal Classes |
Chapter 11, Sections 9, 10 |
Chapter 11, 9.1a, 10.3 |
| 20 |
Ideal Classes (cont.) |
Chapter 11, Sections 9, 10 |
Chapter 11, 9.2 |
| 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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| Rings: Abstract Constructions |
| 26 |
Relations in a Ring |
Chapter 10, Section 4 |
Chapter 10, 4.1, 4.2, 3.34 |
| 27 |
Adjoining Elements |
Chapter 10, Section 5 |
Chapter 10, 5.1, 5.2, 5.4, 5.7, 5.8 |
| Fields: Field Extensions |
| 28 |
Algebraic Elements |
Chapter 13, Sections 1, 2 |
Chapter 13, 1.1, 1.2, 1.3, 2.3, 2.6 |
| 29 |
Degree of a Field Extension |
Chapter 13, Section 3 |
Chapter 13, 3.1, 3.3a, b, c, 3.7a, b, 3.8, 3.12 |
| 30 |
Ruler and Compass |
Chapter 13, Section 4 |
Chapter 4.1, 4.2, 4.8 |
| 31 |
Symbolic Adjunction |
Chapter 13, Section 5 |
Chapter 13, 5.1, 5.2, 5.3, 5.4 |
| 32 |
Finite Fields |
Chapter 13, Section 6 |
Chapter 13, 6.2, 6.4, 6.5, 6.8a, 6.15 |
| Fields: Galois Theory |
| 33 |
The Main Theorem |
Chapter 14, Section 1 |
Chapter 14, 1.1, 1.5, 1.7, 1.9, 1.12 |
| 34 |
Cubic Equations |
Chapter 14, Section 2 |
Chapter 14, 2.1, 2.2a, b, e, 2.3, 2.6 |
| 35 |
Symmetric Functions |
Chapter 14, Section 3 |
Chapter 14, 3.1, 3.3a, c, e, 3.5, 3.7 |
| 36 |
Primitive Elements |
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 |
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