| 1 |
Sylow Theorems |
Problem set 1 out |
| 2 |
Proofs of the Sylow Theorems |
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| Group Representations |
| 3 |
Group Representations and Definitions |
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| 4 |
Unitary Representations |
Problem set 2 out
Problem set 3 out |
| 5 |
Characters |
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| 6 |
Characters (cont.) |
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| 7 |
The Regular Representation and Schur's Lemma |
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| Rings: Basic Definitions |
| 8 |
Rings |
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| 9 |
Homomorphisms |
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| 10 |
Fractions |
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| 11 |
First Quiz |
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| Rings: Factorization |
| 12 |
Unique Factorization |
Problem set 4 out |
| 13 |
Gauss' Lemma |
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| 14 |
Explicit Factorization |
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| 15 |
Maximal Ideals |
Problem set 5 out |
| Quadratic Imaginary Integers |
| 16 |
Gauss Primes |
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| 17 |
Quadratic Integers |
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| 18 |
Ideal Factorization |
Problem set 6 out |
| 19 |
Ideal Classes |
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| 20 |
Ideal Classes (cont.) |
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| Linear Algebra Over a Ring |
| 21 |
Free Modules |
Problem set 7 out |
| 22 |
Integer Matrices |
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| 23 |
Generators and Relations |
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| 24 |
Structure of Abelian groups |
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| 25 |
Second Quiz |
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| Rings: Abstract Constructions |
| 26 |
Relations in a Ring |
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| 27 |
Adjoining Elements |
Problem set 8 out |
| Fields: Field Extensions |
| 28 |
Algebraic Elements |
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| 29 |
Degree of a Field Extension |
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| 30 |
Ruler and Compass |
Problem set 9 out |
| 31 |
Symbolic Adjunction |
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| 32 |
Finite Fields |
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| Fields: Galois Theory |
| 33 |
The Main Theorem |
Problem set 10 out |
| 34 |
Cubic Equations |
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| 35 |
Symmetric Functions |
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| 36 |
Primitive Elements |
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| 37 |
Third Quiz |
| 38 |
Quartic Equations |
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| 39 |
Quintic Equations |
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