| SES # | TOPICS | READINGS | EXERCISES |
|---|---|---|---|
| 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 | ||
| 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 | ||
| 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 | ||
| 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 |
Table of Contents
Study Materials
Readings
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Text
Artin, M. Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1991. ISBN: 9780130047632.
The exercises listed below point to the text and are a suggestion from the professor to the students in every given lecture. These exercises were not turned in and were not corrected.