Text
Artin, M. Algebra (2nd Edition). Addison Wesley, 2010. ISBN: 9780132413770.
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.
SES # | TOPICS | READINGS | EXERCISES |
---|---|---|---|
Group Representations | |||
1 | Group representations | Chapter 10, sections 1, and 4 | Chapter 10, 1.1, and 1.2 |
2 | Unitary representations | Chapter 10, sections 2, and 3 | Chapter 10, 2.1, 2.2, and 3.4 |
3 | Characters | Chapter 10, section 4 | Chapter 10, 4.1, 4.3a, b, and 4.8 |
4 | One-dimensional characters | Chapter 10, section 5 | Chapter 10, 5.1, and 5.3 |
5 | The regular representation | Chapter 10, section 6 | Chapter 10, 6.1, and 6.10 |
6 | Characters (cont.) | Chapter 10, sections 7, and 8 | Chapter 10, 7.1, 7.2, and 7.6 |
Rings: Basic Definitions | |||
7 | Rings, ring homomorphisms | Chapter 11, sections 1, 2, and 3 | Chapter 11, 1.1, 1.5, 1.8, and 1.9 |
8 | Ideals, quotient rings, correspondence theorem | Chapter 11, sections 4, and 5 | Chapter 11, 3.12, 3.13, 4.1, and 4.2 |
9 | Maximal ideals, prime ideals, fractions | Chapter 11, sections 8, and 9 | Chapter 11, 6.1, 7.1, and 8.3 |
Rings: Factoring | |||
10 | Gauss' Lemma | Chapter 12, section 3 | Chapter 12, 2.3, 2.7, and 3.2 |
11 | Unique factorization | Chapter 12, sections 1, and 2 | Chapter 12, 1.1, 1.5, 2.1, and 2.2 |
12 | Factoring integer polynomials | Chapter 12, section 4 | Chapter 12, 4.1a, 4.6, 4.7, and 4.11 |
Quadratic Imaginary Integers | |||
13 | Gauss primes | Chapter 12, section 5 | Chapter 12, 5.1, 5.2a, and 5.3 |
14 | Quadratic integers | Chapter 13, section 1 | Chapter 13, 1.1, 1.2, and 1.3 |
15 | Ideal factorization | Chapter 13, sections 2, and 3 | Chapter 13, 2.1, 3.1, 3.2, and 3.3 |
16 | Prime ideals | Chapter 13, sections 5, and 6 | Chapter 13, 5.3, 6.1, and 6.2 |
17 | Ideal classes | Chapter 11, sections 9, and 10 | Chapter 13, 7.1, 7.2, and 8.2 |
Linear Algebra over a Ring | |||
18 | Integer matrices | Chapter 14, sections 1, and 2 | Chapter 14, 1.1, 2.1, and 2.4 |
19 | Free modules | Chapter 14, sections 3, and 4 | Chapter 14, 3.2, 4.1a, and 4.3 |
20 | Presenting modules | Chapter 12, section 5 | Chapter 14, 5.1, and 5.2 |
21 | Hilbert basis theorem | Chapter 14, section 6 | Chapter 11, 6.1, 6.2, and M.1 |
22 | Structure of abelian groups | Chapter 14, section 7 | Chapter 14, 7.1, 7.2, and 7.5 |
23 | Linear operators | Chapter 14, section 8 | Chapter 14, 8.1, 8.3, and 8.4 |
Fields: Field Extensions | |||
24 | Algebraic elements, degree | Chapter 15, sections 1, and 2 | Chapter 15, 1.1, 1.3, and 2.1 |
25 | Ruler and compass | Chapter 13, section 5 | Chapter 15, 5.1, 5.2, and 5.4 |
26 | Adjoining elements | Chapter 11, section 5, chapter 15, section 6 | Chapter 11, 5.2, and 5.3, chapter 15, 6.1, and 6.3 |
27 | Finite fields | Chapter 15, section 7 | Chapter 15, 7.1, 7.2, and 7.13 |
28 | Primitive elements | Chapter 15, section 8 | Chapter 15, 8.1, and 8.2 |
Fields: Galois Theory | |||
29 | Symmetric functions, discriminant | Chapter 16, sections 1, and 2 | Chapter 16, 1.1a, b, e, 2.1, and 2.2 |
30 | Splitting fields, the Galois group | Chapter 16, sections 3, and 4 | Chapter 16, 3.2, and 4.1 |
31 | Fixed fields, Galois extensions | Chapter 16, sections 5, and 6 | Chapter 16, 5.1b, c, 6.1, and 6.2 |
32 | The main theorem | Chapter 16, section 7 | Chapter 16, 7.1, 7.3, 7.6, and 7.7 |
33 | Cubic and quartic equations | Chapter 16, sections 8, and 9 | Chapter 16, 8.2a, b, c, 9.1, 9.3, and 9.6 |
34 | Quartic equations (cont.) |
Chapter 16, section 9 Handout on The Seventeengon (PDF) |
Chapter 16, 9.12a, b, and 9.16 |
35 | Roots of unity, Kummer extensions | Chapter 16, sections 10, and 11 | Chapter 16, 10.1, 10.3, and 11.1 |
36 | Quintic equations | Chapter 16, section 12 | Chapter 16, 12.1, 12.2, and 12.7 |