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 |
|---|---|---|---|
| 1 | The general linear group GLn, groups, generators | Chapter 1, sections 1-4; chapter 2, sections 1-2 | Chapter 1, 1.7, 3.4, 4.6; chapter 2, 1.1, and 2.3 |
| 2 | The symmetric group Sn, subgroups | Chapter 1, section 5; chapter 2, section 2 | Chapter 1, 5.1, 5.2; chapter 2, 2.4, and 2.5 |
| 3 | Subgroups of Z+, cyclic groups | Chapter 2, sections 3-4 | Chapter 2, 3.1, 3.2, 4.4, 4.5, and 4.9 |
| 4 | Homomorphisms and isomorphisms | Chapter 2, sections 5-7 | Chapter 2, 5.3, 6.2, 6.6, 7.1, and 7.5 |
| 5 | Cosets | Chapter 2, sections 8-9 | Chapter 2, 8.3, 8.4, 8.5, and 8.10 |
| 6 | The correspondence theorem | Chapter 2, section 10 | Chapter 2, 9.4, 9.5, 10.1, and 10.3 |
| 7 | Product groups, quotient groups | Chapter 2, sections 11-12 | Chapter 2, 11.3, 11.4, 12.1, and 12.5 |
| 8 | Fields | Chapter 3, section 1 | Chapter 3, 1.2, 1.3, 1.10, and 1.11 |
| 9 | Vector spaces, bases, dimension | Chapter 3, sections 2-3 | Chapter 3, 2.2, 3.1, 3.7, 3.8, and 4.5 |
| 10 | Computation with bases | Chapter 3, sections 4-5 | Chapter 3, 4.2, 4.3, 4.4, 5.1, and 5.2 |
| 11 | The dimension formula | Chapter 4, section 2 | Chapter 4, 1.1, 1.3, 1.4, 2.1, and 2.3 |
| 12 | Linear operators, eigenvectors | Chapter 4, sections 3-4 | Chapter 4, 3.3, 4.2, 4.4, 4.6, and 4.8 |
| 13 | The characteristic polynomial | Chapter 4, sections 5-6 | Chapter 4, 5.3, 5.5, 5.10, 6.1, and 6.4 |
| 14 | Jordan form | Chapter 4, section 7 | Chapter 4, 6.10, 7.1, 7.3, 7.6, and 7.7 |
| 15 | Rotations | Chapter 5, sections 1-2 | Chapter 5, 1.1, 1.2, 1.5, 2.1, and 2.2 |
| 16 | Isometries | Chapter 6, sections 1-3 | Chapter 6, 1.1, 3.1, 3.2, 3.4, and 3.6 |
| 17 | Finite groups of isometries | Chapter 6, section 4 | Chapter 6, 4.1, 4.2, and 4.3 |
| 18 | Discrete groups of isometries | Chapter 6, section 5 | Chapter 6, 5.1, 5.2, 5.3, 5.5, and 5.6 |
| 19 | Discrete groups of isometries (cont.) | Chapter 6, section 6 | Chapter 6, 5.11, 6.1, 6.12, and 6.3 |
| 20 | Group operations | Chapter 6, sections 7-9 | Chapter 6, 7.2, 7.4, 8.3, 9.1, and 9.6 |
| 21 | Finite rotation groups | Chapter 6, section 12 | Chapter 6, 10.1, 12.1, 12.3, 12.5, and 12.7 |
| 22 | The class equation | Chapter 7, sections 1-3 | Chapter 7, 2.1, 2.5, 2.7, 2.17, and 3.1 |
| 23 | The icosahedral group | Chapter 7, section 4 | 4.1, 4.2, 4.3, and 4.4 |
| 24 | The symmetric and alternating groups | Chapter 6, section 11; chapter 7, sections 4-5 | Chapter 6, 11.9; chapter 7, 4.7, 5.1c, 5.2, and 5.3 |
| 25 | Symmetric and hermitian forms | Chapter 8, sections 1-3 | Chapter 8, 1.1, 2.1, 3.2, 3.3, and 3.4 |
| 26 | Orthogonality | Chapter 8, section 4 | Chapter 8, 4.3, 4.4, 4.5, 4.7, 4.9, and 4.14 |
| 27 | The projection formula | Chapter 8, sections 4-5 | Chapter 8, 4.2, 4.15, 4.21, and 5.4 |
| 28 | The spectral theorem | Chapter 8, section 6 | Chapter 8, 6.3, 6.6, 6.9, 6.14, and 6.18 |
| 29 | Quadrics | Chapter 8, section 7 | Chapter 8, 6.21, 7.1, 7.2, and 7.3 |
| 30 | The special unitary group SU2 | Chapter 9, sections 1-3 | Chapter 9, 1.2, 1.5, 2.1, 3.1, and 3.4 |
| 31 | The rotation group SO3 | Chapter 9, section 4 | Chapter 9, 4.1, 4.2, 4.4a, and 4.7 |
| 32 | One-parameter groups | Chapter 5, section 4; chapter 9, section 4 | Chapter 5, 4.1a, e, 4.4; chapter 9, 5.3, and 5.5 |
| 33 | One-parameter groups (cont.) | Chapter 5, section 4; chapter 9 section 4 | Chapter 5, 4.6; chapter 9, 5.2, 5.7, 5.10, and 7.3 |
| 34 | The lie algebra | Chapter 9, sections 6-7 | Chapter 9, 6.1, 6.2, 6.3, and 7.7 |
| 35 | Simple groups | Chapter 9, section 8 | Chapter 9, 8.1, and 8.5 |