| SES # | TOPICS | READINGS | EXERCISES |
|---|---|---|---|
| 1 | Groups, matrices, permutations | Chapter 2, section 1; chapter 6, section 6 up to 6.10 | Chapters 1, 1.7, 2.12; chapters 2, 1.1b, 1.5, 2.19 |
| 2 | Subgroups, cyclic groups | Chapter 1, section 4; chapter 2, section 2 | Chapters 1, 4.5; chapters 2, 2.1, 2.3, 2.7; chapters 6, 6.9 |
| 3 | Isomorphisms | Chapter 2, sections 2, 3 | Chapters 2, 3.1, 3.7, 3.10, 3.12; chapters 6, 6.2, 6.4 |
| 4 | Homomorphisms | Chapter 2, sections 4, 5 | Chapters 2, 4.1, 4.3, 4,6, 4.16, 5.6, 5.7 |
| 5 | Cosets | Chapter 2, section 6 | Chapters 2, 5.3, 6.7, 6.12, 7.7 |
| 6 | Quotient groups | Chapter 2, sections 8, 10 | Chapters 2, 6.4, 8.3, 10.8, 10.6 |
| 7 | Modular arithmetic, fields | Chapter 2, section 9; chapter 3, section 2 | Chapters 2, 9.2, 9.5; chapters 3, 2.1, 2.3 |
| 8 | Fields | Chapter 2, section 9; chapter 3, section 2 | Chapters 2, 9.8; chapters 3, 2.8, 2.14, 2.17 |
| 9 | Vector spaces, bases, dimension | Chapter 3, sections 1, 3 | Chapters 3, 3.2, 3.4, 3.5, 3.8, 3.11 |
| 10 | Computation with bases | Chapter 3, section 4 | Chapters 3, 4.1–4.3, 4.12 |
| 11 | The dimension formula | Chapter 4, sections 1, 2 | Chapters 4, 1.1, 1.2, 1.4, 2.1, 2.2, 2.4, 2.5 |
| 12 | First quiz | ||
| 13 | Linear operators, Eigen vectors | Chapter 4, section 3 | Chapters 4, 3.1, 3.3–3.5, 3.8 |
| 14 | The characteristic polynomial | Chapter 4, sections 4, 6 | Chapters 4, 4.1, 4.3, 4.4, 6.1, 6.5c, d, 6.7 |
| 15 | Rotations | Chapter 4, section 5 | Chapters 4, 5.1–5.3, 5.5, 5.8 |
| 16 | Isometries | Chapter 4, section 5; chapter 5, sections 1, 2 | Chapters 4, 5.13; chapters 5, 1.3a, c, 2.1, 2.2, 2.9 |
| 17 | Isometries of the plane | Chapter 5, sections 1, 2 | Chapters 5, 1.1a, c, 2.1, 2.2, 2.4, 2.7, 2.9 |
| 18 | Finite groups of isometries | Chapter 5, section 3 | Chapters 5, 3.1–3.3, 3.6, 4.1 |
| 19 | Discrete groups | Chapter 5, section 4 | Chapters 5, 4.2–4.4, 4.6, 4.11 |
| 20 | Discrete groups (cont.) | Chapter 5, section 4 | Chapters 5, 4.8–4.10, 4.12, 4.13 |
| 21 | Group operations | Chapter 5, sections 5, 6, 7 | Chapters 5, 5.3, 5.8, 6.1, 6.5, 7.1–7.3 |
| 22 | Finite rotation groups | Chapter 5, section 9 | Chapters 5, 9.2–9.5, 9.6a, 9.7 |
| 23 | The class equation | Chapter 6, section 1 | Chapters 6, 1.1, 1.2, 1.4–1.6 |
| 24 | Permutation representations | Chapter 5, section 8 | Chapters 5, 8.1, 8.3, 8.5, 9.6b |
| 25 | The alternating group | Chapter 6, sections 2, 6 | Chapters 6, 2.1, 2.3, 2.5, 6.3, 6.13 |
| 26 | Second quiz | ||
| 27 | Bilinear forms | Chapter 7, sections 1, 2 | Chapters 7, 1.2–1.5, 2.1, 2.2, 2.7 |
| 28 | Symmetric forms | Chapter 7, section 3 | Chapters 7, 2.9, 2.10, 2.21, 3.2, 3.11 |
| 29 | Hermitian forms | Chapter 7, section 4 | Chapters 7, 4.2, 4.5, 5.8, 4.10, 4.15, 4.18 |
| 30 | The spectral theorem | Chapter 7, section 5 | Chapters 7, 5.2, 5.4, 5.5a, 5.7, 5.16 |
| 31 | Quadrics | Chapter 7, section 6 | Chapters 7, 6.1, 6.2, 6.4 |
| 32 | The special unitary group SU2 | Chapter 8, sections 1, 2 | Chapters 8, 1.1, 1.5, 2.1–2.3, 2.5 |
| 33 | The rotation group | Chapter 8, section 3 | Chapters 8, 3.1, 3.4, 3.5, 3.10 |
| 34 | One-parameter groups | Chapter 4, section 8; chapter 8, section 5 | Chapters 8, 5.2–5.4, 5.6 |
| 35 | One-parameter groups (cont.) | Chapter 4, section 8 | Chapters 8, 5.5, 5.7, 5.9 |
| 36 | Third quiz | ||
| 37 | The lie algebra | Chapter 8, section 6 | Chapters 8, 6.1, 6.2, 6.5–6.7 |
| 38 | Dimensions of the linear groups | Chapter 8, section 7 | Chapters 8, 7.1a, b, d, 7.2, 7.10 |
| 39 | Simple groups | Chapter 8, section 8 | Chapters 8, 8.2a, 8.3, 8.5 |
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.