| 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 |
