| 1 |
Groups and Subgroups, Matrix Groups |
Chapter 2, Sections 1, 2 |
Chapter 1, 1.7, 2.12; Chapter 2, 1.4, 1.10, 2.3, 2.7 |
| 2 |
Cyclic Groups, Permutations |
Chapter 2, Section 2,
Chapter 6, Sections 6 up to 6.10 |
Chapter 1, 4.5; Chapter 2, 1.1b, 2.1, 2.19; Chapter 6, 6.4, 6.9 |
| 3 |
Generators, Isomorphisms |
Chapter 2, Section 3 |
Chapter 2, 3.1, 3.4, 3.7, 3.10, 3.12; Chapter 6, 6.2 |
| 4 |
Homomorphisms |
Chapter 2, Sections 4, 5, 6 |
Chapter 2, 4.1, 4.3, 4.6, 4.16 |
| 5 |
Cosets |
Chapter 2, Sections 4, 5, 6 |
Chapter 2, 4.21, 5.3, 5.6, 6.7, 6.12 |
| 6 |
Modular Arithmetic |
Chapter 2, Sections 9, 10 |
Chapter 2, 9.2, 9.5, 9.6, 9.8 |
| 7 |
Quotient Groups |
Chapter 2, Sections 8, 10 |
Chapter 2, 6.4, 8.3, 10.8, 10.6 |
| 8 |
Fields and Vector Spaces |
Chapter 3, Sections 1, 2 |
Chapter 3, 1.1, 1.2, 2.1, 2.5, 2.8, 2.10 |
| 9 |
Bases and Dimension |
Chapter 3, Section 3 |
Chapter 3, 3.2, 3.4, 3.5, 3.8, 3.11 |
| 10 |
Computation with Bases |
Chapter 3, Section 4 |
Chapter 3, 4.1–4.3, 4.12 |
| 11 |
The Dimension Formula |
Chapter 4, Section 1, 2 |
Chapter 4, 1.1, 1.2, 1.4, 2.1, 2.2, 2.4, 2.5 |
| 12 |
First Quiz |
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| 13 |
Linear Operators, Eigenvectors |
Chapter 4, Section 3 |
Chapter 4, 3.1, 3.3–3.5, 3.8 |
| 14 |
The Characteristic Polynomial |
Chapter 4, Section 4, 6 |
Chapter 4, 4.1, 4.3, 4.4, 6.1, 6.5c, d, 6.7 |
| 15 |
Rotations |
Chapter 4, Section 5 |
Chapter 4, 5.1–5.3, 5.5, 5.8 |
| 16 |
Isometries |
Chapter 4, Section 5,
Chapter 5, Sections 1, 2 |
Chapter 4, 5.13, Chapter 5, 1.3a, c, 2.1, 2.2, 2.9 |
| 17 |
Isometries of the Plane |
Chapter 5, Sections 1, 2 |
Chapter 5, 1.1a, c, 2.1, 2.2, 2.4, 2.7, 2.9 |
| 18 |
Finite Groups of Motions |
Chapter 5, Section 3 |
Chapter 5, 3.1–3.3, 3.6, 4.1 |
| 19 |
Discrete Groups |
Chapter 5, Section 4 |
Chapter 5, 4.2–4.4, 4.6, 4.11 |
| 20 |
Discrete Groups (cont.) |
Chapter 5, Section 4 |
Chapter 5, 4.8–4.10, 4.12, 4.13 |
| 21 |
Group Operations |
Chapter 5, Sections 5, 6, 7 |
Chapter 5, 5.3, 5.8, 6.1, 6.5, 7.1–7.3 |
| 22 |
Finite Rotation Groups |
Chapter 5, Section 9 |
Chapter 5, 9.2–9.5, 9.6a, 9.7 |
| 23 |
The Class Equation |
Chapter 6, Section 1 |
Chapter 6, 1.1, 1.2, 1.4–1.6 |
| 24 |
Permutation Representations |
Chapter 5, Section 8 |
Chapter 5, 8.1, 8.3, 8.5, 9.6b |
| 25 |
The Icosahedral Group |
Chapter 6, Section 2 |
Chapter 6, 2.1, 2.3, 2.5 |
| 26 |
Second Quiz |
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| 27 |
Bilinear Forms |
Chapter 7, Sections 1, 2 |
Chapter 7, 1.2–1.5, 2.1, 2.2, 2.7 |
| 28 |
Symmetric Forms |
Chapter 7, Section 3 |
Chapter 7, 2.9, 2.10, 2.21, 3.2, 3.11 |
| 29 |
Hermitian Forms |
Chapter 7, Section 4 |
Chapter 7, 4.2, 4.5, 5.8, 4.10, 4.15, 4.18 |
| 30 |
The Spectral Theorem |
Chapter 7, Section 5 |
Chapter 7, 5.2, 5.4, 5.5a, 5.7, 5.16 |
| 31 |
Quadrics |
Chapter 7, Section 6 |
Chapter 7, 6.1, 6.2, 6.4 |
| 32 |
The Special Unitary Group SU2 |
Chapter 8, Sections 1, 2 |
Chapter 8, 1.1, 1.5, 2.1–2.3, 2.5 |
| 33 |
The Rotation Group |
Chapter 8, Section 3 |
Chapter 8, 3.1, 3.4, 3.5, 3.10 |
| 34 |
One-parameter Groups |
Chapter 4, Section 8,
Chapter 8, Section 5 |
Chapter 8, 5.2–5.4, 5.6 |
| 35 |
One-parameter Groups (cont.) |
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Chapter 8, 5.5, 5.7, 5.9 |
| 36 |
The Lie Algebra |
Chapter 8, Section 6 |
Chapter 8, 6.1, 6.2, 6.5–6.7 |
| 37 |
Third Quiz |
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| 38 |
Simple Groups |
Chapter 8, Section 7 |
Chapter 8, 7.1a, b, d, 7.2, 7.10 |
| 39 |
The Alternating Groups |
Chapter 6, Section 6 |
Chapter 6, 6.3, 6.6, 6.11, 6.13 |
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