Readings

Text

Amazon logo 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