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Text


Amazon logo 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.


SES #TOPICSREADINGSEXERCISES
1Groups, matrices, permutationsChapter 2, section 1; chapter 6, section 6 up to 6.10Chapters 1, 1.7, 2.12; chapters 2, 1.1b, 1.5, 2.19
2Subgroups, cyclic groupsChapter 1, section 4; chapter 2, section 2Chapters 1, 4.5; chapters 2, 2.1, 2.3, 2.7; chapters 6, 6.9
3IsomorphismsChapter 2, sections 2, 3Chapters 2, 3.1, 3.7, 3.10, 3.12; chapters 6, 6.2, 6.4
4HomomorphismsChapter 2, sections 4, 5Chapters 2, 4.1, 4.3, 4,6, 4.16, 5.6, 5.7
5CosetsChapter 2, section 6Chapters 2, 5.3, 6.7, 6.12, 7.7
6Quotient groupsChapter 2, sections 8, 10Chapters 2, 6.4, 8.3, 10.8, 10.6
7Modular arithmetic, fieldsChapter 2, section 9; chapter 3, section 2Chapters 2, 9.2, 9.5; chapters 3, 2.1, 2.3
8FieldsChapter 2, section 9; chapter 3, section 2Chapters 2, 9.8; chapters 3, 2.8, 2.14, 2.17
9Vector spaces, bases, dimensionChapter 3, sections 1, 3Chapters 3, 3.2, 3.4, 3.5, 3.8, 3.11
10Computation with basesChapter 3, section 4Chapters 3, 4.1–4.3, 4.12
11The dimension formulaChapter 4, sections 1, 2Chapters 4, 1.1, 1.2, 1.4, 2.1, 2.2, 2.4, 2.5
12First quiz
13Linear operators, Eigen vectorsChapter 4, section 3Chapters 4, 3.1, 3.3–3.5, 3.8
14The characteristic polynomialChapter 4, sections 4, 6Chapters 4, 4.1, 4.3, 4.4, 6.1, 6.5c, d, 6.7
15RotationsChapter 4, section 5Chapters 4, 5.1–5.3, 5.5, 5.8
16IsometriesChapter 4, section 5; chapter 5, sections 1, 2Chapters 4, 5.13; chapters 5, 1.3a, c, 2.1, 2.2, 2.9
17Isometries of the planeChapter 5, sections 1, 2Chapters 5, 1.1a, c, 2.1, 2.2, 2.4, 2.7, 2.9
18Finite groups of isometriesChapter 5, section 3Chapters 5, 3.1–3.3, 3.6, 4.1
19Discrete groupsChapter 5, section 4Chapters 5, 4.2–4.4, 4.6, 4.11
20Discrete groups (cont.)Chapter 5, section 4Chapters 5, 4.8–4.10, 4.12, 4.13
21Group operationsChapter 5, sections 5, 6, 7Chapters 5, 5.3, 5.8, 6.1, 6.5, 7.1–7.3
22Finite rotation groupsChapter 5, section 9Chapters 5, 9.2–9.5, 9.6a, 9.7
23The class equationChapter 6, section 1Chapters 6, 1.1, 1.2, 1.4–1.6
24Permutation representationsChapter 5, section 8Chapters 5, 8.1, 8.3, 8.5, 9.6b
25The alternating groupChapter 6, sections 2, 6Chapters 6, 2.1, 2.3, 2.5, 6.3, 6.13
26Second quiz
27Bilinear formsChapter 7, sections 1, 2Chapters 7, 1.2–1.5, 2.1, 2.2, 2.7
28Symmetric formsChapter 7, section 3Chapters 7, 2.9, 2.10, 2.21, 3.2, 3.11
29Hermitian formsChapter 7, section 4Chapters 7, 4.2, 4.5, 5.8, 4.10, 4.15, 4.18
30The spectral theoremChapter 7, section 5Chapters 7, 5.2, 5.4, 5.5a, 5.7, 5.16
31QuadricsChapter 7, section 6Chapters 7, 6.1, 6.2, 6.4
32The special unitary group SU2Chapter 8, sections 1, 2Chapters 8, 1.1, 1.5, 2.1–2.3, 2.5
33The rotation groupChapter 8, section 3Chapters 8, 3.1, 3.4, 3.5, 3.10
34One-parameter groupsChapter 4, section 8; chapter 8, section 5Chapters 8, 5.2–5.4, 5.6
35One-parameter groups (cont.)Chapter 4, section 8Chapters 8, 5.5, 5.7, 5.9
36Third quiz
37The lie algebraChapter 8, section 6Chapters 8, 6.1, 6.2, 6.5–6.7
38Dimensions of the linear groupsChapter 8, section 7Chapters 8, 7.1a, b, d, 7.2, 7.10
39Simple groupsChapter 8, section 8Chapters 8, 8.2a, 8.3, 8.5

 








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