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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
Group representations
1Todd-Coxeter algorithmChapter 6, sections 7, 8, 9Chapter 6, 8.2, 8.3, 9.2a, b
2Sylow theoremsChapter 6, sections 3, 4Chapter 6, 4.1, 4.2, 4.5, 4.6
3Group representationsChapter 9, sections 1, 4Chapter 9, 1.2, 1.5a, 1.7, 1.8, 4.4
4Unitary representationsChapter 9, sections 2, 3, 4Chapter 9, 2.1, 2.3, 4.1, 4.5
5CharactersChapter 9, section 5Chapter 9, 4.6, 5.2, 5.3, 5.4, 5.6
6The regular representationChapter 9, sections 6, 7Chapter 9, 6.1, 6.2, 6.5
7Characters (cont.)Chapter 9, sections 8, 9Chapter 9, 7.2, 8.1, 9.3
Rings: basic definitions
8Rings, homomorphismsChapter 10, sections 1, 2, 3Chapter 1.2, 1.3, 1.4, 2.1, 2.2a,b, 3.15, 3.17
9Ideals, quotient rings, correspondence theoremChapter 10, sections 3, 4Chapter 10, 3.16, 3.18, 4.6, 4.7
10Maximal ideals, prime ideals, fractionsChapter 10, sections 6, 7Chapter 10, 6.2, 6.3, 6.5, 7.1, 7.2, 7.12a
Rings: factorization
11Gauss' LemmaChapter 11, section 3Chapter 11, 2.2b, 3.4, 3.8, 3.10a
12Criteria for irreducibilityChapter 11, section 4Chapter 11, 4.1a,c, 4.2, 4.4, 4.6
13First quiz
14Unique factorizationChapter 11, sections 1, 2Chapter 11, 1.1, 1.5, 1.6, 2.4
Rings: abstract constructions
15Relations in a ringChapter 10, section 4Chapter 10, 4.1, 4.2, 3.34
16Adjoining elementsChapter 10, section 5Chapter 10, 5.1, 5.2, 5.4, 5.7, 5.8
Quadratic imaginary integers
17Gauss primesChapter 11, section 5Chapter 11, 5.1, 5.2, 5.4, 5.5, 5.7
18Quadratic integersChapter 11, sections 6, 7Chapter 11, 6.1, 6.2, 6.3
19Ideal factorizationChapter 11, section 8Chapter 11, 7.7c,d, 8.1, 8.6
20Ideal classesChapter 11, sections 9, 10Chapter 11, 9.1a, 9.2, 9.7, 10.3
Linear algebra over a ring
21Free modulesChapter 12, sections 1, 2Chapter 12, 1.3, 1.6, 2.1, 2.3, 2.6
22Integer matricesChapter 12, sections 3, 4Chapter 12, 3.1a,c, 4.1, 4.3, 4.5
23Generators and relationsChapter 12, section 5Chapter 12, 4.7, 5.1, 5.2, 5.4
24Structure of abelian groupsChapter 12, section 6Chapter 12, 6.1, 6.2, 6.3a,b, 6.4
25Second quiz
Fields: field extensions
26Algebraic elements, degreeChapter 13, sections 1, 2Chapter 13, 1.3, 2.3, 3.1, 3.3b,c, 3.7a,b, 3.8, 3.12
27Ruler and compassChapter 13, section 4Chapter 4.1, 4.2, 4.8
28Symbolic adjunctionChapter 13, section 5Chapter 13, 5.1, 5.2, 5.3, 5.4
29Finite fieldsChapter 13, section 6Chapter 13, 6.2, 6.4, 6.5, 6.8a, 6.15
30Function fieldsChapter 13, section 7Chapter 13, 4.5a,b,e,f
Fields: Galois theory
31The main theoremChapter 14, section 1Chapter 14, 1.1, 1.5, 1.7, 1.9, 1.12
32Cubic equationsChapter 14, section 2Chapter 14, 2.1, 2.2a,b,e, 2.3, 2.6
33Symmetric functionsChapter 14, section 3Chapter 14, 3.1, 3.3a,c,e, 3.5, 3.7
34Splitting fields, cyclotomic extensionsChapter 14, sections 5, 8Chapter 14, 8.1, 8.4
35Primitive elementsChapter 14, sections 4, 5Chapter 14, 4.1, 4.3a,d, 5.11
36Proof of the main theoremChapter 14, sections 4, 5Chapter 14, 4.1, 4.3a,d, 5.11
37Third quiz
38Quartic equationsChapter 14, section 6Chapter 14, 6.1, 6.3, 6.4, 6.31
39Quintic equationsChapter 14, section 9Chapter 14, 9.1, 9.6a, 9.8

 








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