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    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 # TOPICS READINGS EXERCISES
    Group representations
    1 Todd-Coxeter algorithm Chapter 6, sections 7, 8, 9 Chapter 6, 8.2, 8.3, 9.2a, b
    2 Sylow theorems Chapter 6, sections 3, 4 Chapter 6, 4.1, 4.2, 4.5, 4.6
    3 Group representations Chapter 9, sections 1, 4 Chapter 9, 1.2, 1.5a, 1.7, 1.8, 4.4
    4 Unitary representations Chapter 9, sections 2, 3, 4 Chapter 9, 2.1, 2.3, 4.1, 4.5
    5 Characters Chapter 9, section 5 Chapter 9, 4.6, 5.2, 5.3, 5.4, 5.6
    6 The regular representation Chapter 9, sections 6, 7 Chapter 9, 6.1, 6.2, 6.5
    7 Characters (cont.) Chapter 9, sections 8, 9 Chapter 9, 7.2, 8.1, 9.3
    Rings: basic definitions
    8 Rings, homomorphisms Chapter 10, sections 1, 2, 3 Chapter 1.2, 1.3, 1.4, 2.1, 2.2a,b, 3.15, 3.17
    9 Ideals, quotient rings, correspondence theorem Chapter 10, sections 3, 4 Chapter 10, 3.16, 3.18, 4.6, 4.7
    10 Maximal ideals, prime ideals, fractions Chapter 10, sections 6, 7 Chapter 10, 6.2, 6.3, 6.5, 7.1, 7.2, 7.12a
    Rings: factorization
    11 Gauss' Lemma Chapter 11, section 3 Chapter 11, 2.2b, 3.4, 3.8, 3.10a
    12 Criteria for irreducibility Chapter 11, section 4 Chapter 11, 4.1a,c, 4.2, 4.4, 4.6
    13 First quiz

    14 Unique factorization Chapter 11, sections 1, 2 Chapter 11, 1.1, 1.5, 1.6, 2.4
    Rings: abstract constructions
    15 Relations in a ring Chapter 10, section 4 Chapter 10, 4.1, 4.2, 3.34
    16 Adjoining elements Chapter 10, section 5 Chapter 10, 5.1, 5.2, 5.4, 5.7, 5.8
    Quadratic imaginary integers
    17 Gauss primes Chapter 11, section 5 Chapter 11, 5.1, 5.2, 5.4, 5.5, 5.7
    18 Quadratic integers Chapter 11, sections 6, 7 Chapter 11, 6.1, 6.2, 6.3
    19 Ideal factorization Chapter 11, section 8 Chapter 11, 7.7c,d, 8.1, 8.6
    20 Ideal classes Chapter 11, sections 9, 10 Chapter 11, 9.1a, 9.2, 9.7, 10.3
    Linear algebra over a ring
    21 Free modules Chapter 12, sections 1, 2 Chapter 12, 1.3, 1.6, 2.1, 2.3, 2.6
    22 Integer matrices Chapter 12, sections 3, 4 Chapter 12, 3.1a,c, 4.1, 4.3, 4.5
    23 Generators and relations Chapter 12, section 5 Chapter 12, 4.7, 5.1, 5.2, 5.4
    24 Structure of abelian groups Chapter 12, section 6 Chapter 12, 6.1, 6.2, 6.3a,b, 6.4
    25 Second quiz

    Fields: field extensions
    26 Algebraic elements, degree Chapter 13, sections 1, 2 Chapter 13, 1.3, 2.3, 3.1, 3.3b,c, 3.7a,b, 3.8, 3.12
    27 Ruler and compass Chapter 13, section 4 Chapter 4.1, 4.2, 4.8
    28 Symbolic adjunction Chapter 13, section 5 Chapter 13, 5.1, 5.2, 5.3, 5.4
    29 Finite fields Chapter 13, section 6 Chapter 13, 6.2, 6.4, 6.5, 6.8a, 6.15
    30 Function fields Chapter 13, section 7 Chapter 13, 4.5a,b,e,f
    Fields: Galois theory
    31 The main theorem Chapter 14, section 1 Chapter 14, 1.1, 1.5, 1.7, 1.9, 1.12
    32 Cubic equations Chapter 14, section 2 Chapter 14, 2.1, 2.2a,b,e, 2.3, 2.6
    33 Symmetric functions Chapter 14, section 3 Chapter 14, 3.1, 3.3a,c,e, 3.5, 3.7
    34 Splitting fields, cyclotomic extensions Chapter 14, sections 5, 8 Chapter 14, 8.1, 8.4
    35 Primitive elements Chapter 14, sections 4, 5 Chapter 14, 4.1, 4.3a,d, 5.11
    36 Proof of the main theorem Chapter 14, sections 4, 5 Chapter 14, 4.1, 4.3a,d, 5.11
    37 Third quiz

    38 Quartic equations Chapter 14, section 6 Chapter 14, 6.1, 6.3, 6.4, 6.31
    39 Quintic equations Chapter 14, section 9 Chapter 14, 9.1, 9.6a, 9.8