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18.703

Modern Algebra

3-0-9 units · Undergraduate

Focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics: group theory, emphasizing finite groups; ring theory, including ideals and unique factorization in polynomial and Euclidean rings; field theory, including properties and applications of finite fields. 18.700 and 18.703 together form a standard algebra sequence.

Spring 2013

Topics

  • Groups
  • Subgroups
  • Cosets
  • Cyclic Groups
  • Permutation Groups
  • Conjugation in S n
  • Isomorphisms
  • Homomorphisms and Kernels
  • Quotient Groups
  • The Isomorphism Theorems
  • The Alternating Groups
  • Presentations and Groups of Small Order
  • Sylow Theorems and Applications
  • Rings
  • Midterm 1
  • Basic Properties of Rings
  • Ring Homomorphisms and Ideals
  • Field of Fractions
  • Prime amd Maximal Ideals
  • Special Domains
  • Euclidean Domains
  • Midterm 2
  • Polynomial Rings
  • A Quick Primality Test
  • Group Actions and Automorphisms

Readings

  • Herstein, I. N. Abstract Algebra . Macmillan, 1986. ISBN: 9780023538209.
    Listed reading
  • LEC #: 1 · READINGS: 3.1, and 3.2
    Reading assignment
  • LEC #: 2 · READINGS: 3.3
    Reading assignment
  • LEC #: 3 · READINGS: 6.1, and 6.2
    Reading assignment
  • LEC #: 4 · READINGS: 6.2, and 4.1
    Reading assignment
  • LEC #: 5 · READINGS: 4.2, and 5.1
    Reading assignment
  • LEC #: 6 · READINGS: 5.1, and 5.2
    Reading assignment
  • LEC #: 7 · READINGS: 9.1
    Reading assignment
  • LEC #: 8 · READINGS: 11.1, and 10.1
    Reading assignment
  • LEC #: 9 · READINGS: 10.1, and 11.2
    Reading assignment
  • LEC #: 10 · READINGS: 11.2
    Reading assignment
  • LEC #: 11 · READINGS: 9.2
    Reading assignment
  • LEC #: 12 · READINGS: 13.1
    Reading assignment
  • LEC #: 13 · READINGS: 15.1, and 15.2
    Reading assignment
  • LEC #: 14 · READINGS: 16.1, and 16.2
    Reading assignment
  • LEC #: 15 · READINGS: Review for midterm
    Reading assignment
  • LEC #: 16 · READINGS: 16.3
    Reading assignment
  • LEC #: 17 · READINGS: 18.1, and 16.4
    Reading assignment
  • LEC #: 18 · READINGS: 18.2
    Reading assignment
  • LEC #: 19 · READINGS: 18.2, and 17.2
    Reading assignment
  • LEC #: 20 · READINGS: 17.2, and 17.3
    Reading assignment
  • LEC #: 21 · READINGS: 17.2, and 17.3
    Reading assignment
  • LEC #: 22 · READINGS: 17.3
    Reading assignment
  • LEC #: 23 · READINGS: Review for midterm
    Reading assignment
  • LEC #: 24 · READINGS: 17.3
    Reading assignment

Prerequisites & course information

Prereq: Calculus II (GIR) U (Spring) 3-0-9 units

Sources