1. MATH 421 ABSTRACT ALGEBRA I

Course Syllabus

  1. Basic Properties of Integers
    1. Mathematical Induction
    2. Divisors, Primes and the Division Algorithm
    3. Common Divisors and Factorization
    4. Euclidean Algorithm
    5. Congruences and the Integers Modulo n.
  2. Basic Properties of Groups
    1. Definitions and Examples
    2. Group Tables
    3. Subgroups
    4. Cyclic Groups
    5. Permutation Groups
    6. Dihedral Groups
    7. Order of an Element
  3. Cosets and Quotient Groups
    1. Cosets
    2. LaGrange's Theorem
    3. Normal Subgroups
    4. Quotient Groups
  4. Group Homomorphisms
    1. Definition and Basic Properties
    2. Isomorphism
    3. Isomorphism Theorems
    4. Classification of Cyclic Groups
  5. Introduction to Rings and Fields
    1. Definitions: Ring, Integral Domain, Field
    2. Examples and Basic Properties
    3. Homomorphisms and Isomorphisms
    4. Ideals and Factor Rings
    5. Polynomial Rings
    6. Quotient Fields

Prerequisites: MATH 220 and MATH 240

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