Abstract Algebra Course Info

Course information of Abstract Algbra

Instructor

JungMin Song

Textbook

Abstract Algebra 3rd edition I. N. Herstein

Evaluation

• Mid-term 40%
• Final-term 40%
• Homework 20%

Info

• Preliminary & Review topics
  • Set theory
  • Mappings
  • The Set of Numbers - Integers
  • Mathematical Induction
  • Complex Numbers
• Groups
  • Subgroups, Normal Subgroups, Factor Groups
  • Lagrange’s Theorem
  • Homomorphisms and the Homomorphism Theory
  • Cauchy’s Theorem
  • Direct Products
  • Finite Abelian Groups
  • Conjugacy and Sylow’s Theorem
• The Symmetry Group
  • Cycle Decomposition
  • Odd and Even Permutations
• Ring Theory
  • Ideals, Homomorphisms and Quotient Rings
  • Maximal Ideals
  • Polynomial Rings; Polynomials over the Rationals
  • Field of Quotients of an Integral domain
• Fields
  • Basic Theory of Field Extensions; Vector Spaces
  • Algebraic Extensions, Finite Extensions
  • Splitting Fields and Algebraic Closures
  • Cyclotomic Polynomials and Extensions
  • Liouville’s Criterion