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MATH 4350 & 4360 Abstract Algebra: Getting Started

MATH 4350, MATH 4360

Abstract Algebra

Abstract Algebra
MATH 4350, 4360
Fall 2023

This course is an introduction to the concepts of groups and rings from modern abstract algebra. Group theoretic topics include: modular arithmetic, groups, cyclic groups, permutation groups, normal groups, factor groups, group homomorphism and isomorphism, cosets, Lagrane's theorem, and external (internal) direct products. Ring theoretic topics include: rings, integral domain, ideals, factor rings, ring homomorphism and isomorphism, factorizations, divisibility, and fields.
This course, which is a continuation of Math 4350, further develops the theory of groups and rings and introduces the concept of field theory. Group theoretic topics include: group theory, Sylow's theorem, symmetric groups, Burnsie's theorem. Ring theoretic topics include: ring theory, polynomial rings, factorizations, and divisibility. Field theoretic topics include: extension fields, algebraic extension, finite fields, and Galois theory.

Abstract Algebra I - MATH 4350

Abstract Algebra II - MATH 4360

  1. Define and create examples of groups and rings.
  2. State and apply theorems to interpret (formulate) rigorous mathematical arguments.
  3. Apply techniques developed in this course to analyze and understand abstract mathematical constructs.
  4. Describe the applications of abstract algebra to the arts and nature, computer science, physics, chemistry, and engineering.
  1. Define and create examples of groups, rings and fields.
  2. State and apply theorems to interpret (formulate) rigorous mathematical arguments.
  3. Apply techniques developed in this course to analyze and understand abstract mathematical constructs.
  4. Describe the applications of abstract algebra to other mathematical fields.

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