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Abstract Algebra: Getting Started

Abstract Algebra

Abstract Algebra

Course Numbers:

Abstract Algebra I: MATH 4350

Abstract Algebra II: MATH 4360

Abstract Algebra I:

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.

Abstract Algebra II:  

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

Course Numbers:

Abstract Algebra I: MATH 4350

Abstract Algebra II: MATH 4360

Abstract Algebra I & II Textbook Information:

Abstract Algebra

Course Numbers:

Abstract Algebra I: MATH 4350

Abstract Algebra II: MATH 4360

Abstract Algebra I:

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

Abstract Algebra II:

  • Define and create examples of groups, rings and fields
  • State and apply theorems to interpret (formulate) rigorous mathematical arguments
  • Apply techniques developed in this course to analyze and understand abstract mathematical constructs
  • Describe the applications of abstract algebra to other mathematical fields
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