MATH 362 Algebraic Structures (3)

Catalog Description:


Groups, rings, fields, homomorphisms, and quotient structures. (Offered fall semester only.)

Prerequisites:

 

MATH 261 Linear Algebra

  1. Abstract vector spaces.
  2. Function concept including real-valued function, linear transformations of vector spaces, determinant as a mapping, etc.
  3. Polynomials and rational root test.

Required Course Materials:


John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, Pearson, 2003 (ISBN: 9780201763904)

Course Coordinator:


Angela C. Hare, Ph.D., Professor of Mathematics

Course Audience:


Juniors and seniors majoring in Mathematics

Course Objectives:

  1. To gain an introduction to groups and rings.
  2. Mastery of computational details in algebraic structures is foundational to the work.
  3. Theoretical concepts will be central to cover the major theorems and their proofs.
  4. Deductive proof is the distinctive reasoning and writing form of the mathematical discipline.
  5. Emphasis on deductive proof and problem solving with complete and clear written presentation of solutions.

Topics:

  1. Binary operations and isomorphic structures
  2. Definitions of a group, examples
  3. Subgroups, cyclic groups
  4. Permutation groups, orbits, cycles and alternating groups
  5. Cosets, Lagrange’s theorem
  6. Direct products of groups
  7. Homomorphisms, factor groups
  8. Rings and fields, definitions and examples
  9. Integral Domains
  10. Fermat’s and Euler’s theorems
  11. Quotient fields
  12. Polynomial rings
  13. Homomorphisms, factor rings, ideals

 
Revised: September 2011

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