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

Prerequisites: 
MATH
261 Linear Algebra
 Abstract vector spaces.
 Function concept including realvalued function, linear transformations of
vector spaces, determinant as a mapping, etc.
 Polynomials and rational root test.

Required Course Materials: 
John B. Fraleigh, A First Course in Abstract Algebra,
7^{th} 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: 
 To gain an introduction to groups and rings.
 Mastery of computational details in algebraic structures is foundational to the work.
 Theoretical concepts will be central to cover the major theorems and their proofs.
 Deductive proof is the distinctive reasoning and writing form of the mathematical
discipline.
 Emphasis on deductive proof and problem solving with complete and clear written presentation of solutions.

Topics: 
 Binary operations and isomorphic structures
 Definitions of a group, examples
 Subgroups, cyclic groups
 Permutation groups, orbits, cycles and alternating groups
 Cosets, Lagrange’s theorem
 Direct products of groups
 Homomorphisms, factor groups
 Rings and fields, definitions and examples
 Integral Domains
 Fermat’s and Euler’s theorems
 Quotient fields
 Polynomial rings
 Homomorphisms, factor rings, ideals

