MAT5173
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Introduction to groups and rings.
Sample textbook
[1] Thomas W. Judson and Robert A. Beezer, Abstract Algebra: Theory and Applications, 2008. Freely available online.
Catalog entry
Prerequisite: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
Contents (1) Groups: Cyclic groups, permutation groups and Cayley's theorem, group homomorphisms, normal subroups, quotient groups and Lagrange's theore, the theorems of Euler and Fermat. (2) Rings: Ring homomorphisms, integral domains and fields, maximal and prime ideals. (3) Rings of polynomials: The Division Algorithm and irreducible polynomials.
Topics List
Week  Topic  Sections from the JudsonBeezer book  Subtopics  Prerequisite 

12  Groups  3 

MAT1313, CS2233/2231, or instructor consent. 
45  Cyclic groups  4 
 
56  Permutation groups  5 
 
78  Cosets and Lagrange's Theorem  10 
 
9  Homomorphisms  11  The Isomorphism Theorem  
1011  Rings  16 
 
12end  Rings of Polynomials  17 
