MA 362

MA 362 - Abstract Algebra

1. Preliminaries

a) Sets 
b) Methods of proof 
c) Mappings and operations 

2. Groups

a) Subgroups
b) Permutation groups
c) Cyclic groups
d) Direct products
 

3. Modular Arithmetic

a) Equivalence and congruence relations 
b) Construction of Z/nZ 

4. Closer Examination of Groups

a) Elementary properties
b) Cosets and Lagrange's Theorem
c) Isomorphisms
d) The Fundamental Theorem of Finite Abelian Groups
e) Cayley's Theorem
f) Factor groups

Learning Outcome 1: The student will demonstrate an understanding of basic group theory.

Learning Outcome 2: The student will demonstrate an understanding of Lagrange's Theorem and Noether's Isomorphism Theorems for groups.

Learning Outcome 3: The student will demonstrate an understanding of basic facts on rings and fields.