Introduction to Abstract Algebra
Revised: February 2015
Groups, rings, and fields. Prerequisite: MATH 250. Three semester hours.
Student Learning Objectives
- Know all relevant definitions and correct statements of major theorems;
- Explain the defining structures of quotient groups and rings, rings of polynomials
and field extensions;
- Create examples or counter-examples and apply them appropriately to prove or disprove
statements about algebraic structures;
- Prove statements and solve problems about the structure, size, and nature of groups,
subgroups, factor groups, normal groups, rings, ideals, and field using definitions
and theorems learned in the course;
- Incorporate equivalence relations into group theoretic structures, particularly factor
groups; create factor groups using normal subgroups or the Isomorphism Theorems and
interpret elements of factor groups accurately; and
- Understand permutations and symmetries in a group theoretic context--- particularly
the significance of Cayley's Theorem.
Abstract Algebra, third edition, Wiley 1999
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
- Chapter 1: Things Familiar and Less Familiar (Set Theorey, Mappings, The Integers,
- Chapter 2: Groups (Definition and Examples of Groups, Subgroups, Lagrange's Theorem,
Homomorphisms and Normal Subgroups, Factor
- Groups, The Homomorphism Theorems, Cauchy's Theorem, Direct Products)
- Chapter 3: Symmetric Group (Cycle Decomposition, Odd and even Permutations)
- Chapter 4: Ring Theory (Definitions and Examples, Ideals, Homomorphisms, Maximal Ideals,
- Chapter 5: Fields (Examples of Fields)