# MATH 361 Syllabus

### Introduction to Abstract Algebra

Revised: February 2015

## Course Description

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.

## Text

I.N. Herstein, 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

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

## Course Outline

• Chapter 1: Things Familiar and Less Familiar (Set Theorey, Mappings, The Integers, Mathematical Induction)
• 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, Polynomial Rings)
• Chapter 5: Fields (Examples of Fields)