This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

This is the less theoretical of the two upper level undergraduate abstract algebra courses. (Student's planning graduate work in mathematics should take the other course in abstract algebra, MATH 403.) The course covers the basics of groups, rings, integral domains and fields. There will be a detailed study of several groups, and a study of the properties of integers and polynomials. Emphasis is on the origin of the mathematical ideas studied and the logical structure of the subject. (This course is not open to mathematics graduate students. Credit will only be given for one of Math 402 and 403.) The last item in the list of topics could be replaced by other topics in algebra, for example, coding theory or crystallographic groups.

Prerequisites

MATH 240 or MATH 461 or MATH 341

Topics

Preliminaries

Induction
Equivalence relations
Functions

Groups

Groups and symmetries
Finite groups
Cyclic groups
Subgroups
Permutation groups
Cosets and Lagrange's Theorem
External direct product
Normal subgroups and factor groups
Homomorphisms
The structure of finite abelian groups

Rings

Introduction to rings
Integral domains
Ideals and factor rings
Ring homomorphisms

Polynomial Rings

Division Algorithm
Unique Factorization of Polynomials
Divisibility in Integral Domains

Fields

Extension Fields
Algebraic Extensions
Finite Fields

Geometric Constructions

Constructible numbers
Trisecting an angle
Duplicating a cube
Squaring a circle