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 course discusses the basic elementary facts about the integers, groups, rings, integral domains, and fields. It is recommended strongly for all students planning to go to graduate school in mathemetics. Credit will only be given for one of Math 402 and 403.

Prerequisites

C- or better in (MATH 240, MATH 241, and MATH 310) or (MATH 340, MATH 341, and MATH310)

Topics

Groups

Definition and examples
Subgroups
Normal subgroups and quotient groups
Homomorphisms
Isomorphism theorems
Cyclic groups
Permutation groups, Cayley's Theorem

Rings

Definition and examples
Polynomial rings
Ideals and quotient rings
Integral domains
Euclidean domains, unique factorization
Prime ideals, maximal ideals

Fields

Quotient fields
Extensions
Algebraic extensions
Impossibility of trisection of angle,