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

Algebraic and transcendental elements, Galois theory, constructions with straight-edge and compass, solutions of equations of low degrees, insolubility of the Quintic, Sylow theorems, fundamental theorem of finite Abelian groups.

Prerequisites

Math 403

Topics

Elementary facts about fields

Characteristic
Integral domains
Maximal ideals
Field extensions
Transcendental and algebraic extensions
Liouville numbers
Minimal polynomials

Review of vector spaces

Linear independence
Basis
Dimension
Degree of a field extensions

Straight-Edge and compass constructions

Impossibility constructions
Cyclotomic polynomials
Constructibility of regular n-gons

Splitting fields

Normal extensions
Separable extensions
Simple extensions
Normal closures

Galois extensions

Automorphisms
Fixed fields
Fundamental theorem
Cyclic extensions

Solvable groups

Normal series
Extensions and subgroups
Insolvability of symmetric groups
Solution by radicals