MATH 404 (Field Theory)
| 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 |
| TEXT |
Text(s)
typically used in this course. |
|
