18.702 Algebra II, Spring 2008
Name
18-702-spring-2008/contents/index.htm
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16.06 KB
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Checksum (MD5)
ce448d6fdfb523984113856aba9d0dff
Author(s)
Artin, Michael
Alternative Title
Algebra II
Date Issued
June 2008
Abstract
This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
Subjects
Sylow theorems
Group Representations
definitions
unitary representations
characters
Schur's Lemma
Rings: Basic Definitions
homomorphisms
fractions
Factorization
unique factorization
Gauss' Lemma
explicit factorization
maximal ideals
Quadratic Imaginary Integers
Gauss Primes
quadratic integers
ideal factorization
ideal classes
Linear Algebra over a Ring
free modules
integer matrices
generators and relations
structure of abelian groups
Rings: Abstract Constructions
relations in a ring
adjoining elements
Fields: Field Extensions
algebraic elements
degree of field extension
ruler and compass
symbolic adjunction
finite fields
Fields: Galois Theory
the main theorem
cubic equations
symmetric functions
primitive elements
quartic equations
quintic equations
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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