18.702 Algebra II, Spring 2003

18.702 Algebra II, Spring 2003

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More extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs helpful. First term: group theory, geometry, and linear algebra. Second term: group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field exte...

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Bibliographic Details
Main Author: Artin, Michael
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Learning Object
Language:en-US
Published: 2003
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
Online Access:http://hdl.handle.net/1721.1/45579

Internet

http://hdl.handle.net/1721.1/45579

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