18.702 Algebra II, Spring 2008
MetadataShow full item record
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.
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