Login

18.702 Algebra II, Spring 2003

Show full item record




Title: 18.702 Algebra II, Spring 2003
Author: Artin, Michael
Issue Date: 2003-06
Abstract: 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 extensions, Galois theory. From the course home page: Course Description The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.
URI: http://hdl.handle.net/1721.1/45579
Other Identifiers: 18.702-Spring2003
Other Identifiers: 18.702
IMSCP-MD5-10111c7712e1ce4a5fd5521721bd110a
Keywords: 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, 270102, Algebra and Number Theory

Files in this item

Files Size Format
18-702Spring200 ... g2003/CourseHome/index.htm 13.63Kb text/html

The following license files are associated with this item:

This item appears in the following Collection(s)

Show full item record

Search DSpace@MIT


Advanced Search

Browse

My Account

Links