| dc.contributor.author |
Artin, Michael |
|
| dc.coverage.temporal |
Spring 2003 |
|
| dc.date.accessioned |
2009-06-19T12:10:15Z |
|
| dc.date.available |
2009-06-19T12:10:15Z |
|
| dc.date.issued |
2003-06 |
|
| dc.identifier |
18.702-Spring2003 |
|
| dc.identifier.other |
18.702 |
|
| dc.identifier.other |
IMSCP-MD5-10111c7712e1ce4a5fd5521721bd110a |
|
| dc.identifier.uri |
http://hdl.handle.net/1721.1/45579 |
|
| dc.description.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. |
en |
| dc.description.provenance |
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Previous issue date: 2003-06 |
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| dc.language.iso |
en-US |
|
| dc.rights |
This site (c) Massachusetts Institute of Technology 2003. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license"). The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. |
en |
| dc.subject |
Sylow theorems |
en |
| dc.subject |
Group Representations |
en |
| dc.subject |
definitions |
en |
| dc.subject |
unitary representations |
en |
| dc.subject |
characters |
en |
| dc.subject |
Schur's Lemma |
en |
| dc.subject |
Rings: Basic Definitions |
en |
| dc.subject |
homomorphisms |
en |
| dc.subject |
fractions |
en |
| dc.subject |
Factorization |
en |
| dc.subject |
unique factorization |
en |
| dc.subject |
Gauss' Lemma |
en |
| dc.subject |
explicit factorization |
en |
| dc.subject |
maximal ideals |
en |
| dc.subject |
Quadratic Imaginary Integers |
en |
| dc.subject |
Gauss Primes |
en |
| dc.subject |
quadratic integers |
en |
| dc.subject |
ideal factorization |
en |
| dc.subject |
ideal classes |
en |
| dc.subject |
Linear Algebra over a Ring |
en |
| dc.subject |
free modules |
en |
| dc.subject |
integer matrices |
en |
| dc.subject |
generators and relations |
en |
| dc.subject |
structure of abelian groups |
en |
| dc.subject |
Rings: Abstract Constructions |
en |
| dc.subject |
relations in a ring |
en |
| dc.subject |
adjoining elements |
en |
| dc.subject |
Fields: Field Extensions |
en |
| dc.subject |
algebraic elements |
en |
| dc.subject |
degree of field extension |
en |
| dc.subject |
ruler and compass |
en |
| dc.subject |
symbolic adjunction |
en |
| dc.subject |
finite fields |
en |
| dc.subject |
Fields: Galois Theory |
en |
| dc.subject |
the main theorem |
en |
| dc.subject |
cubic equations |
en |
| dc.subject |
symmetric functions |
en |
| dc.subject |
primitive elements |
en |
| dc.subject |
quartic equations |
en |
| dc.subject |
quintic equations |
en |
| dc.title |
18.702 Algebra II, Spring 2003 |
en |
| dc.title.alternative |
Algebra II |
en |
| dc.audience.educationlevel |
Undergraduate |
|
| dc.subject.cip |
270102 |
en |
| dc.subject.cip |
Algebra and Number Theory |
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