Algebra I Preps
May-05-10
1:55 PM
Selick's 2007 website is at [link] (and in my folder). See also ~/eprints/Dummit (or symlink from classes/1100-AlgebraI).
Course description, as in graduate handbook:
MAT 1100HF, ALGEBRA I, S. Arkhipov
Topics:
Basic notions of linear algebra: brief recollection. The language of Hom spaces and the corresponding canonical isomorphisms. Tensor product of vector spaces. 
Group Theory: Isomorphism theorems, group actions, Jordan-Hölder theorem, Sylow theorems, direct and semidirect products, finitely generated abelian groups, simple groups, symmetric groups, linear groups, nilpotent and solvable groups, generators and relations.
Ring Theory: Rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains.
Modules: Modules and algebras over a ring, tensor products, modules over a principal ideal domain
Textbooks:
Dummit and Foote: Abstract Algebra, 2nd Edition
Lang: Algebra, 3rd Edition.
Other References:
Jacobson: Basic Algebra, Volumes I and II.
Cohn: Basic Algebra
M. Artin: Algebra.
MAT 1101HS, ALGEBRA II, S. Arkhipov
Topics:
Fields: Algebraic and transcendental extensions, normal and separable extensions, fundamental theorem of Galois theory, solution of equations by radicals.
Commutative Rings: Noetherian rings, Hilbert basis theorem, invariant theory, Hilbert Nullstellensatz, primary decomposition, affine algebraic varieties. structure of semisimple algebras, application to representation theory of finite groups.
Textbooks:
Dummit and Foote: Abstract Algebra, 2nd Edition
Lang: Algebra, 3rd Edition.
Other References:
Jacobson: Basic Algebra, Volumes I and II.
Cohn: Basic Algebra
M. Artin: Algebra.
Pasted from <[link]> 
Course timetable: [link]