Lectures	Sections in Text	Brief Description
9/24	1.1	Introduction to groups
9/26	1.3	Cyclic groups
9/29	1.2	Homomorphisms, Dihedral groups
10/1	1.4	Quaternion groups, cosets, Lagrange and related topics
10/3		No class today
10/6	1.5	Normality, quotient groups, isomorphism theorems
10/8	1.5, 2.4	Isomorphism Theorems, Group Actions
10/10	2.4	Group Actions
10/13	2.4, 1.6	Group Actions, Permutation groups
10/15	1.6, 2.5	Permutation Groups, Cauchy's Theorem
10/17	2.5	Sylow Theorems
10/20	2.5, 1.7	Applications of Sylow theorems, category theory
10/22	1.7, 1.8	Direct products, coproducts
10/24	class notes	semidirect products
10/27	class notes, 2.2	Semidirect products, split extensions, free groups, fundamental theorem for finitely generated abelian groups
10/29	2.2, 2.7	FTFGAB (continued), nilpotent groups, normal series
10/31	2.7, 2.8	solvable groups, composition series, Jordan Holder, group extensions and the classification problem for finte groups
11/3	3.1	Intro to rings, homomorphisms, characteristic, integral domains, ideals
11/5	3.1, 3.2	Operations on ideals, isomorphism theorems, prime and maximal ideals
11/7	3.2	Zorn's lemma, maximal ideals exist, characterization of prime and maximal ideals via quotients, examples
11/10	3.2, 3.4	Chinese Remainder Theorem, localization
11/12	3.4, 3.3	Localization, Factorization in commutative rings
11/14	4.1	Modules, torsion
11/17	4.1	Localization of modules
11/19	8.1, 8.4, 3.3	Noetherian integral domains, UFDs, PIDs
11/21	3.6	Division algorithms over commutative rings
11/24	3.6	Irreducibility criteria in polynomial rings
11/26		Thanksgiving break: 11/26 - 11/30
12/1		Introduction to Algebraic varieties
12/3		Introduction to Algebraic varieties

Thomas R. Shemanske
Last updated May 31, 2008 12:23:58 EDT