In the large we shall cover a number of topics if groups, rings, and modules, and I hope to have you provide supplementary lectures in x-hour covering some basic material on linear representations of finite groups and topological groups.

The following is a partial syllabus for the course. This page will be updated weekly.
The Homework Assignments page will always be accurate.

Lectures	Sections in Text	Brief Description
9/22	1.1 - 1.2	Introduction to groups and homomorphisms
9/24	1.2, 1.4	direct products; cyclic groups
9/27	1.4	Subgroups of and homomorphisms from cyclic groups
9/29	1.3	Normal subgroups, isomorphism theorems
9/30 (x-hour)	Serre [Brown/Keum]	Representations, permutation representation, regular representation, examples
10/1	1.3	Solvable, simple groups; refinements of towers
10/4	1.3	Feit-Thompson, Jordan-Holder
10/6	1.5	Group Actions
10/7 (x-hour)	Serre [Caufield/Ghiorse]	Subrepresentations, irreducible representations
10/8	1.5	Group Actions
10/11	1.5	The symmetric group, simplicity of An, Cauchy's Theorem
10/13	1.6	p-groups, Sylow Theorems
10/15	1.6	Applications of Sylow, semidirect products
10/18	1.6, 1.7	semidirect products, split extensions, direct sums
10/20	1.7	free abelian groups
10/21 (x-hour)	Serre [Corduan/Genovese]	Characters of representations
10/22	1.8	finitely-generated abelian groups
10/25	1.11	Category theory, products, coproducts
10/27	1.11, 1.12	functors and free groups (summary)
10/28 (x-hour)	Serre [Brill/Brooks]	Characters of representations
10/29	2.1	Intro to rings, homomorphisms, characteristic, integral domains, ideals
11/1	2.1	Maximal and prime ideals, Zorn's lemma
11/3	2.2, 2.4	Commutative rings, Chinese Remainder Theorem, Localization
11/4 (x-hour)	Serre [Mathews/Ordonez]	Representations of abelian groups and subgroups, examples (cyclic and dihedral groups)
11/5	2.4	Localization
11/8	2.3	Polynomial rings and group rings
11/10	3.1	Modules
11/11 (x-hour)	Serre [Huang/Tiruviluamala]	Induced Representations
11/12	3.1	Modules and localization
11/15	2.5	UFDs, PIDs, Euclidean domains
11/17	4.1	Polynomial rings and division algorithms
11/11 (x-hour)	Serre [Goehle/Mahoney]	Topological groups (an introduction)
11/19	4.1, 4.2	Polynomial rings over UFDs
11/22	4.3, 4.4	Irreducibility conditions, Hilbert Basis Theorem
11/24		Thanksgiving break: 11/24 - 11/28
11/26		Thanksgiving break: 11/24 - 11/28
11/29		Intro to algebraic varieties
12/1		Intro to algebraic varieties

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