Math 101
Topics in Algebra
Last updated May 31, 2008 12:23:58 EDT

### Syllabus

As this is the first time I am teaching out of Lang's book, and a significant amount of additional material needs to be supplemented, I shall be unfolding the ``daily syllabus'' week-by-week.

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