General Information | Syllabus | HW Assignments |
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