Math 111
Last updated June 25, 2009 14:49:13 EDT

General Information Syllabus HW Assignments


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

Lectures Sections in Text Brief Description
Week 1 Chapter 3.1 - 3.2 Modules, Isomorphism Theorems, Exactness properties of Hom as functors
Week 2 Chapter 3.3 - 3.5 Hom and direct sums/products, free and projective modules, vector spaces, rank of free modules over commutative rings
Week 3 class notes,Chapter 3.6, 16.1 Linear algebra over commutative rings, Dual spaces, tensor products
Week 4 class notes, Chapter 16.1, 16.2, 16.3, 16.4 Tensor products: associativity, extending the base, direct sums, free modules, flat modules, multilinear products
Week 5 Chapter 3.7 Finitely generated modules over PIDs, invariant factor theorem
Week 6 Chapter 3.7, 14.2 Elementary divisors theorem and variations, Canonical Forms
Week 7 Chapter 14.2, 14.3 Canonical Forms, Representations of finite groups
Week 8 Chapter 17.2 - 17.4, 18.2 (class notes) Semisimplicity, Wedderburn theorem, Representations of finite groups, Schur relations
Week 9 Chapter 18.2- 18.5 (class notes) Orthogonality relations, characters characterize irreducible representations, decomposing the regular representation, character tables, representations associated to (semi)direct products, applications

Thomas R. Shemanske
Last updated June 25, 2009 14:49:13 EDT