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