General Information | Syllabus | HW Assignments |
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