| Lectures |
Sections in Text |
Brief Description |
| Week 1 |
10.1 - 10.3, 10.5 |
Modules, Isomorphism Theorems,
products and coproducts, Hom as a functor [exactness] |
| Week 2 |
10.3, 10.5 |
Direct sums, products and commutation with Hom, splitting SES, free, projective modules |
| Week 3 |
10.3, 11.1 - 11.3 (and class notes) |
Projective modules, consideration of rank of free modules, linear algebra over commutative rings, dual spaces |
| Week 4 |
10.4, 10.5 (and class notes) |
Tensor products: associativity, extending the base, direct sums, free modules, flat modules, multilinear products |
| Week 5 |
11.5, 12.1 (and class notes) |
Tensor and Exterior algebras, determinants, Finitely generated modules over PIDs, invariant factor theorem |
| Week 6 |
12.1 - 12.2 |
Elementary divisors theorem and variations, Canonical Forms |
| Week 7 |
12.2, 12.3, 18.1 |
Canonical Forms, Representations of finite groups |
| Week 8 |
18.1, 18.2 |
Semisimplicity, Wedderburn theorem, Representations of finite groups, Schur relations, Orthogonality relations, characters characterize irreducible representations |
| Week 9-10 |
18.3, 19.1, 19.3, 19.2 |
Decomposing the regular representation, character tables, one-dimensional representations, induced representations, representations associated to (semi)direct products, applications |
