Math 111
Noncommutative Algebra

Last updated August 02, 2011 13:48:38 EDT

General Information Syllabus HW Assignments


The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

The basic plan is to cover chapters 10-12, 18 and much of 19, as well as assorted embellishments.

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

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T. R. Shemanske
Last updated August 02, 2011 13:48:38 EDT