General Information | Syllabus | HW Assignments |
The following is a partial 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 | 3.5-3.6 | Vector spaces and duality |
Week 2 | 1.1 - 1.3 | Finish duality, Intro to groups, direct products, homomorphisms, cosets and Lagrange's theorem, standard isomorphism theorems, correspondence theorem |
Week 3 | 1.3 - 1.4 | cyclic groups, solvable groups, Hom(Z/nZ,G) |
Week 4 | 1.3, 1.5 | Jordan-Holder, group actions |
Week 5 | 1.5, 1.6, class notes | Sylow theorems, simplicity of An, semidirect products |
Week 6 | 1.7, 1.8 | Direct sums, free abelian groups, finitely generated abelian groups |
Week 7 | 2.1, 2.2, 2.4 | Intro to rings, homomorphisms, characteristic, integral domains, ideals, Commutative rings, Chinese Remainder Theorem |
Week 8 | 2.4, 2.3, 3.1 | Localization of rings, (Polynomial and group rings, localization of modules -- deferred to end) |
Week 9 | 2.5 | UFDs, PIDs; Thanksgiving break |
Week 10 | 4.1, 4.2, 4.3, 4.4 | Euclidean domains, Polynomial Rings, Gauss' Lemma, Irreducibility conditions, Hilbert Basis Theorem |
Time permitting | 1.11, 1.12 | Category theory, products, coproducts, functors and free groups (summary) |
Thomas R. Shemanske
Last updated June 25, 2009 14:49:06 EDT