|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