Math 101

Last updated August 02, 2011 13:48:37 EDT

## Syllabus

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.

Lectures Sections in Text Brief Description
Week 1 Chapter 0, 1.1-1.6, 2.1, 2.2, 2.4, 3.2 Groups, examples, homomorphisms, cosets, Lagrange
Week 2 Chapter 2.3, 3.1, 3.3, 3.4 Cyclic groups, standard isomorphism theorems, solvable groups, composition series
Week 3 Chapter 3.4, 4.1, 4.2, 4.3 Jordan-Hölder theorem, Group actions, G-set structure theorem, class equation, symmetric group
Week 4 Chapter 4.3, 4.5, 4.6, 5.1, 5.4, 5.5 Conjugacy classes in S_n, Sylow theorems, Semidirect Products
Week 5 Chapter 5.5, 5.2, class notes Semidirect Products, split extensions, direct sums, free abelian groups, finitely-generated abelian groups
Week 6 Appendix II, Chapter 6.3, 7.1-7.4 Basic category theory (products, coproducts, functors). free groups, introduction to rings
Week 7 7.4, 7.5, 7.6, 15.4 Prime and maximal ideals, localization, Chinese Remainder Theorem
Week 8 9.1, 9.6, 10.1, 15.4, 8.3 polynomial rings, group rings, modules, localization of modules, irreducibles and primes in rings
Week 9 8.1, 8.2, 8.3, 9.1, 9.2, 9.3 UFDs, PIDs, Euclidean rings, polynomial rings
Week 10 9.3, 9.4, 9.5, 9.6(HBT) Gauss' Lemma and applications, Irreducibility Criteria, Hilbert Basis Theorem, algebraic geometry in 30 minutes

T. R. Shemanske
Last updated August 02, 2011 13:48:37 EDT