MAT 314

Syllabus and Homeworks

There will be weekly homeworks, posted on Th. The homeworks will be announced on the course web page.

The syllabus below is tentative and subject to change.

Week	Dates	Notes	Topics	HW	Due date
1	1/28 - 2/1		Rings and modules. Examples: vector spaces, abelian groups, modules over F[x]. Submodules and quotients	no HW
2	2/4 - 2/8		Kernel, image, isomorphism theorem. Generators and relations.	HW1	Th, 2/14
3	2/11 - 2/15	Class on Tu was cancelled.	Structure theorem for finitely generated modules over Z (aka abelian groups).	HW2	Th, 2/21
4	2/18 - 2/22		Structure theorem for finitely generated abelian groups - completion: bringing an integer matrix to a canonical form. Principal ideal domains.	HW3	Th, 2/28
5	2/25 - 3/1		Structure theorem for modules over a PID. Jordan canonical form.	HW4	Th, 3/7
6	3/4 - 3/8		Group representations: basic definitions, irreducible representations, Schur's lemma.	HW5	Th, 3/14
7	3/11 - 3/15		Group representations: complete reducibility, characters	No HW
	3/18 - 3/22	Spring Break
8	3/25 - 3/29		Fields and extensions. Splitting field of a polynomial	HW6	Th, 4/4
9	4/1 - 4/5		Finite extensions; degree. Algebraic extensions.	No HW
10	4/8-4/12		Algebraic extensions continued. Constructions with ruler and compass	HW7	Th, 4/18
11	4/15-4/19		Cyclotomic polynomials; constructions of regular n-gon. Normal extensions.	HW8	Th, 4/25
12	4/22-4/26		Galois group. Main theorem of Galois theory	HW9	Th, 5/2
13	4/29 - 5/3		Examples of Galois group. Symmetric polynomials	HW10	Th, 5/9