Pries, Spring 2016, Abstract Algebra II: Syllabus
Week
1
2
3
4
5
6
7
8
Starts
1/20
1/25
2/1
2/8
2/15
2/22
2/29
3/7
9
10
11
12
13
14
15
3/21
3/28
4/4
4/11
4/18
4/25
5/2
Topics
13.1, 13.2, 13.6 Introduction to field extensions
13.4, 13.5, 14.1 Galois extensions (splitting fields, separable), guestMW,
14.2, 14.5 Fundamental theorem of Galois theory
14.4, 14.7 Insolvability of the Quintic
14.9 Galois theory of function fields, Fquiz
10.1, 11.1, 11.2 Modules, vector spaces and linear transformations
10.2, 10.3 Module homomorphisms and quotients
10.4 tensor products of modules
spring break
10.5 projective, injective, flat modules
11.5 Algebras, Fquiz
12.1 Structure of modules over PID
12.2, 12.3 Canonical forms
11.3 dual vector spaces, characters
18.1, 18.2, 18.3 Introduction to representation theory
Open problems in algebra, Wguest
Important Dates:
Quiz 1: Friday 2/19
Quiz 2: Friday 4/1
Final: Wednesday 5/11, 4:10-6:10 pm.
Homework is from Dummit and Foote:
Homework 1: due Monday 1/25
S13.2: #3,4,5,7,10,13,14,21.
Homework 2: due Monday 2/1
S13.4: #1,4; S13.5: #3,4,5; S13.6: #5,8