Math 380C: Prelim Algebra
MWF 2-3 in RLM 9.166
Prof. David Helm
RLM 9.118
dhelm@math.utexas.edu
Office Hours: Mon 12-2
Course description
This is the first half of a two semester sequence designed primarily to provide the algebraic background necessary
for the algebra prelim. The syllabus for the algebra prelim can be found
online; we will
aim to cover the sections on Groups and Rings and Modules, along with some supplemental topics if time permits.
Textbook
Dummit and Foote, Abstract Algebra, Third Edition.
Grading
Grades will be based on weekly problem sets (50%), a take-home midterm (20%), and the three-hour final exam (30%).
The midterm will be handed out on Wednesday, Oct. 10 and due the following Wednesday.
Problem Sets
Problem sets will be posted here on a weekly basis.
Problem Set 1 (due Wed 9-5): Dummit and Foote 1.3 #14,15,17; 1.4 #10,11; 1.6 #13,16,18,19; 1.7 #4,8,16-19,21
Problem Set 2 (due Wed 9-12): Dummit and Foote 2.1 #10,13,14; 2.2 #6,7,10,14; 2.3#5,9; 3.1 #1,2,9,12,14
Problem Set 3 (due Wed 9-19): Dummit and Foote 3.1 #36,38,39; 3.2 #4,9; 3.3 #4,9; 3.5 #10,15,17
Problem Set 4 (due Wed 9-26): Dummit and Foote 3.4 #6, 4.1 #4,7,8,10; 4.2 #2,6,10,11,12,14; 4.3 #2,8,10,18,22
Problem Set 5 (due Wed 10-3): Dummit and Foote 4.4 #3,5,7,8bc,13,18; 4.5 #4,5,10,11,13,19,28,30,33,39,40
Problem Set 6 (due Wed 10-10): Dummit and Foote 4.6 #3; 5.4 #7,9,13,15; 5.5 #6,10; 6.3 #5,6
Take-home Midterm due Wed 10-17
Problem Set 7 (due Wed 10-24): Dummit and Foote 7.1 #23,24,26,27; 7.2 #3,5; 7.3 #22,29,33; 7.4 #30,32,33,34; 7.6 #1
Problem Set 8 (due Wed 10-31): Dummit and Foote 8.1 #3,4,9,10; 8.2 #3,5; 8.3 #8; 9.2 #1,2,3,4,7
Problem Set 9 (due Wed 11-7): Dummit and Foote 9.3 #1-4; 9.4 #2,3,8,10,12; 9.5 #4,5,6
Problem Set 10 (due Wed 11-14): Dummit and Foote 10.1 #2,4,8,9,18,19; 10.2 #6,8,13; 10.3 #2,4,5,9,11,12,15
no set due Wed 11-21
Problem Set 11 (due Wed 11-28): Dummit and Foote 10.4 #3-5,7-9,16,21,24,26,27; 10.5 #2,6,8,12,15,16
Problem Set 12 (due Fri 12-7): Dummit and Foote 12.1 #2,6,9,13,22; 12.2 #3,4,7,8,14,16; 12.3 #9,17,18,20,24,32
Syllabus
-
Groups
- Definitions and Examples
- Homomorphisms
- Subgroups and Quotient Groups
- Group Actions
- The Sylow Theorems
-
Ring Theory
- Ideals and Homomorphisms
- Factorization in rings
- Polynomial rings
- Semisimple Algebras
-
Module Theory
- Basic definitions and examples
- Module homomorphisms
- Tensor products
- Modules over PIDs
- Canonical Forms
-
Possible Supplemental Topics
- Category Theory
- Homological Algebra
- Basic Commutative Algebra