Math 380D: Algebra

Prof. David Helm
RLM 9.118
dhelm@math.utexas.edu
Office Hours: Wed 2-4
TA: David Paige

Problem Sets

Problem Set 1 (due Fri 1-30): Dummit and Foote 8.1 #3,4; 8.2 #3,4,5; 9.2 #1
Problem Set 2 (due Fri 2-6): Dummit and Foote 9.2 #2,3; 9.4 #2,10,11,13,14
Problem Set 3 (due Fri 2-13)
Problem Set 4 (due Fri 2-20): Dummit and Foote 10.4 #4,5,6,7,19; 12.1 #2,4,11
Problem Set 5 (due Fri 2-27)
Problem Set 6 (due Fri 3-6)
Problem Set 7 (due Fri 3-13): Dummit and Foote 13.4 #2; 13.5 #5; 13.6 #9,11,14-17
Problem Set 8 (due Fri 3-27): Dummit and Foote 14.1 #6,7,9; 14.2 #12,13,17,18,29
Problem Set 9 (due Fri 4-10): Dummit and Foote 14.6 #3,11,12,14,15,25 14.7 #7,20
Problem Set 10 (due Fri 4-17): Dummit and Foote 14.6 #28,29,43,47,48,49 14.9 #7,17
Problem Set 11 (due Mon 5-4)

Midterm

Midterm (due Fri 4-3)

Final Exam

Final Exam (due Sun 5-17)

Course format and syllabus

Grades will be based on weekly problem sets, a take-home midterm, and the three-hour final exam. The course will cover (roughly) the following material:

  1. Factorization in Rings

  2. Modules over PIDs

  3. Field Theory

  4. Algebraic Geometry (provisional)


The first three sections of the course are basically drawn from the syllabus of the prelim exam, and represent the material we MUST get through. For that part I will follow Dummit and Foote fairly closely. For the remainder of the course I thought I'd talk some about algebraic geometry, but I'm open to suggestions if there are other things people want to learn. I'm not a huge fan of Dummit and Foote's approach to algebraic geometry, so my perspective on the material will probably be somewhat different from theirs.