Math 410: Galois Theory (Fall 2024)
Galois Theory is the study of symmetry in the solutions to polynomial equations. In its modern formulation, it describes a beatiful correspondence between field extensions and certain symmetry groups. We will develop this theory starting from a basic knowledge of groups, rings, and fields. One of our main goals will be to prove that there is no general version of the quadratic formula for a polynomial of degree five or more. Along the way, we will also show that a circular cake can be divided into 17 (but not 7) equal slices using only a straight-edged knife.
Time and location
- Monday, Wednesday, and Friday, 2:00-2:50am (SMUD 204)
Help hours
- My office hours in SMUD 401 are:
- Tuesday 9:15-10:45
- Wednesday 9:15-10:45
- Friday 10:30-11:30
Handouts and links
Problem Sets
- Homework is submitted via Gradescope; our course code is G386G6.
- Problem Set 1 (due Friday 9/13 at 10pm)
- Problem Set 2 (due Friday 9/20 at 10pm)
- Problem Set 3 (due Wednesday 9/25 at 10pm)
- Problem Set 4 (due Wednesday 10/2 at 10pm)
- Problem Set 5 (due Wednesday 10/9 at 10pm)
- Problem Set 6 (due
Wednesday 10/23Friday 10/25 at 10pm) - Problem Set 7 (due Friday 11/1 at 10pm)
- Problem Set 8 (due Wednesday 11/20 at 10pm)
- Problem Set 9 (due
Wednesday 12/4Friday 12/6 at 10pm) - Problem Set 10 (due Wednesday 12/11 at 10pm)
Exams
There will be a take-home midterm exam, likely in the first week of November, and a take-home final exam due during finals period.
- Midterm exam (due Wednesday 11/13 at 10pm)