# 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 10/23~~Friday 10/25 at 10pm) - Problem Set 7 (due Friday 11/1 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)