# 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
**temporary**office hours in**SMUD 401**(to be revised in the fourth week of classes) are:- Tuesday 11:00-12:30
- Wednesday 9:00-9:50
- Thursday 2:30-3:30

### 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)

### 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. More details will be announced later.