Math 422/501

Fields and Galois Theory

Fall  2019      Course Information

Time: MWF 14:00-14:50

Place: Math Annex 1102.

Instructor: Kai Behrend

Office hours:

Wed 3-4, Thu 2-3 in Math 227.

Text Book: We will mostly be following the notes by James Milne, which you can get here: pdf

You might also consult other textbooks on algebra, such as those by Dummit and Foote, Lang, Herstein, or Artin.

Prerequisites: Math 322 or equivalent. You have to have a good working knowledge of group theory, especially quotient groups and group actions.

Course Outline: This is a standard course in Galois Theory, the study of the symmetries of polynomials and their roots.

Not only does Galois theory itself appear in many diverse areas, but the principles of symmetry we cover appear in different guises throughout mathematics. This, or a course like it, is a must for anyone serious about mathematics. Besides, Galois theory is beautiful and fun!

Highlights include Ruler and Compass constructions: the impossibility of doubling the cube or trisecting an angle. Impossibility of solving the quintic by radicals.

Our goal is to cover the first 5 chapters of the text. If time permits, we will cover some of the other subjects covered there.

Exams: There will be one midterm exam and one final exam.

Homework: Homework will be assigned throughout the semester. Please do all homework assignments.

Class Notes: Photographs of blackboards.

Marking: Your mark will be made up as follows:

Homework: 40%
Midterm: 20%
Final: 40%