MMA310 Galois Theory
Course PM
This page contains the program of the course lectures. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Lectures
| Day | Sections | Content |
|---|---|---|
| 5/11--22/11 | 1-10, 12 | Algebraic equations, field extension, irreducibility of polynomials, splitting fields, automorphism groups of fields, normal extensions, separable polynomials/extension, Galois extensions, cyclotomic fields, solvable groups |
| 27/11 | 11, 12, 13 | Hilbert's theorem 90, solvability of equations of degrees 3 and 4, fundamental theorem of algebra via Galois theory |
| 28/11 | 14 | Geometric constructions, angle trisection |
| 29/11 | 14 | Constructible polygons |
| 03/12 | 1-10 | Repetition: questions and answers |
| 04/12 | Self-studying/repetition: fundamental theorem of algebra via Galois theory, solvable groups | |
| 06/12 | Self-studying/repetition: solvability of equations of degrees 3 and 4 via Sylow subgroups | |
| 10/12 | Self-studying/repetition: impossibility of angle trisection | |
| 11/12 | Self-studying/repetition: constructible polygons | |
| 13/12 | Summarizing of the course content | |
| 08/01 | 11 | Galois cohomology, non-abelian Galois cohomology |
| 10/01 | Course summary, exam preparation |
Remarks about examination
Update (2020-03-13): In case of online examination the rules may be changed. The information will be updated later.
Written examination consists of three problems, which can give at most 7 points. At least one of these problems is related to one of the following topics:
- Solvability of equations of degrees 3, 4, and 5
- Constructible polygons
- Angle trisection
- Fundamental theorem of algebra via Galois theory
VG: 6+ points. Students with 5 points can get VG by doing an additional oral examination
G: 4 points. Students with 3 points can get G by doing an additional oral examination
Dates for additional oral examinations can be discussed during "tentagranskningen". Tentagranskningen takes place at the end of January, 2020. The exact date will be announced later.
Course summary:
| Date | Details | Due |
|---|---|---|