Galois Theory

The course is a continuation of TMA4150 (and having taken MA3201 Rings and modules will be an advantage). Basic properties of field extensions will be discussed, and the interplay between group theory and field theory, formulated via Galois theory. Several applications will be discussed, in particular the insolvability of a general equation of degree five.

1. Knowledge. The student masters various types of field extensions, for example normal extensions, and has a good understanding of the interplay between group theory and field theory. In particular, the student understands how Galois theory is applied to the question of solvability of the quintic.

2. Skills. The student is able to describe the Galois group of a given field extension, and to find correspondences between subgroups and intermediate fields.

Lectures. Students may answer either in Norwegian or English on assessments.

The course will be given in spring in years of odd numbers.