MATM41 Galois Theory, 7.5 credits, is an alternative-compulsory course at advanced level for a Master of Science degree in Mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the second half of the autumn semester. The language of instruction is English.

Course Content
The course aims to provide a deeper understanding of field extensions, and a connection between the theory of polynomial equations and group theory.

The course covers

Field extensions: splitting fields, normal extensions and separable extensions, field automorphisms, normal closures.
Galois groups: Galois extensions, the Galois Correspondence, the Fundamental Theorem of Galois Theory.
Polynomial equations: solvability by radicals, insolvable quintics, symmetric polynomials, cyclotomic extension.

Teaching
The teaching consists of lectures and some seminars.

Assessment
The examination consists of a written examination (5 credits) followed by an oral examination (2.5 credits) at the end of the course. The oral examination may only be taken by those students who passed the written examination. More information about the examination and grading can be found in the official course description below.

Course Literature (optional)

Stewart: Galois Theory, 3rd ed., Chapman & Hall/CRC Mathematics, London 2003. ISBN: 978-1584883937 (main textbook)
A. Cox: Galois Theory, 2nd ed., John Wiley & Sons, 2012. ISBN: 978-1439854297 (additional recommended reading)
Rotman: Galois Theory, 2nd ed., Springer, 1990. ISBN: 978-0387985411 (additional recommended reading)

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science