2023-2024 / MATH2250-1

Galois theory


30h Th, 20h Pr

Number of credits

 Bachelor in mathematics5 crédits 


Emilie Charlier

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The aim of this course is to present the Galois theory : fields extensions, normal and algebraic closures, Galois correspondance, solvability of polynomial equations by radicals. The course also contains an application to the rule-and-compas constructible polygons.

Learning outcomes of the learning unit

At the end of the course, the student will be able to present the finite Galois theory, with the historically important application of an example of a polynomial whose roots cannot be calculated by radicals.

Prerequisite knowledge and skills

Good basic knowledge of general algebra (groups, rings, fields and linear algebra).

Planned learning activities and teaching methods

The course will be mainly given with chalk and blackboard. Some illustrations might be given using the Mathematica software.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Additional information:

Face-to-face learning.

Recommended or required readings

The course will be freely based on the syllabus of G. Hansoul, which is available at the secretariat of the Mathematics Institute. Other references are :

Exam(s) in session

Any session

- In-person

written exam AND oral exam

Additional information:

One written examination (exerices only) and one oral examination (theory). The assessment methods are identical for both examination periods.

Work placement(s)

Organisational remarks and main changes to the course

This course is organized at the second semester. Information available on eCampus.


Emilie Charlier (teacher) - Savinien Kreczman (teaching assistant)

Institute of Mathematics - Bât. B37
Allée de la découverte, 12 - 4000 Liège

Tél. : 04/366.93.84
E-mails : echarlier@uliege.be - savinien.kreczman@uliege.be

Association of one or more MOOCs