Galois theory

Duration

30h Th, 30h Pr

Number of credits

Lecturer

Emilie Charlier

Substitute(s)

Georges Hansoul

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

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.

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 learning.

Organisational adjustments related to the current health context

For this year 2020-2021, traditionnal exams: oral exam for theory, and written exam of exercices.

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 :

• A. Baker, An introduction to Galois theory.
• I. Stewart, Galois theory, fourth edition, CRC Press (2015).

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

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

Work placement(s)

Organizational remarks

This course is organized at the second semester once every two years : 2018-2019, 2020-2021... More informations can be found on http://www.discmath.ulg.ac.be/charlier/enseignement.html.

Contacts

Emilie Charlier (teacher) - Adeline Massuir (teaching assistant)
Institute of Mateématics - Bât. B37 Allée de la découverte, 12 - 4000 Liège
Tél. : 04/366.94.69 Fax : 04/366.96.47 E-mails : echarlier@uliege.be - a.massuir@uliege.be