Fiches de cours 2018-2019

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Galois theory

MATH-317

Enseignant(s) :

Eisenbrand Friedrich

Langue:

English

Summary

This course is in an introduction to Galois theory, which is the study of automorphism groups of field extensions. Galois theory is essential for many fields of mathematics such as number theory, algebraic geometry, topology and many more.

Content

Ruler and compass constructions

Algebraic and transcendal numbers

Splitting fields, normaility and separability, soluble and simple groups

Automorphis groups of algebraic extensions and the Galois correspondence

Solution of polynomial equations by radical expressions and impossibility thereof for the quintic

Algorithms for calculating Galois groups

Construction of regular n-gons, theorem of Gauss-Wantzel

Keywords

polynomials, fields, algebraic extensions, group, Galois group

Learning Prerequisites

Required courses

Algèbre linéaire avancée I & II

Anneaux et corps

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex-cathedra lectures and exercises

Expected student activities

Independent solution of exercises that are proposed during the course.

Assessment methods

Written exam

Supervision

Office hours Yes
Assistants Yes
Forum Yes

Resources

Bibliography

Ian Stewart, Galois Theory, Chapman &Hall

Ressources en bibliothèque

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14  MAA110  
14-15    
15-16 MAA112   
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand