Fiches de cours

Algebra

MATH-310

Enseignant(s) :

Lachowska Anna

Langue:

English

Summary

Study basic concepts of modern algebra: groups, rings, fields.

Content

- Algebraic structures: sets, groups, rings, fields. 

- Groups. Subgroups. Homomorphisms of groups, normal subgroups, quotients. Cyclic groups, permutation groups. Structure of finite abelian groups. 

- Rings. Homomorphisms of rings. Ideals, principal, prime and maximal ideals, principal rings, factorial rings. Quotient rings. The Chinese remainder theorem. 

- Examples of rings. Integers. basic properties. Euler's and Fermat's theorems. Polynomial rings. GCD, unique factorization. 

- Fields. Algebraic extensions. Finite fields. Primitive elements. 

 

Keywords

Group, homomorphism, subgroup, normal subgroup, quotient group, cyclic group, symmetric group, order of the group, order of an element, ring, ideal, principal ideal, prime ideal, maximal ideal, unique factorization, Euler's totient function, principal ring, factorial ring, field, finite field, field extension, characteristic of a field, primitive element of a finite field. 

Learning Prerequisites

Required courses

Linear Algebra I, Analyse I  

Recommended courses

Linear Algebra I, Analyse I, Analyse II 

Learning Outcomes

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

Teaching methods

Lectures and exercise sessions

Assessment methods

Written exam 

 

 

Supervision

Office hours No
Assistants Yes
Forum No

Resources

Bibliography

1. S. Lang, Undergraduate Algebra. Undergraduate texts in Mathematics. Springer-Verlag, Inc.  New York, second edition, 1990. 

2. L. Childs, A Concrete Introduction to Higher Algebra. Undergraduate texts in Mathematics, Springer-Verlag, Inc. New York, 1995. 

Ressources en bibliothèque

Dans les plans d'études

    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      3
    • Matière examinée
      Algebra
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      1 Heure(s) hebdo x 14 semaines
    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      3
    • Matière examinée
      Algebra
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      1 Heure(s) hebdo x 14 semaines
  • Passerelle HES - SC, 2018-2019, Semestre automne
    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      3
    • Matière examinée
      Algebra
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      1 Heure(s) hebdo x 14 semaines
    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      3
    • Matière examinée
      Algebra
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      1 Heure(s) hebdo x 14 semaines
    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      3
    • Matière examinée
      Algebra
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      1 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14PO01 Polydôme    
14-15    
15-16PO01 Polydôme    
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