MATH-310 / 3 crédits

Enseignant: Lachowska Anna

Langue: Anglais

## Summary

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

## Keywords

Group, homomorphism, subgroup, normal subgroup, quotient group, cyclic group, symmetric group, order of the group, order of an element in the group, finite abelian groups.  Ring, ideal, principal ideal,  maximal ideal, unique principal ideal domain, Euler's totient function,  field, finite field, characteristic of a field.

## 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:

• Apply concepts and ideas of the course
• Reason rigorously using the notions of the course
• Choose an appropriate method to solve problems
• Identify the concepts relevant to each problem
• Apply concepts to solve problems similar to the examples shown in the course and in problem sets
• Solve new problems using the ideas of the course
• Implement appropriate methods to investigate the structure of a given group, ring or field, and study their properties

## Teaching methods

Lectures and exercise sessions

## Assessment methods

Written homework assignment (15% of the grade)

Written exam (85 % of the grade)

## Supervision

 Office hours No Assistants Yes Forum Yes

## Bibliography

1. D.S. Dummit, R. M. Foote, Abstract Algebra. Wiley, Third Edition

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

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

## Notes/Handbook

Complete lecture notes will be available in PDF

## Dans les plans d'études

• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• 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 (session d'hiver)
• 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 (session d'hiver)
• 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 (session d'hiver)
• 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 (session d'hiver)
• 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 (session d'hiver)
• Matière examinée: Algebra
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 1 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 11-12 12-13 13-14 PO01 14-15 15-16 PO01 16-17 17-18 18-19 19-20 20-21 21-22

Lundi, 13h - 15h: Cours PO01

Lundi, 15h - 16h: Exercice, TP PO01