Coursebooks

Algebra

MATH-310

Lecturer(s) :

Lachowska Anna

Language:

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, symmetric groups. Classification of finite abelian groups. 

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

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

- Fields. Finite fields. Characteristic of a field. 

 

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.

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

Three short in-class tests (15% of the grade)

Written exam (85 % of the grade)

 

 

Supervision

Office hours No
Assistants Yes
Forum No

Resources

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. 

Ressources en bibliothèque
Notes/Handbook

Complete lecture notes will be available in PDF

Moodle Link

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14PO01    
14-15    
15-16PO01    
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German