2018-2019 / MATH0246-2

Algebraic structures

Duration

30h Th, 30h Pr

Number of credits

 Bachelor in mathematics6 crédits 

Lecturer

Céline Esser, Georges Hansoul

Coordinator

Georges Hansoul

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

  • Group Theory : groups, subgroups, cyclic group, normal subgroups, quotient groups, Lagrange's theorem, isomorphism theorems. Cauchy theorem, Sylow theorems and p-group. Classification of finite commutative groups. Product of groups.
  • Ring and field theory : modular arithmetic and ring of polynomials, field of fractions of a commutative domain, extension field by an algebraic number, degree of an extension
  • Application to basic cryptography and to constructions with ruler and compass.

Learning outcomes of the learning unit

Develop the student's abilities and give sufficient basic knowledge of the concepts and methods of abstact algebra.

Prerequisite knowledge and skills

None.

Planned learning activities and teaching methods

Mode of delivery (face-to-face ; distance-learning)

A two semesters course at the Institute of Mathematics (B37).

Recommended or required readings

Two syllabus : theory, and exercices.

Assessment methods and criteria

First session (either January or June) : two exams : a written one with only exercices and an oral one with one or two questions of theory out a previously given list of questions.
Second session (September) : only one oral exam, theory and exercices.

Work placement(s)

Organizational remarks

Contacts

HANSOUL Georges
Institute of Mathématics - B37
Office 059
Grande Traverse, 12 - 4000 Liège
(Sart Tilman)
Phone : 04/366.94.69
Fax : 04/366.95.47
E-mail : G.Hansoul@ulg.ac.be

Julien RASKIN
Phone : 04/366.94.32
E-mail : J.Raskin@ulg.ac.be
 
Laurent DE RUDDER
Phone : 04/366.94.06
E-mail : L.DeRudder@ulg.ac.be