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MATH0205-1

General Algebra

[ version française ]

Duration :45h Th, 22,5h Pr
Credits/ECTS :
2nd "candidature" in mathematical sciences7,5
Holder(s) :Georges Hansoul
Course 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.
Course objective : Develop the student's abilities and give sufficient basic knowledge of the concepts and methods of abstact algebra.
Prerequisites : None.
Organization : A two semesters course at the Institute of Mathematics (B37).
Written notes : Two syllabus : theory, and exercices.
Assessment : 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.
Contacts : HANSOUL Georges,
Institute of Mathematics - B37, Office 059
Grande Traverse, 12 - 4000 Liege
(Sart Tilman)
Phone : 04/366.94.69 - Fax : 04/366.96.47
E-mail : G.Hansoul@ulg.ac.be
TEHEUX Bruno - Phone : 04/366.96.36
E-mail : B.Teheux@ulg.ac.be




ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 27/02/2006
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