Study Programmes 2016-2017
MATH0250-1  
Algebra III
Duration :
20h Th, 20h Pr
Number of credits :
Bachelor in mathematics4
Lecturer :
Georges Hansoul
Language(s) of instruction :
French language
Organisation and examination :
Teaching in the second semester
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Learning unit contents :
a) Galois theory : fields extensions, normal and algebraic closures, Galois correspondance, solvability of polynomial equations by radicals.

b) Universal algebra : structures on a first order language; Birkhoff's theorems; Lös theorem and application to non-standard analysis.
Learning outcomes of the learning unit :
They are twofolds. First illustrate the algebraic material studied before with the classical (finite) Galois theory, with the historically important application of an example of a polynomial whose roots cannot be calculated by radicals.

Next, give an introduction to non classical algebra, such as algebraic logic.
Prerequisite knowledge and skills :
Basic knowledge of general algebra (groups, rings, fields and linear algebra).
Planned learning activities and teaching methods :
Illustration of Galois correspondance and of the basic concepts of universal algebra.
Mode of delivery (face-to-face ; distance-learning) :
One semester course at the Institute of Mathematics.
Recommended or required readings :
Besides a syllabus, one can read :

a) Galois theory de Ian Steward,

b) A course in universal algebra de Burris and Sankappanavar.
Assessment methods and criteria :
For the first session, one written examination (exerices only) and one oral examination (theory). In September, only one oral examination (exerices and theory).
Work placement(s) :
Organizational remarks :
Due to time limitations, the universal algebra part might be skipped.
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


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