 | |
| MATH0215-1 | Algebra
 |
|
| Duration : | 30h Th, 10h Pr |
|
| Credits/ECTS : |
|
|
| Holder(s) : | Georges Hansoul |
|
| Language : | Langue française |
|
| Course 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.
|
|
| Course objective : | 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. |
|
| Prerequisites : | Basic knowledge of general algebra (groups, rings, fields and linear algebra). |
|
| Workshops : | Illustration of Galois correspondance and of the basic concepts of universal algebra. |
|
| Organization : | One semester course at the Institute of Mathematics. |
|
| Written notes : | Besides a syllabus, one can read :
a) Galois theory de Ian Steward,
b) A course in universal algebra de Burris and Sankappanavar.
|
|
| Assessment : | In June, one written examination (exerices only) and one oral examination (theory). In September, only one oral examination (exerices and theory). |
|
| 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
|
|
|
| |
