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| MATH0250-1 | Algebra III | |||||
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| Duration : | 30h Th, 30h Pr | |||||
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| Holder(s) : | Georges Hansoul | |||||
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| 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. | |||||
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| 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. | |||||
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| Prerequisites : | Basic knowledge of general algebra (groups, rings, fields and linear algebra). | |||||
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| Workshops : | Illustration of Galois correspondance and of the basic concepts of universal algebra. | |||||
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| Organization : | One semester course at the Institute of Mathematics. | |||||
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| Written notes : | Besides a syllabus, one can read : a) Galois theory de Ian Steward, b) A course in universal algebra de Burris at Sankappanavar. | |||||
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| Assessment : | In June, one written examination (exerices only) and one oral examination (theory). In September, only one oral examination (exerices and theory). | |||||
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| Contacts : | HANSOUL Georges Institut de Mathématiques - Bât. B37, bureau 059 Grande Traverse, 12 - 4000 Liège (Sart Tilman) Téléphone : 04/366.94.69, e-mail : G.Hansoul@ulg.ac.be, TEHEUX Bruno : téléphone : 04/366.96.36, e-mail : B.Teheux@ulg.ac.be, POUSSART Claire : téléphone : 04/366.27.22, e-mail : cpoussart@ulg.ac.be. | |||||
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ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 18/05/2007
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