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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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| Language : | Langue française |
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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 and 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,
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