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| MATH0250-1 | Algebra III
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Georges Hansoul |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| 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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Learning outcomes of the course :
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| 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 and co-requisites/ Recommended optional programme components :
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| Basic knowledge of general algebra (groups, rings, fields and linear algebra). |
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Planned learning activities and teaching methods :
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| Illustration of Galois correspondance and of the basic concepts of universal algebra. |
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Mode of delivery (face-to-face ; distance-learning) :
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| One semester course at the Institute of Mathematics. |
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Recommended or required readings :
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| 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 methods and criteria :
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| For the first session, one written examination (exerices only) and one oral examination (theory). In September, only one oral examination (exerices and theory). |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| 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
CAVUS Rukiye
Phone : 04/366.94.04
E-mail : R.Cavus@ulg.ac.be |
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