Study Programmes 2015-2016
| MATH0250-1 | ||||||||
| Algebra III | ||||||||
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Duration :
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| 20h Th, 20h Pr | ||||||||
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Number of credits :
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Lecturer :
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| 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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Units courses prerequisite and corequisite :
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| Prerequisite or corequisite units are presented within each program | ||||||||
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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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Prerequisite knowledge and skills :
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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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