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| MATH0017-3 | Mathematical Logic and Set Theory
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Number of credits : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | 8 |
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| Master en sciences mathématiques, à finalité spécialisée en statistique, 1st year | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | 8 |
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| Master in Mathematical Sciences | | 8 |
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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 first semester, examination in June |
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Course contents :
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| This course is an introduction to the study of formal systems. One begins with propositional logic, modal logic and first-order logic up to Gödel's completeness theorems and compacity's theorem. We continue with a presentation of set theory with classes in which Russell paradox does not appear. The developed topics are : well-founded sets and Von Neuman recursion theorem, ordinals and ordinal arithmetic, cardinals - with and without the axiom of choice. |
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Learning outcomes of the course :
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| They are twofold : first to develop technical tools to investigate foundations of mathematics but also to get an insight on mathematicians as human beings. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| None. |
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Planned learning activities and teaching methods :
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| The exercices lessons have a double objective : first illustrate the concepts and results of the theoretical part and second give a true intuition of mathematical logic. |
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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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| There is a syllabus. Another interesting source book is : Basic Set Theory of Levy (Springer-Verlag). |
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Assessment methods and criteria :
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| In June two parts :
1) one written examination with exercices only,
2) one oral examination with theory and small exercices. |
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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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