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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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| Credits/ECTS : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences | | Second semester | | 8 |
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| Holder(s) : | Georges Hansoul |
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| Language : | French language |
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| Course contents : | 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. 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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| Course objective : | 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 : | None. |
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| Workshops : | 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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| Organization : | One semester course at the Institute of Mathematics. |
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| Written notes : | There is a syllabus. Another interesting source book is : Basic Set Theory of Levy (Springer-Verlag). |
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| Assessment : | In June two parts :
1) one written examination with exercices only,
2) one oral examination with theory and small exercices. |
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| Contacts : | 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
TEHEUX Bruno - Phone : 04/366.96.36
E-mail : B.Teheux@ulg.ac.be
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