Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Bachelor in mathematics | 6 crédits | |||
| Master in mathematics (120 ECTS) | 8 crédits | |||
| Master in mathematics (60 ECTS) | 8 crédits |
Lecturer
Coordinator
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit 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 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.
Learning outcomes of the learning unit
They are twofold : first to develop technical tools to investigate foundations of mathematics but also to get an insight on mathematicians as human beings.
Prerequisite knowledge and skills
None.
Planned learning activities and teaching methods
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.
Mode of delivery (face-to-face ; distance-learning)
One semester course at the Institute of Mathematics.
Recommended or required readings
There is a syllabus. Another interesting source book is : Basic Set Theory of Levy (Springer-Verlag).
Assessment methods and criteria
In June two parts :
1) one written examination with exercices only,
2) one oral examination with theory and small exercices.
Work placement(s)
Organizational remarks
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
Julien RASKIN
Phone : 04/366.94.32
E-mail : J.Raskin@ulg.ac.be
Laurent DE RUDDER
Phone : 04/366.94.06
E-mail : L.DeRudder@ulg.ac.be
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
Assessment subjects
Assessment methods
Contacts
Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session
Assessment subjects
No change with first quadrimester.
Assessment methods
This will be a written examination, sent by mail to each student.
It will contain exercices, as usual. For the theory, the student may choose between yes or no questions (with justifications) in the written part. Or present a project on a subject choosen in accordance with the course holder.
Contacts
G. Hansoul and J. Leroy.