2019-2020 / MATH0017-3

Mathematical Logic and Set Theory

Duration

30h Th, 10h Pr, 20h Mon. WS

Number of credits

 Bachelor in mathematics6 crédits 
 Master in mathematics (120 ECTS)8 crédits 
 Master in mathematics (60 ECTS)8 crédits 

Lecturer

Georges Hansoul, Julien Leroy

Coordinator

Julien Leroy

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

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.