Study programme 2020-2021Français
Mathematical logic I
Programme component of Bachelor's in Mathematics à la Faculty of Science

Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid-19 assessment methods are possibly planned for the end of Q3

CodeTypeHead of UE Department’s
contact details
US-B3-SCMATH-005-MCompulsory UEMICHAUX ChristianS838 - Logique mathématique
  • MICHAUX Christian

of instruction
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-021Mathematical logic I3515000Q1
S-MATH-019Seminar of mathematical logic I05000Q2
Programme component

Objectives of Programme's Learning Outcomes

  • Understand "elementary" mathematics profoundly
    • Use vector spaces, linear applications and the techniques associated with them
    • Understand and use the naive set theory
    • Understand basic algebraic structures
    • Manipulate previously acquired knowledge that appears in a question
    • Give examples and counterexamples for definitions, properties, theorems, etc.
  • Understand and produce strict mathematical reasoning
    • Write clearly and concisely
    • Use mathematical vocabulary and formalism appropriately
    • Make sense of formal expressions
    • Rely on a picture to illustrate a concept, rationale, etc.
  • Solve new problems
    • Abstract and manipulate theories and use these to solve problems
    • Adapt an argument to a similar situation
    • Use knowledge from different fields to address issues
  • Address literature and interact within other scientific fields
    • Have sufficient knowledge of English in order to read and understand scientific texts, especially in the field of mathematics.

Learning Outcomes of UE

At the end of the instruction, the students will be able to understand the role of model theory in mathematics, and more generally of mathematical logic.

Content of UE

Reminder of the topics of the course of B2 (seminar of introduction to mathematical logic). Basic elements of model theory (languages,formulas, theories, complete theories, model-complete theories, quantifiers elimination),  models build by ultraproducts and their use in mathematics (for example to non standard model of real numbers). Completeness Theorem (without the proof), Compactness Theorem, Los Theorem, Constants'Method, Lowenhein-Skolem Theorem, applications (if possible) to types, algebraically closed and real closed fields...  

Prior Experience

Basic notions of mathematcial logic ( similar to the content of the seminar of introduction to mathematical logic) and of algebra, linear algebra and topology.

Type of Assessment for UE in Q1

  • Written examination
  • Graded tests

Q1 UE Assessment Comments

Only Exercices

Type of Assessment for UE in Q2

  • Oral Examination

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

  • Oral examination
  • Written examination

Q3 UE Assessment Comments

Exercices + writen examination in a single day

Type of Resit Assessment for UE in Q1 (BAB1)

  • N/A

Q1 UE Resit Assessment Comments (BAB1)

not applicable

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
  • Cours magistraux
  • Exercices dirigés

Mode of delivery

AAMode of delivery
  • Face to face
  • Face to face

Required Reading


Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-021See the pages on Moodle platform.
S-MATH-019Not applicable

Recommended Reading


Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-021Marker, D., Model theory. An introduction. Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002. 
S-MATH-019Not applicable

Other Recommended Reading

AAOther Recommended Reading
S-MATH-021Chang et Keisler, Model Theory, North-Holland. Barwise, Handbook of mathematical logic, North-Holland. Poizat B., Cours de théorie des modèles, 1985, Nur Al-Mantiq Wal-Ma'rifah. [Version anglaise éditée chez Springer en 2000.]

Hodges, W., Model theory. Encyclopedia of Mathematics and its Applications, 42. Cambridge University Press, Cambridge, 1993.
S-MATH-019Not applicable
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de génération : 09/07/2021
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