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 Q2

• Written examination

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Written examination

Q3 UE Assessment Comments

Not applicable