Objectives of general skills

• Understand "elementary" mathematics profoundly
• 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
• Collaborate on mathematical subjects
• Present mathematical results orally and in a structured manner
• Solve new problems
• Abstract and manipulate theories and use these to solve problems
• 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.

UE's Learning outcomes

Be comfortable with the basic notions of  Model Theory and with solving simple exercices.

UE Content

Lowenheim-Skolem theorems, kappa-categorical theories and Vaught Theorem. Back and Forth and dense linear orders. Quantifier-elimination criteria and applications to algebraically closed fields and real-closed fields. Model-complete theories and Lindström theorem. Stone spaces of types and aleph_0-categorical theories.

Prior experience

Notions of first-order Logic, of (sub)-structures, morphisms. Compacity Theorem and Completeness Theorem. Ultraproducts and Los Theorem. Some notions of naive set theory (ordinals, cardinals),some notion of topology (basis of open sets, compacity), some notions of algebra ((ordered) groups, (ordered) fields, polynomial rings, Boolean algebras).

Term 1 for Integrated Assessment - type

• N/A

Term 1 for Integrated Assessment - comments

The evaluation consists in a written exam on exercices (1/3) and is completed by an oral exam (2/3).

Term 2 for Integrated Assessment - type

• Oral Examination
• Written examination

Term 2 for Integrated Assessment - comments

The evaluation consists in a written exam on exercices (1/3) and is completed by an oral exam (2/3).

Term 3 for Integrated Assessment - type

• Written examination

Term 3 for Integrated Assessment - comments

The evaluation consists in a written exam on exercices and a theoretical knowledge of the material.

Resit Assessment for IT - Term 1 (B1BA1) - Comments

Not applicable