Objectives of general skills

• Have integrated and elaborate mathematical knowledge.
• Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
• Use prior knowledge to independently learn high-level mathematics.
• Research mathematical literature in an efficient and relevant way.
• Read research articles in at least one discipline of mathematics.
• Carry out major projects.
• Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Apply innovative methods to solve an unprecedented problem in mathematics or within its applications.
• Mobilise knowledge, and research and analyse various information sources to propose innovative solutions targeted unprecedented issues.
• Communicate clearly.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.

UE's Learning outcomes

Be able to read the Model theory book of Dave Marker (Model Theory, An introduction, Graduate Texts in Mathematics, 217, Springer-Verlag, New York, 2002).

UE Content

The aim of the course is to understand the proof of Morley's Theorem on aleph_1-categorical theories.
We begin by Ryll-Nardewski's Theorem on  aleph_0-categorical theories. Then we will study the following notions:
-saturation, indiscernible sequences.
-Ramsey theorem and Ehrenfeucht-Mostwski's models.
-Vaught pairs, strongly minimal sets and pregeometries.
Finally of time permits:
- Morley and Cantor-Bendixon's ranks.
-  definable types, heirs and co-heirs. Application in theories of modules.
- Fraïssé limits (e.g. the random graph).

Prior experience

This course follows the model theory course 1, given in Bac 3.

Term 1 for Integrated Assessment - type

• N/A

Term 1 for Integrated Assessment - comments

Not applicable

Term 2 for Integrated Assessment - type

• Oral Examination

Term 2 for Integrated Assessment - comments

Not applicable

Term 3 for Integrated Assessment - type

• Oral examination

Term 3 for Integrated Assessment - comments

Not applicable

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

Not applicable