Program Overview

Program Overview

The CA: Formalisation mathématique program is designed to provide an introduction to mathematical formalization, a discipline that focuses on making mathematical definitions and proofs accessible to computers for rigorous verification and to gain new insights into the formalized theories.

Course Description

The course aims to introduce students to the formalization of mathematical concepts, using the theory of dependent types and the calculus of inductive constructions as foundations, and the Lean software with its Mathlib library as the tool for formalization. The course will alternate between theoretical lectures, practical sessions using Lean, and computer-based exercises.

Course Characteristics

• Duration: 21 hours of lectures + 21 hours of practical work
• Validation Method: Examination + Presentation(s)
• ECTS Credits: 6 (lectures) + 6 (practical work)

Department of Mathematics and Applications

The program is part of the Department of Mathematics and Applications, which has several research teams, including those focused on algebra and geometry, analysis, and probabilities and statistics. The department also offers various formations, stages, and exposés, and has a strong emphasis on international relations and research activities.

Research Areas

The research within the department encompasses several areas, including:

• Équipes (teams) focused on specific mathematical disciplines
• Séminaires (seminars) for the discussion of current research
• Publications and the dissemination of research findings
• Thèses & HDR (theses and higher doctorates)
• Invitations and visits from international researchers
• Anciens membres (alumni) activities
• Annales de l'ENS (annual publications of the École Normale Supérieure)
• Activités de diffusion (outreach activities)

Teaching and Formation

The department offers a range of teaching and formation activities, including:

• Présentation de la formation (presentation of the formation)
• Formations (training programs)
• Stages et exposés (internships and presentations)
• Responsables pédagogiques (pedagogical responsibles)
• Calendrier (calendar of events)
• Brochure (information brochure)

Conclusion

The CA: Formalisation mathématique program offers a unique opportunity for students to engage with the formalization of mathematical concepts, using state-of-the-art tools and foundations. It is part of a broader range of activities within the Department of Mathematics and Applications, which is committed to research, teaching, and outreach in the field of mathematics.