I love teaching. I enjoy sharing and transmitting, and am comitted to do my best to digest the material I have to present in order to make it accessible for the audience, no matter the level. Teaching is not only an opportunity to permanently relearn my fields of knwoledge, but also a pedagogical and didactical challenge I deeply care about.
Analytic Number Theory
In 2018-2019, I proposed an open lecture to the math teachers of the Franco-Chinese institute of nuclear energy (IFCEN) in Zhuhai, China. The current syllabus is:
- Introduction
Proofs of Euclide, Fermat and Euler of the infinity of primes
Towards the Prime Number Theorem: a short history - Dirichlet Series
Generating functions
Convergence domain and bounds
Absolute convergence domain
Vertical growth - Arithmetic functions
Multiplicative functions
Euler products
Convolution and inversions - Average orders
Average of convolutions
Hyperbola method - Chebyshev's estimates
Chebyshev's estimates
Mertens' estimates
Bertrand postulate - Primes in arithmetic progressions
Additive characters
Multiplicative characters - Primes in arithmetic progressions
Dirichlet's theorem - Zero-free region
Complex analysis toolbox
Zero-free region
Prime number theorem
Relations with other quantities - A precise application of PNT
- Functional equations
- Explicit formulas and RH improvements
Previous Teaching
Exercise sessions
While a graduate student at Université Paris 13, I had the opportunity to be teaching assistant for the following courses:
- Differential Calculus and Optimization (L3)
- Linear Algebra (L2)
- Arithmetic (L2)
- Analysis (L1)
- Introduction to Mathematic Structures (L1)
Oral Examinations
I spent many years giving oral examinations (khôlles) for the French system of "prepa", in MPSI and MP sections. These have been given at the lycées Lakanal and Janson de Sailly, as well as at the Franco-Chinese institute for nuclear energy (IFCEN). The exercises I ended considering as interesting for their pedagogical and mathematical virtues have been compiled into this document. I hope that, despite most of them not being particularly original, these exercises could prove that nice proofs, sometimes leading to beautfiul theorems, can be grasped while staying at an elementary undergraduate level.
Agrégation
I spent a year preparing the Agrégation, the French national contest for professorship. This year 2012-2013 at the ENS Cachan turned out to be a year dedicated to synthesizing and deepening many mathematical fields taught until the M1 level. I gathered here the fruits of the reflexions born from the various lectures and discussions of this year:
- mes leçons en détails : god.pdf
- liste des développements et des références
- réflexions sur l'agrégation : idées et conseils
Many of these "Développements" have been properly written in a book, 131 Développements pour l'oral, hoping it will make accessible different beautiful mathematical topics to students and teachers.
I would be glad to read all your remarks, ideas and critics concerning theses attempts to structure and compile the knowledge required for the agrégation, and will try to improve the file accordingly! An interesting companion document is the one of Jill-Jênn Vie.
Scientific culture
The Groupe pour l'Initiative et la Culture Scientifiques (GICS) is a French association established in November 2010, whose aims are to transform the will and passion of the universities students into a way to efficiently share, at a large scale and on a regular basis, the culture and spirit of sciences to high school students.
I remain deeply interested in promotion of scientific culture, for instance I am a reviewer at Image des Mathématiques and will be organizing a MATHs.en.JEANS activity in Hong Kong next year.