Textbook: How to teach
Mathematics (Steven G. Krantz)
My tools: tool
1 - tool 2. Example of application: proof
of Lévy's theorem on two blackboards.
Teacher
portrait
Condensation phenomena in random trees (2024 CRM-PIMS Summer School in Probability mini-course)
Advanced probability topics MAP575 (since 2019)
Course delivered in the 3rd year of the Engineer program at École
polytechnique. See the
course webpage.
Condensation phenomena in random trees (ETH, Master, 2023-2024)
Student Seminar in Probability Theory (ETH, Bachelor/Master, 2023-2024)
Probability Theory (ETH, Bachelor/Master, 2023-2024)
Discrete mathematics MAA 103 (École polytechnique,
Bachelor, 2017-2019)
Discrete Mathematics MAA 103 (Year 1) had two main objectives: (i)
teach fundamental concepts in discrete mathematics, which are the
building blocks of many different areas of science and of advanced
mathematics (ii) teach how to write proofs. The course started with
elementary logic (e.g. quantifiers, different methods of proof), sets,
and functions. The second part of the course introduced students to
combinatorics and probability (on finite sets). The course consisted of
16 weeks (1h30 lecture and 1h30 exercise session per week).
Course material:
Exercises:
Exam papers and solutions:
Condensation in random trees (Random Trees and Graphs
Summer School 2019)
Scaling limits of large random discrete structures (Back to
school FMJH Master day)
Slides of the last lecture(
Keynote,
52 Mo -
PDF, 45 Mo)
Lévy processes and random discrete structures (Lévy 2016 -
Summer school on Lévy processes)
Lecture notes - Slides of
the last lecture (
Keynote,
62 Mo -
PDF, 55 Mo)
Geometry of random trees (Zürich, 2014-2015)
Master course, lecture notes:
- Lecture 1 and addendum
(Galton-Watson process), exercise
given at the end of the lecture, its
solution.
- Lecture 2 (plane trees and the
cycle lemma, exercise given at the
end of the lecture, its
solution.
- Lecture 3 (proof of the cyclic
lemma, generating series and Lagrange's inversion formula), exercise
given at the end of the lecture, its
solution.
- Lecture 4 (end of the proof of
Lagrange's inversion formula, definition of Galton-Watson trees), exercise
given at the end of the lecture, its
solution.
- Lecture 5 (coding Galton-Watson
trees by random walks), exercise
given at the end of the lecture, its
solution.
- Lecture 6 (Local limit
theorem).
- Lecture 7 (applications of the
local limit theorem and local convergence of Galton-Watson trees), exercise
given at the end of the lecture, its
solution.
- Lecture 8 (height process of a
forest, scaling limit of a random walk), exercise
given at the end of the lecture, its
solution.
- Lecture 9 (Recurrence criteria
for an integer valued random walk, space of continuous functions on
[0,1])), exercise given at the end
of the lecture, its
solution.
- Lecture 10 (théorème
d'invariance de Donsker).
- Lecture 11 (scaling limit of
the height process of a forest of trees, Brownian bridge).
- Lecture 12 (Brownian bridge,
Brownian excursion, scaling limit of the height process of a large
Galton-Watson trees).