At its core, it is a functional analysis course for physicists and covers the basics of measure theory, function spaces and linear operators.
Section of Physics
Teachers: Aru Juhan
Language: french
Academic term: 2023-2024
Introduction to the theory of martingales in discrete time, in particular convergence and optional sampling theorems. Application to branching processes. Introduction to Brownian motion and its main properties.
Section of Mathematics
Teachers: Jego Antoine Pierre François
Language: french
Academic term: 2023-2024
This year we will be looking into probabilistic study of some models of mathematical physics.
Section of Mathematics
Teachers: Aru Juhan
Language: english
Academic term: 2023-2024
Undergraduate teaching
- Analyse 4 for physics (4th semester BA, lecture notes)
- Probability (3rd semester BA, lecture notes)
- Metric and topological spaces (3rd semester BA, lecture notes)
- Martingales and Brownian motion (student written lecture notes)
Postgraduate teaching
- Topics in high-dimensional probability
- Gaussian processes (partial lecture notes)
- Topics in 2D random geometry (partial lecture notes)
Popularisation
With co-authors we wrote a book on high-school mathematics “The evening textbook of mathematics”. It tries to make sometimes seemingly difficult and dry mathematics more lively and warm — more like it actually is. The book is freely available here (in Estonian). I occasionly write about mathematics in Estonian; and have also ad the opportunity to share my passion in mathematics at several general audience talks, including a TEDx talk on “Structures of randomness” here (in Estonian).