Teaching

  • Analysis IV

    At its core, it is a functional analysis course for physicists and covers the basics of measure theory, function spaces and linear operators.



    MA
    Teachers: Juhan Aru
    Language: Fr
    Academic term: Bachelor semestre 4
  • Gaussian processes

    This is an introductory course on Gaussian fields and processes - or more shortly, on Gaussian magic. By discussing both the general theory and concrete examples, we will try to understand where and how Gaussian processes appear, and how to study them.



    MA, MA
    Teachers: Juhan Aru
    Language: En
    Academic term: Master semestre 1, Semestre automne
  • Introduction to random geometry

    We will discuss and study several models of random geometry - these are probabilistic models of random curves, surfaces, metrics often stemming from statistical physics and or field theories.



    MA
    Teachers: Juhan Aru
    Language: En
    Academic term: Master semestre 2
  • Lattice Gauge Theories

    The aim of this course is to learn about lattice gauge theories, but also a bit about their (potential) continuum limits.



    EDMA
    Teachers: Juhan Aru
    Language: En
    Academic term:
  • Martingales and Brownian motion

    Introduction to the theory of discrete-time martingales (optional stopping and convergence theorems) and its applications (gambler's ruin, branching processes, Pólya urns...). Introduction to Brownian motion.



    MA
    Teachers: Guillaume Blanc
    Language: En
    Academic term: Bachelor semestre 6
  • Probability

    The course is an introduction to probability theory. We aim to introduce the modern formalism (based on the notion of measure), to connect it with the 'intuitive' aspect of probabilities, but also to become familiar with the probabilistic way of thinking.



    MA
    Teachers: Juhan Aru
    Language: Fr
    Academic term: Bachelor semestre 3

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).