Universiteit Leiden

nl en

Probability, Operations, and Dynamics


The information below concerns courses that our group teaches in Leiden. 

During the bachelor phase, the language of stochastic reasoning and the key principles behind randomness and complexity are taught. During the master phase, a variety of specific topics is covered at the frontline of modern research. This training allows students to confront some of the most challenging problems in science, technology and society, and prepares them for a career in academics, industry, business or administration. People who are trained in dealing with complexity, uncertainty and risk, and who have the skill to analyse theories, experiments and data, are in great demand worldwide.   

A broad palette of introductory and advanced courses is offered in each of the three POD-areas, with a core programme of courses that are available each year (either mandatory or optional), and a flanking programme of courses that are available every two or three years. The curriculum aims to prepare students to face the most challenging questions surrounding complex systems and stochastic dynamics, both theoretical and applied.


  •  Pre-university college (Block II)
  •  Pre-university classes
  •  Networks masterclass

1st year BSc

  • Mathematical Structures (semester 1, compulsory)
  • Introduction to Probability Theory (semester 2, compulsory)
  • Combinatorics and Optimisation (semester 2, compulsory)

2nd year BSc

  •  Markov Chains and Applications (semester 1, choice, starting 2021)
  •  Introduction to Measure Theory (semester 2, compulsory)

 2nd/3rd year BSc

  • Random Walks (semester 1 or 2, choice)
  • Discrete Optimisation (semester 1, choice)
  • Stochastic Optimisation (seester 2, choice)
  • Introduction to Dynamical Systems (semester 2, choice)

3rd year BSc

  •  Bachelorseminar (semester 2)

3rd year BSc and MSc

  • Complex Networks (semester 1)
  • Probability Seminar (semester 1)
  • Operations Research 4 (homework course)
  • Caleidoscope
  • Ergodic Theory and Fractals (semester 2) or Modern Dynamics (semester 2)
  • Random Dynamical Systems (semester 2)
  • Combinatorial Games 


  • Coupling Theory (semester 2)
  • Stochastic Models for Genetic Evolution (semester 2)
  • Random Matrices


  • Stochastic Processes
  • Complex Networks (semester 2)
  • Ergodic Theory (semester 1)
  • Interacting Particle Systems (semester 1)
  • Random Walks (semester 1, 2021)


  •  Markov Decision Processes

Lecture notes

Random walks (Avena, Heydenreich, den Hollander, Verbitskiy, van Zuijlen) Lecture notes
Large Deviations (den Hollander) Link to book
Random Polymers (den Hollander) Link to book
Interacting Particle Systems (van Enter, den Hollander) Lecture notes
Coupling techniques (den Hollander)  Lecture notes
Stochastic Models for Genetic Evolution (den Hollander)  Lecture notes
Stochastic Analysis (Maassen, den Hollander) Lecture notes
Stochastic Processes (Spieksma) Lecture notes
This website uses cookies.  More information.