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Monte Carlo Methods

Module PH2222

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2018

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2020SS 2018SS 2015

Basic Information

PH2222 is a semester module in English language at Master’s level which is offered in summer semester.

This module description is valid from SS 2015 to WS 2019/20.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2222 in the version of SS 2018 was Allen C. Caldwell.

Content, Learning Outcome and Preconditions


You will learn many different techniques for generating (pseudo) random numbers according to arbitrary probability distributions, as well as numerical techniques for implementing them.  This module will also familiarize you with advanced techniques for solving high-dimensional integrals, performing optimization and regression tasks and for simulating physical situations.

Learning Outcome

After successful completion of this module, the student is able

  • to apply different techniques for generating (pseudo) random numbers according to arbitrary probability distributions.
  • to know and apply Monte Carlo based integration techniques such as accept/reject, sample mean, importance sampling and stratified sampling.
  • to understand the fundamentals of random walks.
  • to use Markov Chain Monte Carlo techniques for sampling from distributions.
  • to use simulated annealing techniques to solve optimization problems.


The student will be expected to program algorithms and produce graphical output. Access to a computer and practical knowledge of a computing language is necessary.

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

This module consists of a lecture and an exercise class. The lectures will present the learning content (in English).  Examples will be drawn from a range of physics areas.  A number of exercises will be assigned that the students will be expected to solve over the course of the semester and submit in a written report. 

A recitation session will precede the lectures, where students will present their solutions to the exercises and where further examples will be presented.


Presentation, blackboard. Lecture notes will be provided. You will need access to a computer.


  • C.P. Robert & G. Casella: Monte Carlo Statistical Methods, 2nd Edition, Springer Verlag, (2004)
  • W.R. Gilks, S. Richardson & D.J. Spiegelhalter: Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC, (1996)
  • R.Y. Rubinstein & D.P. Kroese: Simulation and the Monte Carlo Method, Wiley-Interscience, (2007)
  • N.J. Giordano and H. Nakanishi: Computational Physics, 2nd Edition, Pearson, (2006)
  • W.H. Press, B.P. Flannery, S.A. Teukolsky & W.T. Vetterling: Numerical Recipes. The Art of Scientific Computing, Cambridge Universitty Press, (1989)

Module Exam

Description of exams and course work

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using final projects independently prepared by the students. The exam of 25 minutes consists of the presentation of the project’s results and a subsequent discussion.

Exam Repetition

The exam may be repeated at the end of the semester.

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