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.

Basic Information

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

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

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 75 h 5 CP

Responsible coordinator of the module PH2222 is Allen C. Caldwell.

Content, Learning Outcome and Preconditions


- introduction to random number generation - transforming among different probability densities - accept/reject methods - Monte Carlo integration: sample-mean, importance sampling - Random walks - Monte Carlo optimization: stochastic exploration, simulated annealing, ... - Markov Chain Monte Carlo methods - Other techniques - Applications: simulating physical systems, statistical analysis

Learning Outcome

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


You need to have access to a computer, and need some familiarity with programming.  You will be expected to write your own programs, produce numerical results and produce graphical output.  A basic knowledge of undergraduate mathematics is expected.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 4 Monte Carlo Methods Caldwell, A.
Mitwirkende: Schulz, O.
Montag, 16:00–18:00
sowie Termine in Gruppen

Learning and Teaching Methods

The material will be introduced in lectures, and the students will then have exercises that they will need to solve by programming algorithms on their computers.  50% of the course grade will come from carrying out calculational tasks on the computer, and 50% from an exam on the final day of lecture that will cover the conceptual aspects.


You will need access to a computer.


A good reference for this course is 'Monte Carlo Statistical Methods', second edition, Christian Robert and George Casella

Module Exam

Description of exams and course work

The learning outcome is tested in the exercises by programming projects and a written exam of 60 minutes with comprehension questions and sample problems. The module grade is determined by
- 50% solutions to the programming projects
- 50% written exam.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.