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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 2015

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 75 h 5 CP

Responsible coordinator of the module PH2222 in the version of SS 2015 was 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

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.  There will also be 'pen and pencil' type exercises.  The students can work in teams, but each student will be expected to write an individual report with the solutions to the exercises.


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

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

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