### Timetable

### Description

Master's Programme in Materials Research is responsible for the course.

Modules where the course belongs to:

**MATR300 Advanced Studies in Materials Research.**

Optional for:- Study Track in Computational Materials Physics
- Study Track in Medical Physics and Biophysics

**PAP300 Advanced Studies in Particle Physics and Astrophysical Sciences.**

Optional for:- Study Track in Astrophysical Sciences
- Study Track in Particle Physics and Cosmology

**TCM300 Advanced Studies in Theoretical and Computational Methods**

The course is available to students from other degree programmes.

The programming skills are mandatory. Basic knowledge of probability theory is recommended.

Monte Carlo in Physics

After completion the course you will be able:

- Generate uniform and non-uniform random numbers by using different methods
- Apply pseudo- and quasirandom numbers for different tasks
- Perform Monte Carlo integration of multidimensional functions
- Estimate the statistical error of the mean for different methods
- Generate the synthetic data to improve on estimation of the average and the error of the mean
- Improve the convergence of the Monte Carlo integration result using different methods
- Create your own Game of life by using the Cellular automata principle

The course can be taken at any time, when it is available.

The course is given annually during the third teaching period (spring term).

Uniform random numbers

- Pseudo-Random Number Generators (RNG):
- linear algorithms: congruential and generalised feedback shift register(GFSR)
- non-linear algorithms: developments of congruential and twisted GFSR and Mersenne Twister RNG

- Stratified methods
- Quasi- RNG

Non-uniform random numbers

- Inversion, hit and miss and combined methods
- Markov chain

Monte Carlo integration, improving convergence of the Monte Carlo integration

Analysis of Monte Carlo integration result: estimation of the error of the mean

Generation of synthetic data to improve the analysis

Cellular automata and self-organized critical phenomena

- Lecture notes and Supplementary material
- Numerical Recipes in C,
- The art of scientific computing, 2nd edition
- W.H. Press, S.A. Teukolsky, W.T.Vetterling, B.P.Flannery

Exercises are designed to help students to understand better the material of the course. Regular programming will help to implement the received knowledge during the course in practice.

The final exam is held in form of answering theoretical questions in form of essays, however, the grade for the exercises performed during the course give 50% of the total weight.

The attendance of the lectures is recommended. Returning home completed exercises is mandatory. The exercises are aimed to test the programming skills of students. These will contribute equalliy to the final grade of the exam along with the answers to the exam questions.