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MATR323 Basics of Monte Carlo Simulations, 5 cr 
Code MATR323  Validity 01.01.2017 -
Name Basics of Monte Carlo Simulations  Abbreviation Basics of Monte 
Scope5 cr   
TypeAdvanced studies
TypeCourse   
  GradingGeneral scale 
  no
    Can be taken more than onceno
Unit Master's Programme in Materials Research 

Description
Target group 

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:
    1. Study Track in Computational Materials Physics
    2. Study Track in Medical Physics and Biophysics
  • PAP300 Advanced Studies in Particle Physics and Astrophysical Sciences.
    Optional for:
    1. Study Track in Astrophysical Sciences
    2. 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.

 
Timing 

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

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

 
Learning outcomes 

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
 
Completion methods 

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.

 
Prerequisites 

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

 
Recommended optional studies 

Monte Carlo in Physics

 
Contents 

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

 
Study materials and literature 
  • 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
 
Activities and teaching methods in support of learning 

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.

 
Assessment practices and criteria 

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.

 


Current and future instruction
Functions Name Type cr Teacher Schedule
registration period has not begun Basics of Monte Carlo simulations  Lecture Course  Flyura Djurabekova 
14.01.20 -25.02.20 tue 12.15-14.00
16.01.20 -27.02.20 thu 12.15-14.00

Future examinations
Functions Name Type cr Teacher Schedule
Registration Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
08.11.19fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
13.12.19fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
17.01.20fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
14.02.20fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
13.03.20fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
17.04.20fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
08.05.20fri 12.00-16.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
05.06.20fri 10.00-14.00
registration period has not begun Basics of Monte Carlo Simulations  General Examination  Flyura Djurabekova 
14.08.20fri 10.00-14.00
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