F7110 Introduction to Monte Carlo simulation as a numerical tool

Přírodovědecká fakulta
podzim 2021
Rozsah
1/1/0. 3 kr. Ukončení: k.
Vyučující
Dominique Alain Geffroy, Ph.D. (přednášející)
Garance
Dominique Alain Geffroy, Ph.D.
Ústav fyziky kondenzovaných látek – Fyzikální sekce – Přírodovědecká fakulta
Kontaktní osoba: Dominique Alain Geffroy, Ph.D.
Dodavatelské pracoviště: Ústav fyziky kondenzovaných látek – Fyzikální sekce – Přírodovědecká fakulta
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
During this course, the students will be exposed to Monte Carlo method as a flexible and powerful numerical tool for solving a variety of problems, going from statistical mechanics to financial derivatives valuation, including some simple quantum physics phenomena. The sessions will include a lecture introducing the concepts, followed by practice sessions started in class, to be completed from home as a homework. A large emphasis will be put on the use by the students of good coding practices and efficient workflow, which will be introduced in class and during the practice sessions. Python is the recommended language for following the course, but other languages are possible, depending on the students' experience, as long as they allow for object oriented design.
Výstupy z učení
After completing the course, a student will be able to:
- identify the potential of Monte Carlo techniques for the resolution of complex physical problems;
- identify the situations where direct sampling or Markov chain samplings may be applicable;
- write elaborate Monte Carlo algorithms in python, using a modern workflow including source control tools;
- Get a basic understanding of the role played by statistical physics in phase transitions;
- Understand the Feynman path integral approach for quantum physics problems;
- Model some exotic financial products using a Monte Carlo approach.
Osnova
  • Monte Carlo algorithms: basics.
  • From dynamics to statistical mechanics.
  • Phase transitions
  • Integration by sampling
  • Quantum mechanics I: introduction to path integrals
  • Quantum mechanics II: Bose Einstein condensation
  • Statistical Physics: Ising model
  • Monte Carlo and financial models
Výukové metody
NB: The practice sessions will be the opportunity for the students to practice the following concepts, introduced in class: Introduction to Python, source control, coding workflow Object Oriented programming, efficient code design.
Metody hodnocení
"continuous assessment", where the quality of the work of the students on the exercises given in class along the semester determines their grade.
Informace učitele
Reading material:
David P. Landau and Kurt Binder: A guide to Monte-Carlo simulations in Statistical Physics, 3rd edition, Cambridge University Press.
Werner Krauth: Statistical mechanics, algorithms and computations, Oxford University Press.
Justin London: Modeling financial derivatives in C++, John Wiley and Sons.
Další komentáře
Předmět je vyučován každoročně.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích podzim 2016, podzim 2017, jaro 2018, podzim 2018, jaro 2019, podzim 2019, podzim 2020, podzim 2022.