The Monte–Carlo Method

  • Simon ŠircaEmail author
Part of the Graduate Texts in Physics book series (GTP)


The Monte–Carlo method is introduced as a generic tool for the solution of mathematical physics models by means of computer simulation. These problems range from simple one-dimensional integration to sophisticated multi-dimensional models involving elaborate geometries and complex system states. A historical introduction and an exposition of the basic idea are followed by a basic treatment of numerical integration and discussing methods of variance reduction like importance sampling and use of quasi-random sequences. Markov-chain Monte Carlo is presented as a powerful method to generate random numbers according to arbitrary, even extremely complicated distributions. A specific implementation in the form of the Metropolis–Hastings algorithm is offered.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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