Monte Carlo Methods Utilizing Mathematica®: Applications in Inverse Transform and Acceptance-Rejection Sampling

ISBN-13: 9783031232930 / Angielski / Twarda / 2023 / 168 str.

Sujaul Chowdhury

Opis

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica.  Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions.  A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.  

Spis treści

Introduction for Part I.- Evaluation of Definite Integrals Using Inverse Transform Sampling Utilizing Mathematica.- Introduction for Part II.- Evaluation of Definite Integrals Using Acceptance-rejection Sampling Utilizing Matematica.- Variational Monte Carlo Method Applied to Ground State of Simple Harmonic Oscillator Using Acceptance-rejection Sampling Utilizing Mathematica.

O autorze

Sujaul Chowdhury, Ph.D., is a Professor in Department of Physics at Shahjalal University of Science and Technology. He also received his B.Sc. and M.Sc. in Physics from Shahjalal University of Science and Technology, before earning his Ph.D. at The University of Glasgow. After completing his Ph.D., Dr. Chowdhury was a Humboldt Research Fellow for one year at The Max Planck Institute. He is the author of many books, including Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel, which is also in the Synthesis Lectures on Mathematics & Statistics series published by SpringerNature. His research interests include nanoelectronics, magnetotransport in semiconductor nanostructures, and nanostructure physics.

Blurb

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica and using random variates sampled by the inverse transform method. The author covers the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. This book also contains a chapter applying the Variational Quantum Monte Carlo method to a simple harmonic oscillator. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the information can be applied.