Acceptance-Rejection Sampling and Multi-dimensional Monte Carlo Integrations Utilizing Mathematica®

Sujaul Chowdhury

Apr 2025 · American Academic Press

About this ebook

We have chosen suitable multi-variable probability density functions and obtained corresponding random variates using the random sampling method called acceptance-rejection method. This book provides hands-on and practical demonstrations of evaluation of multi-dimensional or high-dimensional definite integrals using Monte Carlo method. We have evaluated 2, 3, 5, 7 and 10 dimensional definite integrals. We performed symbolic computations using programs written in Mathematica(R), in which we performed the variate sampling and evaluated the integrals. The book is self-contained.

About the author

Sujaul Chowdhury, Ph.D., is a Professor in Physics at Shahjalal University of Science and Technology (SUST). He received his B.Sc. and M.Sc. in Physics from SUST before earning his Ph.D. at The University of Glasgow in 2001. After completing his Ph.D., Dr. Chowdhury was a Humboldt Research Fellow for one year at The Max Planck Institute, Stuttgart. He is the author of many books, including 11 on different topics of Computational Physics with which to conduct the course and Lab titled Computational Physics or Computational Mathematics. His research interests include nanoelectronics, magnetotransport in semiconductor nanostructures, and Nanostructure Physics. Further details about the author and his CV are available at www.sust.edu