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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.
This book on Monte Carlo Methods Using Inverse Transform and Acceptance-Rejection Sampling Utilizing Mathematica is intended for undergraduate students of Mathematics, Statistics, and Physics who wish to know how Monte Carlo methods work with calculations done using a user-friendly program Mathematica. All treatments have been done as less manually as practicable. All calculations except for gathering accepted values of random variate in acceptance-rejection sampling have been done using Mathematica.
All necessary background materials are covered. A separate chapter has been dedicated to variational Monte Carlo method applied to ground state of simple harmonic oscillator. Necessary background on variational method has been covered so that readers need not consult Quantum Mechanics textbooks.
The book is on Monte Carlo methods. These are numerical methods for Computational Physics. These are parts of the syllabus for undergraduate students of Mathematics and Physics for the course titled “Computational Physics”. Besides the four referenced books, this is the only book to teach how basic Monte Carlo methods work. This is possibly the 1st Mathematica-based book on the topic