Explorations in Monte Carlo Methods

Ronald W. Shonkwiler, Franklin Mendivil

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English

Springer International Publishing AG
15 June 2024

Probability & statistics; Game theory; Stochastics; Algorithms & data structures; Maths for computer scientists

Series: Undergraduate Texts in Mathematics

Monte Carlo Methods are among the most used, and useful, computational tools available today. They provide efficient and practical algorithms to solve a wide range of scientific and engineering problems in dozens of areas many of which are covered in this text. These include simulation, optimization, finance, statistical mechanics, birth and death processes, Bayesian inference, quadrature, gambling systems and more.

This text is for students of engineering, science, economics and mathematics who want to learn about Monte Carlo methods but have only a passing acquaintance with probability theory. The probability needed to understand the material is developed within the text itself in a direct manner using Monte Carlo experiments for reinforcement. There is a prerequisite of at least one year of calculus and a semester of matrix algebra.

Each new idea is carefully motivated by a realistic problem, thus leading to insights into probability theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. All examples in the text are coded in Python as a representative language; the logic is sufficiently clear so as to be easily translated into any other language. Further, Python scripts for each worked example are freely accessible for each chapter. Along the way, most of the basic theory of probability is developed in order to illuminate the solutions to the questions posed. One of the strongest features of the book is the wealth of completely solved example problems. These provide the reader with a sourcebook to follow towards the solution of their own computational problems. Each chapter ends with a large collection of homework problems illustrating and directing the material.

This book is suitable as a textbook for students of engineering, finance, and the sciences as well as mathematics. The problem-oriented approach makes it ideal for an applied course in basic probability as well as for a more specialized course in Monte Carlo Methods. Topics include probability distributions, probability calculations, sampling, counting combinatorial objects, Markov chains, random walks, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, random number generation, Bayesian Inference, Gibbs Sampling and Monte Carlo integration.

By: Ronald W. Shonkwiler, Franklin Mendivil
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Second Edition 2024
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031559631
ISBN 10: 3031559630
Series: Undergraduate Texts in Mathematics
Pages: 280
Publication Date: 15 June 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Ronald W. Shonkwiler is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces. Franklin Mendivil is a professor at Acadia University in Nova Scotia. He received his BSCE in Civil Engineering and his PhD in 1996 at Georgia Institute of Technology. In addition to the first edition of this text, Professor Mendivil co-authored ""Fractal-Based Methods in Analysis"" 2012.