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Reviewer: Robert M. Lynch

Monte Carlo is a place for fun. This book, however, cannot compete with the light entertainment found in the Mediterranean resort of the same name. Instead, it was designed to give the uninitiated, and those with a flirting acquaintance, a solid introduction into an area of mathematics where the blend of probabilistic methods and statistical computing is applied to study phenomena. Perhaps it is better said that this blend is used to “mimic” phenomena. Recently, the area has acquired a large following; to a large degree, its growth and diversity of application has been correlated with developments in computer system technology. The book is organized into two distinct parts: a mathematical introduction to Monte Carlo methods and a well-developed set of applications. The first part begins with some definitions and a brief history of Monte Carlo methods, followed by some elementary probability theory. The following 77 pages are the substance of the book. A number of techniques used to develop different sampling distributions are presented, followed by a discussion of variance reduction techniques in Monte Carlo quadrature. The three variance reduction approaches presented are importance sampling, correlation methods, and expected value substitutions. In the second part, the applications presented are all closely aligned with the physical sciences. The first application describes Monte Carlo methods in statistical physics. The second focuses on radiation transport (as in interaction with the atom). The third gives an overview of the Green's function Monte Carlo method. A number of appendices present information on statistical computing and pseudo-random number generation, with particular attention to establishing the quality of the generated data sets. Adequate bibliographies are provided at the end of each chapter. The book is well written and to the point. A reader with a basic exposure to calculus and probability theory should be able to go through the body of the text, though the applications may not serve the professional needs of a number of potential readers. The lack of examples and exercises throughout the main body of the text and its focus on the physical sciences make it less attractive as a text and limit its audience. It could be improved by adding more on statistical computing, and a selection of applications outside the physical sciences. On balance, for the individual curious about the underpinnings of Monte Carlo methods, these shortcomings can be overlooked. The book represents a good introduction to the area.