Explorations in Monte Carlo Methods

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Springer Science & Business Media, Aug 11, 2009 - Mathematics - 243 pages

Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.

Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material.

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

 

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Contents

Introduction to Monte Carlo Methods
1
Some Probability Distributions and Their Uses
51
Markov Chain Monte Carlo
101
Optimization by Monte Carlo Methods
139
Random Walks
164
Generating Uniform Random Numbers
213
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About the author (2009)

Ronald Shonkwiler is also publishing Mathematical Biology: An Introduction with Maple and Matlab, that will will be available in 2008. He is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic processes, optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces.

Franklin Mendevil is a professor at Acadia University in Nova Scotia. He received his PhD in 1996 at Georgia Institute of Technology. He has co-authored numerous papers and publications, several of which were with Dr. Shonkwiler.