Explorations in Monte Carlo Methods - Shonkwiler, Ronald W.; Mendivil, Franklin; SpringerLink (Online service) (New York, NY : Springer New York, 2009)
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.
to Monte Carlo Methods -- Some Probability Distributions and Their Uses -- Markov Chain Monte Carlo -- Optimization by Monte Carlo Methods -- Random Walks.
Keywords: MATHEMATICS; COMPUTER SCIENCE; COMPUTER SIMULATION; ALGORITHMS; MATHEMATICAL OPTIMIZATION; DISTRIBUTION (PROBABILITY THEORY).; MATHEMATICS; PROBABILITY THEORY AND STOCHASTIC PROCESSES; PROBABILITY AND STATISTICS IN COMPUTER SCIENCE; ALGORITHMS; GAME THEORY, ECONOMICS, SOCIAL AND BEHAV. SCIENCES; SIMULATION AND MODELING; OPTIMIZATION