04838nam a22005775i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001900153072001600172072001700188072002300205072001500228072001600243100008300259245011000342250001800452264006900470300006400539336002600603337002600629338003600655347002400691490005100715505043500766520239001201650001903591650003503610650002903645650001603674650001703690650002503707650003103732650002403763650005203787650001603839650001703855650002403872650001803896700008103914710003403995773002604029776003604055776003604091776003604127830005104163856004604214978-3-031-55964-8DE-He21320251030112310.0cr nn 008mamaa240614s2024    sz |    s    |||| 0|eng d  a97830315596487 a10.1007/978-3-031-55964-82doi 4aQA273.A1-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema1 aShonkwiler, Ronald W.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aExplorations in Monte Carlo Methodsh[electronic resource] /cby Ronald W. Shonkwiler, Franklin Mendivil.  a2nd ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXV, 280 p. 92 illus., 28 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x2197-56040 a1. Introduction to Monte Carlo Methods -- 2. Some Probability Distributions and Their Uses -- 3. Markov Chain Monte Carlo -- 4. Random Walks -- 5. Optimization by Monte Carlo Methods -- 6. More on Markov Chain Monte Carlo -- A. Generating Uniform Random Numbers -- B. Perron Frobenius Theorem -- C. Kelly Allocation for Correlated Investments -- D. Donsker's Theorem -- E. Projects -- References -- List of Notation -- Code Index.  aMonte 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. 0aProbabilities. 0aComputer sciencexMathematics. 0aMathematical statistics. 0aAlgorithms. 0aGame theory. 0aComputer simulation. 0aMathematical optimization.14aProbability Theory.24aProbability and Statistics in Computer Science.24aAlgorithms.24aGame Theory.24aComputer Modelling.24aOptimization.1 aMendivil, Franklin.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155963108iPrinted edition:z978303155965508iPrinted edition:z9783031559662 0aUndergraduate Texts in Mathematics,x2197-560440uhttps://doi.org/10.1007/978-3-031-55964-8