LEADER 05435nam 22008535 450 001 9910865269003321 005 20251215135303.0 010 $a3-031-55964-9 024 7 $a10.1007/978-3-031-55964-8 035 $a(MiAaPQ)EBC31479613 035 $a(Au-PeEL)EBL31479613 035 $a(CKB)32291995900041 035 $a(DE-He213)978-3-031-55964-8 035 $a(EXLCZ)9932291995900041 100 $a20240614d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExplorations in Monte Carlo Methods /$fby Ronald W. Shonkwiler, Franklin Mendivil 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (290 pages) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 08$a3-031-55963-0 327 $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. 330 $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. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aProbabilities 606 $aComputer science$xMathematics 606 $aMathematical statistics 606 $aAlgorithms 606 $aGame theory 606 $aComputer simulation 606 $aMathematical optimization 606 $aProbability Theory 606 $aProbability and Statistics in Computer Science 606 $aAlgorithms 606 $aGame Theory 606 $aComputer Modelling 606 $aOptimization 606 $aAlgorismes$2thub 606 $aMčtode de Montecarlo$2thub 606 $aProcessos estocāstics$2thub 606 $aRutes aleatōries (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aProbabilities. 615 0$aComputer science$xMathematics. 615 0$aMathematical statistics. 615 0$aAlgorithms. 615 0$aGame theory. 615 0$aComputer simulation. 615 0$aMathematical optimization. 615 14$aProbability Theory. 615 24$aProbability and Statistics in Computer Science. 615 24$aAlgorithms. 615 24$aGame Theory. 615 24$aComputer Modelling. 615 24$aOptimization. 615 7$aAlgorismes 615 7$aMčtode de Montecarlo. 615 7$aProcessos estocāstics 615 7$aRutes aleatōries (Matemātica) 676 $a518.282 700 $aShonkwiler$b Ronald W$0472338 701 $aMendivil$b Franklin$0506095 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910865269003321 996 $aExplorations in Monte Carlo methods$9785037 997 $aUNINA