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Probabilistic Methods In Applied Mathematics
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Book Synopsis Ten Lectures on the Probabilistic Method by : Joel Spencer
Download or read book Ten Lectures on the Probabilistic Method written by Joel Spencer and published by SIAM. This book was released on 1994-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties.
Book Synopsis The Probabilistic Method by : Noga Alon
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Book Synopsis Methods of Mathematics Applied to Calculus, Probability, and Statistics by : Richard W. Hamming
Download or read book Methods of Mathematics Applied to Calculus, Probability, and Statistics written by Richard W. Hamming and published by Courier Corporation. This book was released on 2012-06-28 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.
Book Synopsis Probabilistic Methods in Applied Mathematics by : A. T. Bharucha-Reid
Download or read book Probabilistic Methods in Applied Mathematics written by A. T. Bharucha-Reid and published by Elsevier. This book was released on 2014-05-10 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Methods in Applied Mathematics, Volume 3 focuses on the influence of the probability theory on the formulation of mathematical models and development of theories in many applied fields. The selection first offers information on statistically well-set Cauchy problems and wave propagation in random anisotropic media. Discussions focus on extension to biaxial anisotropic random media; an effective medium description for a random uniaxial anisotropic medium and the resulting dyadic Green's function; evolution of the spectral matrix measure; and well-set Cauchy problems. The text then examines stochastic processes in heat and mass transport, including mass transport, velocity field, temperature transport, and coupling of mass and heat transport. The manuscript takes a look at the potential theory for Markov chains and stochastic differential games. Topics include formal solutions for some classes of stochastic linear pursuit-evasion games; solution of a stochastic linear pursuit-evasion game with nonrandom controls; problems of potential theory; and hitting distributions. The selection is a vital source of data for mathematicians and researchers interested in the probability theory.
Book Synopsis Probability and Partial Differential Equations in Modern Applied Mathematics by : Edward C. Waymire
Download or read book Probability and Partial Differential Equations in Modern Applied Mathematics written by Edward C. Waymire and published by Springer. This book was released on 2011-12-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
Book Synopsis Statistical and Probabilistic Methods in Actuarial Science by : Philip J. Boland
Download or read book Statistical and Probabilistic Methods in Actuarial Science written by Philip J. Boland and published by CRC Press. This book was released on 2007-03-05 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical and Probabilistic Methods in Actuarial Science covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. The book builds on students' existing knowledge of probability and statistics by establishing a solid and thorough understanding of
Book Synopsis Applied Probability by : Kenneth Lange
Download or read book Applied Probability written by Kenneth Lange and published by Springer Science & Business Media. This book was released on 2008-01-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.
Book Synopsis Probability and Computing by : Michael Mitzenmacher
Download or read book Probability and Computing written by Michael Mitzenmacher and published by Cambridge University Press. This book was released on 2005-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Book Synopsis Introduction to Matrix Analytic Methods in Stochastic Modeling by : G. Latouche
Download or read book Introduction to Matrix Analytic Methods in Stochastic Modeling written by G. Latouche and published by SIAM. This book was released on 1999-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.
Book Synopsis Probabilistic Methods in Applied Mathematics by : Albert T. Bharucha-Reid
Download or read book Probabilistic Methods in Applied Mathematics written by Albert T. Bharucha-Reid and published by . This book was released on 1970 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probabilistic and Statistical Methods in Computer Science by : Jean-François Mari
Download or read book Probabilistic and Statistical Methods in Computer Science written by Jean-François Mari and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic and Statistical Methods in Computer Science
Book Synopsis Matrix-Exponential Distributions in Applied Probability by : Mogens Bladt
Download or read book Matrix-Exponential Distributions in Applied Probability written by Mogens Bladt and published by Springer. This book was released on 2017-05-18 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distributions and related processes that will allow practitioners to calibrate models to real data. Aimed as a textbook for graduate students in applied probability and statistics, the book provides all the necessary background on Poisson processes, Markov chains, jump processes, martingales and re-generative methods. It is our hope that the provided background may encourage researchers and practitioners from other fields, like biology, genetics and medicine, who wish to become acquainted with the matrix-exponential method and its applications.
Book Synopsis Finitary Probabilistic Methods in Econophysics by : Ubaldo Garibaldi
Download or read book Finitary Probabilistic Methods in Econophysics written by Ubaldo Garibaldi and published by Cambridge University Press. This book was released on 2010-08-19 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Econophysics applies the methodology of physics to the study of economics. However, whilst physicists have good understanding of statistical physics, they may be unfamiliar with recent advances in statistical conjectures, including Bayesian and predictive methods. Equally, economists with knowledge of probabilities do not have a background in statistical physics and agent-based models. Proposing a unified view for a dynamic probabilistic approach, this book is useful for advanced undergraduate and graduate students as well as researchers in physics, economics and finance. The book takes a finitary approach to the subject, discussing the essentials of applied probability, and covering finite Markov chain theory and its applications to real systems. Each chapter ends with a summary, suggestions for further reading, and exercises with solutions at the end of the book.
Book Synopsis From Finite Sample to Asymptotic Methods in Statistics by : Pranab K. Sen
Download or read book From Finite Sample to Asymptotic Methods in Statistics written by Pranab K. Sen and published by Cambridge University Press. This book was released on 2010 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad view of exact statistical inference and the development of asymptotic statistical inference.
Book Synopsis A Probabilistic Theory of Pattern Recognition by : Luc Devroye
Download or read book A Probabilistic Theory of Pattern Recognition written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Each chapter concludes with problems and exercises to further the readers understanding. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.
Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib
Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.
Book Synopsis Thinking Probabilistically by : Ariel Amir
Download or read book Thinking Probabilistically written by Ariel Amir and published by Cambridge University Press. This book was released on 2020-12-17 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text providing the reader with a thorough background to the rich world of applications of stochastic processes.
