The Random Walks Of George Polya
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The Random Walks Of George Polya
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Author : Gerald L. Alexanderson
language : en
Publisher: Cambridge University Press
Release Date : 2000-04-27
The Random Walks Of George Polya written by Gerald L. Alexanderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-27 with Biography & Autobiography categories.
Both a biography of Pólya's life, and a review of his many mathematical achievements by today's experts.
Random Walks And Electric Networks
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Author : Peter G. Doyle
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Random Walks And Electric Networks written by Peter G. Doyle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Electric network topology categories.
Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
How To Solve It
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Author : George Polya
language : en
Publisher: Princeton University Press
Release Date : 2014-10-27
How To Solve It written by George Polya and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-27 with Education categories.
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
Algebraic Combinatorics
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Author : Richard P. Stanley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-17
Algebraic Combinatorics written by Richard P. Stanley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Mathematics categories.
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Fundamentals Of Probability
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Author : Saeed Ghahramani
language : en
Publisher: CRC Press
Release Date : 2015-11-04
Fundamentals Of Probability written by Saeed Ghahramani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-04 with Mathematics categories.
Fundamentals of Probability with Stochastic Processes, Third Edition teaches probability in a natural way through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. The author takes a mathematically rigorous approach while closely adhering to the historical development of probability
Random Walk A Modern Introduction
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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Very First Steps In Random Walks
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Author : Norbert Henze
language : en
Publisher: Springer Nature
Release Date : 2025-02-11
Very First Steps In Random Walks written by Norbert Henze and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-11 with Mathematics categories.
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Random Walk And The Heat Equation
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-11-22
Random Walk And The Heat Equation written by Gregory F. Lawler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Mathematics categories.
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.
Random Walks On Infinite Graphs And Groups
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Author : Wolfgang Woess
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Random Walks On Infinite Graphs And Groups written by Wolfgang Woess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Coin Turning Random Walks And Inhomogeneous Markov Chains
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Author : Janos Englander
language : en
Publisher: World Scientific
Release Date : 2024-11-22
Coin Turning Random Walks And Inhomogeneous Markov Chains written by Janos Englander and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-22 with Mathematics categories.
This research monograph explores new frontiers in Markov chains. Although time-homogeneous Markov chains are well understood, this is not at all the case with time-inhomogeneous ones. The book, after a review on the classical theory of homogeneous chains, including the electrical network approach, introduces several new models which involve inhomogeneous chains as well as related new types of random walks (for example, 'coin turning', 'conservative' and 'Rademacher' walk). Scaling limits, the breakdown of the classical limit theorems as well as recurrence and transience are investigated. The relationship with urn models is the subject of two chapters, providing additional connections to other parts of probability theory.Random walks on random graphs are discussed as well, as an area where the method of electric networks is especially useful. This is illustrated by presenting random walks in random environments and random labyrinths.The monograph puts emphasis on showing examples and open problems besides providing rigorous analysis of the models.Several figures illustrate the main ideas, and a large number of exercises challenge the interested reader.