Counterexamples In Probability And Real Analysis
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Counterexamples In Probability And Real Analysis
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Author : Gary L. Wise
language : en
Publisher: Oxford University Press
Release Date : 1993-10-07
Counterexamples In Probability And Real Analysis written by Gary L. Wise and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-07 with Mathematics categories.
A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.
Counterexamples In Analysis
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Author : Bernard R. Gelbaum
language : en
Publisher: Courier Corporation
Release Date : 2012-07-12
Counterexamples In Analysis written by Bernard R. Gelbaum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-12 with Mathematics categories.
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Counterexamples In Probability And Real Analysis
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Author : Gary L. Wise
language : en
Publisher:
Release Date : 1993
Counterexamples In Probability And Real Analysis written by Gary L. Wise and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Electronic books categories.
Counterexamples In Probability
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Author : Jordan M. Stoyanov
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
Counterexamples In Probability written by Jordan M. Stoyanov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
"While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--
Counterexamples In Calculus
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Author : Sergiy Klymchuk
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-12-31
Counterexamples In Calculus written by Sergiy Klymchuk 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 2010-12-31 with Mathematics categories.
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Measure Integration Real Analysis
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Author : Sheldon Axler
language : en
Publisher: Springer
Release Date : 2019-12-24
Measure Integration Real Analysis written by Sheldon Axler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.
Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Counterexamples In Probability And Statistics
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Author : Joseph P. Romano
language : en
Publisher: CRC Press
Release Date : 1986-06-01
Counterexamples In Probability And Statistics written by Joseph P. Romano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-06-01 with Mathematics categories.
This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.
Counterexamples In Probability And Statistics
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Author : A.F. Siegel
language : en
Publisher: Routledge
Release Date : 2017-11-22
Counterexamples In Probability And Statistics written by A.F. Siegel and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.
Counterexamples In Topology
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Author : Lynn Arthur Steen
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Counterexamples In Topology written by Lynn Arthur Steen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.