Counterexamples
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Counterexamples
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Author : Andrei Bourchtein
language : en
Publisher: CRC Press
Release Date : 2014-09-09
Counterexamples written by Andrei Bourchtein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-09 with Mathematics categories.
This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples.In this book, the
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 Several previously unpublished works are included.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 Topology
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Author : L.A. Steen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Counterexamples In Topology written by L.A. Steen 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 2012-12-06 with Mathematics categories.
The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples. Al though it would be hazardous to claim that the creation of significant examples is less demanding than the development of theory, we have dis covered that focusing on examples is a particularly expeditious means of involving undergraduate mathematics students in actual research. Not only are examples more concrete than theorems-and thus more accessible-but they cut across individual theories and make it both appropriate and neces sary for the student to explore the entire literature in journals as well as texts. Indeed, much of the content of this book was first outlined by under graduate research teams working with the authors at Saint Olaf College during the summers of 1967 and 1968. In compiling and editing material for this book, both the authors and their undergraduate assistants realized a substantial increment in topologi cal insight as a direct result of chasing through details of each example. We hope our readers will have a similar experience. Each of the 143 examples in this book provides innumerable concrete illustrations of definitions, theo rems, and general methods of proof. There is no better way, for instance, to learn what the definition of metacompactness really means than to try to prove that Niemytzki's tangent disc topology is not metacompact. The search for counterexamples is as lively and creative an activity as can be found in mathematics research.
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.
Counterexamples In Operator Theory
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Author : Mohammed Hichem Mortad
language : en
Publisher: Springer Nature
Release Date : 2022-05-03
Counterexamples In Operator Theory written by Mohammed Hichem Mortad and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-03 with Mathematics categories.
This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students. The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief “Basics” section for the readers’ reference, and many of the counterexamples included are the author’s original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.
Counterexamples In Measure And Integration
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Author : René L. Schilling
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-17
Counterexamples In Measure And Integration written by René L. Schilling 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 2021-06-17 with Mathematics categories.
Explore measure and integration theory by asking 'What can go wrong if...' with this selection of over 300 counterexamples.
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
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Author : Ĭordan Stoi︠a︡nov
language : en
Publisher: John Wiley & Sons
Release Date : 1987
Counterexamples In Probability written by Ĭordan Stoi︠a︡nov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Counterexamples (in the usual mathematical sense) are powerful tools of mathematical theory. In this book the author gives more than 250 drawn from the whole field of probability theory and stochastic processes. The counterexamples are selected for their interest and for the importance of the theory they illustrate. Each section starts with a summary of definitions and main results, followed by counterexamples ordered by content and difficulty. Full references and additional sources are given.
Methoden Und Beschreibungssprachen Zur Modellierung Und Verifikation Von Schaltungen Und Systemen
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Author : Carsten Gremzow
language : en
Publisher: Univerlagtuberlin
Release Date : 2009
Methoden Und Beschreibungssprachen Zur Modellierung Und Verifikation Von Schaltungen Und Systemen written by Carsten Gremzow and has been published by Univerlagtuberlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
The Role Of Counterexamples In The Development Of Mathematical Concepts Of Eighth Grade Mathematics Students
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Author : Richard James Shumway
language : en
Publisher:
Release Date : 1969
The Role Of Counterexamples In The Development Of Mathematical Concepts Of Eighth Grade Mathematics Students written by Richard James Shumway and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Concepts categories.