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Counterexamples In Analysis
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Book Synopsis Counterexamples in Analysis by : Bernard R. Gelbaum
Download or read book Counterexamples in Analysis written by Bernard R. Gelbaum and published by Courier Corporation. This book was released on 2012-07-12 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Counterexamples in Analysis by : Bernard R. Gelbaum
Download or read book Counterexamples in Analysis written by Bernard R. Gelbaum and published by Courier Corporation. This book was released on 2003-06-04 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
Book Synopsis Counterexamples in Topology by : Lynn Arthur Steen
Download or read book Counterexamples in Topology written by Lynn Arthur Steen and published by Courier Corporation. This book was released on 2013-04-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theorems and Counterexamples in Mathematics by : Bernard R. Gelbaum
Download or read book Theorems and Counterexamples in Mathematics written by Bernard R. Gelbaum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.
Book Synopsis Counterexamples in Probability and Real Analysis by : Gary L. Wise
Download or read book Counterexamples in Probability and Real Analysis written by Gary L. Wise and published by Oxford University Press. This book was released on 1993-10-07 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Counterexamples in Calculus by : Sergiy Klymchuk
Download or read book Counterexamples in Calculus written by Sergiy Klymchuk and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis CounterExamples by : Andrei Bourchtein
Download or read book CounterExamples written by Andrei Bourchtein and published by CRC Press. This book was released on 2014-09-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 authors present an overview of important concepts and results in calculus and real analysis by considering false statements, which may appear to be true at first glance. The book covers topics concerning the functions of real variables, starting with elementary properties, moving to limits and continuity, and then to differentiation and integration. The first part of the book describes single-variable functions, while the second part covers the functions of two variables. The many examples presented throughout the book typically start at a very basic level and become more complex during the development of exposition. At the end of each chapter, supplementary exercises of different levels of complexity are provided, the most difficult of them with a hint to the solution. This book is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.
Book Synopsis Counterexamples in Probability by : Jordan M. Stoyanov
Download or read book Counterexamples in Probability written by Jordan M. Stoyanov and published by Courier Corporation. This book was released on 2014-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
Book Synopsis Counterexamples in Measure and Integration by : René L. Schilling
Download or read book Counterexamples in Measure and Integration written by René L. Schilling and published by Cambridge University Press. This book was released on 2021-06-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
Book Synopsis Lectures on Counterexamples in Several Complex Variables by : John Erik Fornæss
Download or read book Lectures on Counterexamples in Several Complex Variables written by John Erik Fornæss and published by American Mathematical Soc.. This book was released on with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornaess and Stensones look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampere equations, CR geometry, function theory, and the $\bar\partial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.
Book Synopsis Introduction to Analysis by : Maxwell Rosenlicht
Download or read book Introduction to Analysis written by Maxwell Rosenlicht and published by Courier Corporation. This book was released on 2012-05-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
Book Synopsis Counterexamples on Uniform Convergence by : Andrei Bourchtein
Download or read book Counterexamples on Uniform Convergence written by Andrei Bourchtein and published by John Wiley & Sons. This book was released on 2017-02-13 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and thorough analysis of concepts and results on uniform convergence Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals presents counterexamples to false statements typically found within the study of mathematical analysis and calculus, all of which are related to uniform convergence. The book includes the convergence of sequences, series and families of functions, and proper and improper integrals depending on a parameter. The exposition is restricted to the main definitions and theorems in order to explore different versions (wrong and correct) of the fundamental concepts and results. The goal of the book is threefold. First, the authors provide a brief survey and discussion of principal results of the theory of uniform convergence in real analysis. Second, the book aims to help readers master the presented concepts and theorems, which are traditionally challenging and are sources of misunderstanding and confusion. Finally, this book illustrates how important mathematical tools such as counterexamples can be used in different situations. The features of the book include: An overview of important concepts and theorems on uniform convergence Well-organized coverage of the majority of the topics on uniform convergence studied in analysis courses An original approach to the analysis of important results on uniform convergence based\ on counterexamples Additional exercises at varying levels of complexity for each topic covered in the book A supplementary Instructor’s Solutions Manual containing complete solutions to all exercises, which is available via a companion website Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals is an appropriate reference and/or supplementary reading for upper-undergraduate and graduate-level courses in mathematical analysis and advanced calculus for students majoring in mathematics, engineering, and other sciences. The book is also a valuable resource for instructors teaching mathematical analysis and calculus. ANDREI BOURCHTEIN, PhD, is Professor in the Department of Mathematics at Pelotas State University in Brazil. The author of more than 100 referred articles and five books, his research interests include numerical analysis, computational fluid dynamics, numerical weather prediction, and real analysis. Dr. Andrei Bourchtein received his PhD in Mathematics and Physics from the Hydrometeorological Center of Russia. LUDMILA BOURCHTEIN, PhD, is Senior Research Scientist at the Institute of Physics and Mathematics at Pelotas State University in Brazil. The author of more than 80 referred articles and three books, her research interests include real and complex analysis, conformal mappings, and numerical analysis. Dr. Ludmila Bourchtein received her PhD in Mathematics from Saint Petersburg State University in Russia.
Book Synopsis Topology for Analysis by : Albert Wilansky
Download or read book Topology for Analysis written by Albert Wilansky and published by Courier Corporation. This book was released on 2008-10-17 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.
Book Synopsis Counterexamples in Topological Vector Spaces by : S.M. Khaleelulla
Download or read book Counterexamples in Topological Vector Spaces written by S.M. Khaleelulla and published by Springer. This book was released on 2006-11-17 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Real Mathematical Analysis by : Charles Chapman Pugh
Download or read book Real Mathematical Analysis written by Charles Chapman Pugh and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler
Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. For errata and updates, visit https://measure.axler.net/
Book Synopsis Counterexamples in Probability by : Jordan M. Stoyanov
Download or read book Counterexamples in Probability written by Jordan M. Stoyanov and published by Wiley. This book was released on 1997-07-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Counterexamples (in the mathematical sense) are powerful tools of mathematical theory. This book covers counterexamples from probability theory and stochastic processes. This new expanded edition includes many examples and the latest research results. The author is regarded as one of the foremost experts in the field. Contains numbers examples.
