[PDF] Counterexamples In Calculus eBook

Author : Sergiy Klymchuk
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 47,63 MB
Release : 2010-12-31
Category : Mathematics
ISBN : 0883857650

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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.

Author : Bernard R. Gelbaum
Publisher : Courier Corporation
Page : 226 pages
File Size : 16,7 MB
Release : 2012-07-12
Category : Mathematics
ISBN : 0486134911

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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.

Author : Sergiy Klymchuk
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 24,90 MB
Release : 2010-12-31
Category : Mathematics
ISBN : 161444109X

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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.

Author : Bernard R. Gelbaum
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 12,21 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461209935

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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.

Author : Andrei Bourchtein
Publisher : CRC Press
Page : 358 pages
File Size : 46,84 MB
Release : 2014-09-09
Category : Mathematics
ISBN : 1482246686

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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

Author : Lynn Arthur Steen
Publisher : Courier Corporation
Page : 274 pages
File Size : 36,25 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486319296

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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.

Author : John Mason
Publisher :
Page : 124 pages
File Size : 33,84 MB
Release : 2009
Category : Mathematics
ISBN : 9781848163591

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This book makes accessible to calculus students in high school, college and university a range of counter-examples to "conjectures" that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems.

Author : John H Mason
Publisher : Imperial College Press
Page : 116 pages
File Size : 21,35 MB
Release : 2009-05-25
Category : Mathematics
ISBN : 191129850X

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This book makes accessible to calculus students in high school, college and university a range of counter-examples to “conjectures” that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems./a

Author : Gary L. Wise
Publisher : Oxford University Press
Page : 224 pages
File Size : 45,46 MB
Release : 1993-10-07
Category : Mathematics
ISBN : 019536130X

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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.