Theorems And Counterexamples In Mathematics PDF Download
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Author | : Bernard R. Gelbaum |
Publisher | : Springer Science & Business Media |
Total Pages | : 339 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209935 |
Download Theorems and Counterexamples in Mathematics Book in PDF, ePub and Kindle
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 | : Bernard R. Gelbaum |
Publisher | : Courier Corporation |
Total Pages | : 224 |
Release | : 2012-07-12 |
Genre | : Mathematics |
ISBN | : 0486134911 |
Download Counterexamples in Analysis Book in PDF, ePub and Kindle
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. |
Total Pages | : 113 |
Release | : 2010-12-31 |
Genre | : Mathematics |
ISBN | : 0883857650 |
Download Counterexamples in Calculus Book in PDF, ePub and Kindle
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 | : Lynn Arthur Steen |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 0486319296 |
Download Counterexamples in Topology Book in PDF, ePub and Kindle
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 | : Sabita Mahanta |
Publisher | : |
Total Pages | : 296 |
Release | : 2014 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : 9789350843161 |
Download Theorems and Counterexamples in Mathematics Book in PDF, ePub and Kindle
Author | : Michael G. Charalambous |
Publisher | : Springer Nature |
Total Pages | : 261 |
Release | : 2019-10-08 |
Genre | : Mathematics |
ISBN | : 3030222322 |
Download Dimension Theory Book in PDF, ePub and Kindle
This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Author | : Jordan M. Stoyanov |
Publisher | : Courier Corporation |
Total Pages | : 368 |
Release | : 2014-01-15 |
Genre | : Education |
ISBN | : 0486499987 |
Download Counterexamples in Probability Book in PDF, ePub and Kindle
"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"--
Author | : Imre Lakatos |
Publisher | : Cambridge University Press |
Total Pages | : 190 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : 9780521290388 |
Download Proofs and Refutations Book in PDF, ePub and Kindle
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Author | : Martin Aigner |
Publisher | : Springer Science & Business Media |
Total Pages | : 194 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662223430 |
Download Proofs from THE BOOK Book in PDF, ePub and Kindle
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author | : Andrei Bourchtein |
Publisher | : CRC Press |
Total Pages | : 363 |
Release | : 2014-09-09 |
Genre | : Mathematics |
ISBN | : 1482246678 |
Download CounterExamples Book in PDF, ePub and Kindle
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.