Release on 2013-04-22 | by Lynn Arthur Steen,J. Arthur Seebach
Author: Lynn Arthur Steen,J. Arthur Seebach
Pubpsher: Courier Corporation
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.
Release on 1986-06-01 | by Joseph P. Romano,A.F. Siegel
Author: Joseph P. Romano,A.F. Siegel
Pubpsher: CRC Press
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 Several previously unpublished works are included.
"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"--
Release on 1993-10-07 | by Gary L. Wise,Eric B. Hall
Author: Gary L. Wise,Eric B. Hall
Pubpsher: Oxford University Press
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.
Release on 2014-09-09 | by Andrei Bourchtein,Ludmila Bourchtein
From Elementary Calculus to the Beginnings of Analysis
Author: Andrei Bourchtein,Ludmila Bourchtein
Pubpsher: CRC Press
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
Release on 2012-07-12 | by Bernard R. Gelbaum,John M. H. Olmsted
Author: Bernard R. Gelbaum,John M. H. Olmsted
Pubpsher: Courier Corporation
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 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.
This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.
Release on 2012-12-06 | by Bernard R. Gelbaum,John M.H. Olmsted
Author: Bernard R. Gelbaum,John M.H. Olmsted
Pubpsher: Springer Science & Business Media
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.