Nonstandard Analysis Axiomatically
DOWNLOAD
Download Nonstandard Analysis Axiomatically PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Nonstandard Analysis Axiomatically book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Nonstandard Analysis Axiomatically
DOWNLOAD
Author : Vladimir Grigorʹevich Kanoveĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-11
Nonstandard Analysis Axiomatically written by Vladimir Grigorʹevich Kanoveĭ 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 2004-08-11 with Mathematics categories.
The book is devoted to nonstandard set theories that serve as foundational basis for nonstandard mathematics. Several popular and some less known nonstandard theories are considered, including internal set theory IST, Hrbacek set theory HST, and others. The book presents the basic structure of the set universe of these theories and methods to effectively develop "applied" nonstandard analysis, metamathematical properties and interrelations of these nonstandard theories between each other and with ZFC and some variants of ZFC, foundational problems of the theories, including the problem of external sets and the Power Set problem, and methods of their solution. The book is oriented towards a reader having some experience in foundations (set theory, model theory) and in nonstandard analysis.
Nonstandard Analysis Axiomatically
DOWNLOAD
Author : Vladimir Kanovei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Nonstandard Analysis Axiomatically written by Vladimir Kanovei 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 2013-03-09 with Mathematics categories.
In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
Nonstandard Analysis
DOWNLOAD
Author : Alain Robert
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Nonstandard Analysis written by Alain Robert and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.
Non Standard Analysis
DOWNLOAD
Author : Abraham Robinson
language : en
Publisher: Princeton University Press
Release Date : 2016-08-11
Non Standard Analysis written by Abraham Robinson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-11 with Mathematics categories.
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
A Primer Of Infinitesimal Analysis
DOWNLOAD
Author : John L. Bell
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-07
A Primer Of Infinitesimal Analysis written by John L. Bell 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 2008-04-07 with Mathematics categories.
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Real Analysis Through Modern Infinitesimals
DOWNLOAD
Author : Nader Vakil
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-17
Real Analysis Through Modern Infinitesimals written by Nader Vakil 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 2011-02-17 with Mathematics categories.
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Lectures On The Hyperreals
DOWNLOAD
Author : Robert Goldblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On The Hyperreals written by Robert Goldblatt 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.
There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem.
Nonstandard Analysis
DOWNLOAD
Author : Martin Väth
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Nonstandard Analysis written by Martin Väth 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 2007 with Mathematics categories.
This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
The Strength Of Nonstandard Analysis
DOWNLOAD
Author : Imme van den Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03
The Strength Of Nonstandard Analysis written by Imme van den Berg 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 2007-12-03 with Mathematics categories.
Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.