Nonstandard Analysis Axiomatically
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Nonstandard Analysis Axiomatically
Author | : Vladimir Kanovei,Michael Reeken |
Publsiher | : Springer Science & Business Media |
Total Pages | : 421 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9783662089989 |
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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.
Non standard Analysis
Author | : Abraham Robinson |
Publsiher | : Princeton University Press |
Total Pages | : 308 |
Release | : 2016-08-11 |
Genre | : Mathematics |
ISBN | : 9781400884223 |
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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.
Nonstandard Analysis
Author | : Alain Robert |
Publsiher | : Courier Corporation |
Total Pages | : 184 |
Release | : 2003-01-01 |
Genre | : Mathematics |
ISBN | : 0486432793 |
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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.
Nonstandard Analysis Axiomatically
Author | : Vladimir Kanovei,Michael Reeken |
Publsiher | : Unknown |
Total Pages | : 428 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 3662089998 |
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A Primer of Infinitesimal Analysis
Author | : John L. Bell |
Publsiher | : Cambridge University Press |
Total Pages | : 7 |
Release | : 2008-04-07 |
Genre | : Mathematics |
ISBN | : 9780521887182 |
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A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Standard and Nonstandard Analysis
Author | : R. F. Hoskins |
Publsiher | : Ellis Horwood |
Total Pages | : 280 |
Release | : 1990 |
Genre | : Mathematical analysis |
ISBN | : UCSC:32106009921864 |
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A course in the foundations of elementary analysis, this book provides an introduction to non-standard concepts and techniques. The text aims to be accessible to mathematicians, physicists, engineers and students in related disciplines.
Real Analysis Through Modern Infinitesimals
Author | : Nader Vakil |
Publsiher | : Cambridge University Press |
Total Pages | : 587 |
Release | : 2011-02-17 |
Genre | : Mathematics |
ISBN | : 9781107002029 |
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A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
The Strength of Nonstandard Analysis
Author | : Imme van den Berg,Vitor Neves |
Publsiher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2007-12-03 |
Genre | : Mathematics |
ISBN | : 9783211499054 |
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This book reflects the progress made in the forty years since the appearance of Abraham 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.