A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton`s Principia, Jacques Fleuriot

Название: Nonstandard analysis for the working mathematician
ISBN: 9401773262 ISBN-13(EAN): 9789401773263
Издательство: Springer
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Описание: it is often used as a `secret weapon` by those who know the technique.This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory.

Автор: A.E. Hurd
Название: Nonstandard Analysis - Recent Developments
ISBN: 3540122796 ISBN-13(EAN): 9783540122791
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Автор: Vladimir Kanovei; Michael Reeken
Название: Nonstandard Analysis, Axiomatically
ISBN: 3642060773 ISBN-13(EAN): 9783642060779
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Описание: 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.

Автор: Sem?n Samsonovich Kutateladze
Название: Nonstandard Analysis and Vector Lattices
ISBN: 9401058636 ISBN-13(EAN): 9789401058636
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Автор: R. Lutz; M. Goze
Название: Nonstandard Analysis.
ISBN: 3540108793 ISBN-13(EAN): 9783540108795
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Автор: Leif O. Arkeryd; Nigel J. Cutland; C. Ward Henson
Название: Nonstandard Analysis
ISBN: 079234586X ISBN-13(EAN): 9780792345862
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Описание: A detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis. Articles concerning more advanced applications in functional analysis include those on stochastic differential equations.

Автор: Newton, Sir Isaac
Название: The Principia
ISBN: 0520088174 ISBN-13(EAN): 9780520088177
Издательство: Wiley
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Описание: In his 1687 work "Philosphiae Naturalis Principia Mathematica", known as the "Principia", Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. This text is a translation, based on the third (1726) edition.

Автор: Imme van den Berg
Название: Nonstandard Asymptotic Analysis
ISBN: 3540177671 ISBN-13(EAN): 9783540177678
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Описание: Considers the subject of asymptotics from a nonstandard view point. Noting that within nonstandard analysis, `small`, `large`, and `domain of validity of asymptotic behaviour` have a precise meaning, this research monograph develops a nonstandard alternative to classical asymptotics.

Автор: A.G. Kusraev; Sem?n Samsonovich Kutateladze
Название: Nonstandard Methods of Analysis
ISBN: 940104497X ISBN-13(EAN): 9789401044974
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Автор: A. Hurd; P. Loeb
Название: Victoria Symposium on Nonstandard Analysis
ISBN: 354006656X ISBN-13(EAN): 9783540066569
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Автор: Imme van den Berg; Vitor Neves
Название: The Strength of Nonstandard Analysis
ISBN: 3211998926 ISBN-13(EAN): 9783211998922
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Описание:

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.

Автор: Leif O. Arkeryd; Nigel J. Cutland; C. Ward Henson
Название: Nonstandard Analysis
ISBN: 9401063354 ISBN-13(EAN): 9789401063357
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Описание: Proceedings of the NATO Advanced Study Institute on Nonstandard Analysis and its Applications, International Centre for Mathematical Studies, Endinburgh, Scotland, 30 June-13 July 1996