Nonstandard Analysis : Theory and Applications

Language: English

Published by Springer, 2012

9401063354 / 9789401063357

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Druck auf Anfrage Neuware - Printed after ordering - 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.

Seller Inventory # 9789401063357

Title
Nonstandard Analysis : Theory and Applications
Author
Nigel J. Cutland
Publisher
Springer
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
9401063354
ISBN 13
9789401063357
Item weight
612 grams
Dimensions
240x160x21 mm

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