Nonstandard Analysis: Theory and Applications
Gespeichert in:
| Weitere Verfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | NATO ASI Series, Series C: Mathematical and Physical Sciences
493 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 important 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 recur. 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 approach 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 applicability of NSA more widely known and available to research mathematicians |
| Beschreibung: | 1 Online-Ressource (XIV, 366 p) |
| ISBN: | 9789401155441 9789401063357 |
| ISSN: | 1389-2185 |
| DOI: | 10.1007/978-94-011-5544-1 |
Internformat
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| 246 | 1 | 3 | |a 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 |
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| 490 | 1 | |a NATO ASI Series, Series C: Mathematical and Physical Sciences |v 493 |x 1389-2185 | |
| 500 | |a 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 important 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 recur. 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 approach 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 applicability of NSA more widely known and available to research mathematicians | ||
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Datensatz im Suchindex
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
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| spelling | Arkeryd, Leif O. edt Nonstandard Analysis Theory and Applications edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson 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 Dordrecht Springer Netherlands 1997 1 Online-Ressource (XIV, 366 p) txt rdacontent c rdamedia cr rdacarrier NATO ASI Series, Series C: Mathematical and Physical Sciences 493 1389-2185 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 important 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 recur. 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 approach 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 applicability of NSA more widely known and available to research mathematicians Mathematics Global analysis (Mathematics) Functional analysis Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Functional Analysis Applications of Mathematics Fluid- and Aerodynamics Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Nonstandard-Analysis (DE-588)4137021-1 s 2\p DE-604 Cutland, Nigel J. edt Henson, C. Ward edt NATO ASI Series, Series C Mathematical and Physical Sciences 493 (DE-604)BV000902768 493 https://doi.org/10.1007/978-94-011-5544-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nonstandard Analysis Theory and Applications Mathematics Global analysis (Mathematics) Functional analysis Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Functional Analysis Applications of Mathematics Fluid- and Aerodynamics Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)1071861417 |
| title | Nonstandard Analysis Theory and Applications |
| title_alt | 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 |
| title_auth | Nonstandard Analysis Theory and Applications |
| title_exact_search | Nonstandard Analysis Theory and Applications |
| title_full | Nonstandard Analysis Theory and Applications edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson |
| title_fullStr | Nonstandard Analysis Theory and Applications edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson |
| title_full_unstemmed | Nonstandard Analysis Theory and Applications edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson |
| title_short | Nonstandard Analysis |
| title_sort | nonstandard analysis theory and applications |
| title_sub | Theory and Applications |
| topic | Mathematics Global analysis (Mathematics) Functional analysis Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Functional Analysis Applications of Mathematics Fluid- and Aerodynamics Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Functional analysis Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Functional Analysis Applications of Mathematics Fluid- and Aerodynamics Mathematik Nonstandard-Analysis Konferenzschrift |
| url | https://doi.org/10.1007/978-94-011-5544-1 |
| volume_link | (DE-604)BV000902768 |
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