Nonstandard Analysis for the Working Mathematician:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
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Schriftenreihe: | Mathematics and Its Applications
510 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of nonstan dard analysis in Part I, and then to illuminate some of its most striking applications. Much of the book, in particular Part I, can be used in a graduate course; problems are posed in all chapters. After Part I, each chapter takes up a different field for the application of nonstandard analysis, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use nonstandard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insight into the field under consideration. The applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In all of these areas, the intuitive notion of an infinitely small or infinitely large quantity plays an essential and helpful role in the creative process. For example, Brownian motion is often thought of as a random walk with infinitesimal increments; the spectrum of a selfadjoint operator is viewed as the set of "almost eigenvalues"; an ideal economy consists of an infinite number of agents each having an infinitesimal influence on the economy. Already at the level of calculus, one often views the integral as an infinitely large sum of infinitesimal quantities |
Beschreibung: | 1 Online-Ressource (XIV, 311 p) |
ISBN: | 9789401141680 9780792363415 |
DOI: | 10.1007/978-94-011-4168-0 |
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Datensatz im Suchindex
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institution | BVB |
isbn | 9789401141680 9780792363415 |
language | English |
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spelling | Loeb, Peter A. Verfasser aut Nonstandard Analysis for the Working Mathematician edited by Peter A. Loeb, Manfred Wolff Dordrecht Springer Netherlands 2000 1 Online-Ressource (XIV, 311 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 510 This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of nonstan dard analysis in Part I, and then to illuminate some of its most striking applications. Much of the book, in particular Part I, can be used in a graduate course; problems are posed in all chapters. After Part I, each chapter takes up a different field for the application of nonstandard analysis, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use nonstandard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insight into the field under consideration. The applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In all of these areas, the intuitive notion of an infinitely small or infinitely large quantity plays an essential and helpful role in the creative process. For example, Brownian motion is often thought of as a random walk with infinitesimal increments; the spectrum of a selfadjoint operator is viewed as the set of "almost eigenvalues"; an ideal economy consists of an infinite number of agents each having an infinitesimal influence on the economy. Already at the level of calculus, one often views the integral as an infinitely large sum of infinitesimal quantities Mathematics Logic, Symbolic and mathematical Distribution (Probability theory) Real Functions Probability Theory and Stochastic Processes Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Nonstandard-Analysis (DE-588)4137021-1 s 1\p DE-604 Wolff, Manfred Sonstige oth https://doi.org/10.1007/978-94-011-4168-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Loeb, Peter A. Nonstandard Analysis for the Working Mathematician Mathematics Logic, Symbolic and mathematical Distribution (Probability theory) Real Functions Probability Theory and Stochastic Processes Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
subject_GND | (DE-588)4137021-1 |
title | Nonstandard Analysis for the Working Mathematician |
title_auth | Nonstandard Analysis for the Working Mathematician |
title_exact_search | Nonstandard Analysis for the Working Mathematician |
title_full | Nonstandard Analysis for the Working Mathematician edited by Peter A. Loeb, Manfred Wolff |
title_fullStr | Nonstandard Analysis for the Working Mathematician edited by Peter A. Loeb, Manfred Wolff |
title_full_unstemmed | Nonstandard Analysis for the Working Mathematician edited by Peter A. Loeb, Manfred Wolff |
title_short | Nonstandard Analysis for the Working Mathematician |
title_sort | nonstandard analysis for the working mathematician |
topic | Mathematics Logic, Symbolic and mathematical Distribution (Probability theory) Real Functions Probability Theory and Stochastic Processes Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
topic_facet | Mathematics Logic, Symbolic and mathematical Distribution (Probability theory) Real Functions Probability Theory and Stochastic Processes Mathematical Logic and Foundations Mathematik Nonstandard-Analysis |
url | https://doi.org/10.1007/978-94-011-4168-0 |
work_keys_str_mv | AT loebpetera nonstandardanalysisfortheworkingmathematician AT wolffmanfred nonstandardanalysisfortheworkingmathematician |