Overview
- Presents the version of nonstandard analysis that has had the greatest success and the widest scope of applications
- Includes some of the most recent applications in various fields of mathematical analysis and probability
- Each chapter, covering a different application of nonstandard analysis, begins with a gentle introduction for the non-expert
- Includes supplementary material: sn.pub/extras
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Table of contents (11 chapters)
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Front Matter
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An Introduction to Nonstandard Analysis
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Front Matter
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Functional Analysis
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Front Matter
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Compactifications
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Front Matter
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Measure and Probability Theory
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Front Matter
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Economics and Nonstandard Analysis
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Front Matter
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Combinatorial Number Theory
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Front Matter
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Back Matter
Keywords
About this book
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; 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. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems.
All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Editors and Affiliations
Bibliographic Information
Book Title: Nonstandard Analysis for the Working Mathematician
Editors: Peter A. Loeb, Manfred P. H. Wolff
DOI: https://doi.org/10.1007/978-94-017-7327-0
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2015
Hardcover ISBN: 978-94-017-7326-3Published: 03 September 2015
Softcover ISBN: 978-94-017-7624-0Published: 23 October 2016
eBook ISBN: 978-94-017-7327-0Published: 26 August 2015
Edition Number: 2
Number of Pages: XV, 481
Topics: Functional Analysis, Measure and Integration, Operator Theory, Game Theory, Economics, Social and Behav. Sciences, Mathematical Logic and Foundations, Number Theory