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Nonstandard Analysis for the Working Mathematician

Editors: Loeb, Peter, Wolff, Manfred P. H. (Eds.)

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  • 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
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eBook $84.99
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  • ISBN 978-94-017-7327-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for Mexico
Softcover $109.99
price for Mexico
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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $84.99
price for Mexico
  • ISBN 978-94-017-7327-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for Mexico
Softcover $109.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Nonstandard Analysis for the Working Mathematician
Editors
  • Peter Loeb
  • Manfred P. H. Wolff
Copyright
2015
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-7327-0
DOI
10.1007/978-94-017-7327-0
Hardcover ISBN
978-94-017-7326-3
Softcover ISBN
978-94-017-7624-0
Edition Number
2
Number of Pages
XV, 481
Topics