The Strength of Nonstandard Analysis
Editors: Berg, Imme van den, Neves, Vitor (Eds.)
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- About this book
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Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations.
This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
- Table of contents (25 chapters)
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The strength of nonstandard analysis
Pages 3-26
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The virtue of simplicity
Pages 27-32
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Analysis of various practices of referring in classical or non standard mathematics
Pages 33-46
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Stratified analysis?
Pages 47-63
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ERNA at work
Pages 64-75
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Table of contents (25 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- The Strength of Nonstandard Analysis
- Editors
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- Imme van den Berg
- Vitor Neves
- Copyright
- 2007
- Publisher
- Springer-Verlag Wien
- Copyright Holder
- Springer-Verlag Vienna
- eBook ISBN
- 978-3-211-49905-4
- DOI
- 10.1007/978-3-211-49905-4
- Hardcover ISBN
- 978-3-211-49904-7
- Softcover ISBN
- 978-3-211-99892-2
- Edition Number
- 1
- Number of Pages
- XX, 401
- Number of Illustrations
- 16 b/w illustrations
- Topics
