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Nonstandard Methods and Applications in Mathematics

Nonstandard Methods and Applications in Mathematics

$79.00 USD

Part of Lecture Notes in Logic

Vieri Benci, Mauro Di Nasso, Marco Forti, Sergio Fajardo, H. Jerome Keisler, Karel Hrbacek, Peter A. Loeb, David A. Ross, Renling Jin, Angus Macintyre, Nigel J. Cutland, Manfred P. H. Wolff, Richard O'Donovan, John Kimber
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  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108621298

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About the Authors
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.

    • Contains survey articles and research papers by leading logicians
    • Includes a paper detailing an innovative attempt to use a modern infinitesimal approach in teaching high school calculus
    • Updates older surveys and includes research articles on applications too recent to be included in older volumes
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    Product details

    • format: Adobe eBook Reader
    • isbn: 9781108621298
    • contains: 3 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Foundations: the eigtfold path to nonstandard analysis Vieri Benci, Mauro Di Nasso and Marco Forti
    2. Neoclosed forcing Sergio Fajardo and H. Jerome Keisler
    3. Nonstandard objects in set theory Karel Hrbacek
    4. Pure mathematics: the microscopic behavior of measurable functions Peter A. Loeb
    5. Nonstandard measure constructions – solutions and problems David A. Ross
    6. Inverse problem for upper asymptotic density Renling Jin
    7. Nonstandard analysis and cohomology Angus Macintyre
    8. Applied mathematics: Loeb space methods for stochastic Navier–Stokes equations Nigel J. Cutland
    9. Discrete approximation of compact operators and approximation of their spectra Manfred P. H. Wolff
    10. Teaching: nonstandard analysis at pre-university level: naive magnitude analysis Richard O'Donovan and John Kimber.

  • Editors

    Nigel J. Cutland, University of York
    Nigel J. Cutland is a Professor of Mathematics at the University of York where he researches logic and foundations of mathematics, stochastic analysis and nonstandard analysis and its applications.

    Mauro Di Nasso, Università degli Studi, Pisa
    Mauro Di Nasso is a Professor at the Università degli Studi, Pisa where he researches model theory and nonstandard analysis.

    David A. Ross, University of Hawaii, Manoa
    David A. Ross is a Professor at the University of Hawaii, Manoa where he researches nonstandard analysis and probability theory.

    Contributors

    Vieri Benci, Mauro Di Nasso, Marco Forti, Sergio Fajardo, H. Jerome Keisler, Karel Hrbacek, Peter A. Loeb, David A. Ross, Renling Jin, Angus Macintyre, Nigel J. Cutland, Manfred P. H. Wolff, Richard O'Donovan, John Kimber

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