The Strength of Nonstandard Analysis / Edition 1

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More About This Textbook

Overview

This book reflects the progress made in the forty years since the appearance of Abraham Robinson’s revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and shastic differential equations and in education. The contributions are clear and essentially self-contained.

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Product Details

  • ISBN-13: 9783211998922
  • Publisher: Springer Vienna
  • Publication date: 4/6/2011
  • Edition description: Softcover reprint of hardcover 1st ed. 2007
  • Edition number: 1
  • Pages: 401
  • Product dimensions: 0.87 (w) x 6.69 (h) x 9.61 (d)

Table of Contents

Foundations: The strength of nonstandard analysis (J. Keisler); The virtue of simplicity (E. Nelson); Analysis of various practices of referring in classical or non standard mathematics (Y. Péraire); Stratified analysis? (K. Hrbacek); ERNA at work (C. Impens/S. Sanders); The Sousa Pinto approach to nonstandard generalised functions (R. F. Hoskins); Neutrices in more dimensions (I. van den Berg).- Number theory: Nonstandard methods for additive and combinatorial number theory. A survey (R. Jin); Nonstandard methods and the Erdös-Turán conjecture (S. C. Leth).- Statistics, probability and measures: Nonstandard likelihood ratio test in exponential families (J. Bosgiraud); A finitary approach for the representation of the infinitesimal generator of a markovian semigroup (S. Benhabib); On two recent applications of nonstandard analysis to the theory of financial markets (F. S. Herzberg); Quantum Bernoulli experiments and quantum shastic processes (M. Wolff); Applications of rich measure spaces formed from nonstandard models (P. Loeb); More on S-measures (D. A. Ross); A Radon-Nikodým theorem for a vector-valued reference measure (G. B. Zimmer); Differentiability of Loeb measures (E. Aigner).- Differential systems and equations: The power of Gâteaux differentiability (V. Neves); Nonstandard Palais-Smale conditions (N. Martins/V. Neves); Averaging for ordinary differential equations and functional differential equations (T. Sari); Path-space measure for shastic differential equation with a coefficient of polynomial growth (T. Nakamura); Optimal control for Navier-Stokes equations (N. J. Cutland/K. Grzesiak); Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations (J. P. Teixeira).- Infinitesimals and education: Calculus with infinitesimals (K. D. Stroyan); Pre-University Analysis (R. O’Donovan).

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