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The Strength of Nonstandard Analysis

  • Imme van den Berg
  • Vítor Neves

Table of contents

  1. Front Matter
    Pages i-xx
  2. Foundations

    1. Front Matter
      Pages 1-1
    2. H. Jerome Keisler
      Pages 3-26
    3. Edward Nelson
      Pages 27-32
    4. Karel Hrbacek
      Pages 47-63
    5. C. Impens, S. Sanders
      Pages 64-75
    6. Imme van den Berg
      Pages 92-116
  3. Number theory

  4. Statistics, probability and measures

  5. Differential systems and equations

  6. Infinitesimals and education

    1. Front Matter
      Pages 367-367
    2. Keith D. Stroyan
      Pages 369-394
    3. Richard O’Donovan
      Pages 395-401

About this book

Introduction

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.

Keywords

Likelihood Problem solving Stochastic processes calculus differential equation differential equations education infinitesimals measure number theory ordinary differential equation probability ratio test statistics stochastic process

Editors and affiliations

  • Imme van den Berg
    • 1
  • Vítor Neves
    • 2
  1. 1.Departamento de MatemáticaUniversidade de ÉvoraÉvoraPortugal
  2. 2.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal

Bibliographic information