The strength of nonstandard analysis

The strength of nonstandard analysis

by Berg, Imme van den Neves, Vitor Manuel Carvalho das

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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,…

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Title Statements

  • Full title :The strength of nonstandard analysis / Imme van den Berg, Vítor Neves (eds.).

Summary

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.

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Edition Statements

  • Publication Date:©2007.

Publication Statements

  • Publisher(s):Springer
  • Place of Publication:Wien
  • Language:eng
  • Publication Date:©2007.

The Physical Object

  • Description:1 online resource (xx, 401 pages) : : illustrations

Edition Identifiers

  • ISBN:9783211499054, 3211499059, 9783211499047, 3211499040
  • DOI:10.1007/978-3-211-49905-4
  • oclc:ocn232363427
  • LC Classification:QA299.82
  • Dewey Decimal:515

Table of Contents

pt. I. Foundations -- pt. II. Number theory -- pt. III. Statistics, probability and measures -- pt. IV. Differential systems and equations -- pt. V. Infinitesimals and education.

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Subjects

Actes de congrès Analyse mathématique non standard -- Co… Conference papers and proceedings Congress MATHEMATICS -- Calculus Mathematics -- Mathematical Analysis Nonstandard mathematical analysis Nonstandard mathematical analysis -- Co…

Writers

Berg, Imme van den Neves, Vitor Manuel Carvalho das

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