rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Strength of Nonstandard Analysis
  name:
    name part: Berg, Imme van den.
    role:
      role term: editor.
  name:
    name part: Neves, Vítor.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: au
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 401 p. 16 illus. online resource.
  abstract: 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: Foundations -- The strength of nonstandard analysis -- The virtue of simplicity -- Analysis of various practices of referring in classical or non standard mathematics -- Stratified analysis? -- ERNA at work -- The Sousa Pinto approach to nonstandard generalised functions -- Neutrices in more dimensions -- Number theory -- Nonstandard methods for additive and combinatorial number theory. A survey -- Nonstandard methods and the Erd?s-Turán conjecture -- Statistics, probability and measures -- Nonstandard likelihood ratio test in exponential families -- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup -- On two recent applications of nonstandard analysis to the theory of financial markets -- Quantum Bernoulli experiments and quantum stochastic processes -- Applications of rich measure spaces formed from nonstandard models -- More on S-measures -- A Radon-Nikodým theorem for a vector-valued reference measure -- Differentiability of Loeb measures -- Differential systems and equations -- The power of Gâteaux differentiability -- Nonstandard Palais-Smale conditions -- Averaging for ordinary differential equations and functional differential equations -- Path-space measure for stochastic differential equation with a coefficient of polynomial growth -- Optimal control for Navier-Stokes equations -- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations -- Infinitesimals and education -- Calculus with infinitesimals -- Pre-University Analysis.
  note: edited by Imme van den Berg, Vítor Neves.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Partial differential equations
  subject:
    topic: History
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Number Theory
  subject:
    topic: History of Mathematical Sciences
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783211499054
  identifier: http://dx.doi.org/10.1007/978-3-211-49905-4
  record info:
    record creation date: 100301
    record change date: 20151204164554.0
    record identifier: 978-3-211-49905-4