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:
    title: Kolmogorov’s Heritage in Mathematics
  name:
    name part: Charpentier, Éric.
    role:
      role term: editor.
  name:
    name part: Lesne, Annick.
    role:
      role term: editor.
  name:
    name part: Nikolski, Nikolaï K.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 318 p. 38 illus. online resource.
  abstract: A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results. The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).
  table of contents: The youth of Andrei Nikolaevich and Fourier series -- Kolmogorov’s contribution to intuitionistic logic -- Some aspects of the probabilistic work -- Infinite dimensional Kolmogorov equations -- From Kolmogorov’s theorem on empirical distribution to number theory -- Kolmogorov’s ?-entropy and the problem of statistical estimation -- Kolmogorov and topology -- Geometry and approximation theory in A. N. Kolmogorov’s works -- Kolmogorov and population dynamics -- Resonances and small divisors -- The KAM Theorem -- From Kolmogorov’s Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics -- From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem -- Kolmogorov Complexity -- Algorithmic Chaos and the Incompressibility Method.
  note: edited by Éric Charpentier, Annick Lesne, Nikolaï K. Nikolski.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Fourier analysis
  subject:
    topic: Mathematical logic
  subject:
    topic: Probabilities
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Fourier Analysis
  subject:
    topic: Topology
  classification: QA8.9-10.3
  classification: 511.3
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783540363514
  identifier: http://dx.doi.org/10.1007/978-3-540-36351-4
  record info:
    record creation date: 100301
    record change date: 20151204161849.0
    record identifier: 978-3-540-36351-4