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  • © 2007

Kolmogorov's Heritage in Mathematics

  • Several world experts present one part of the mathematical heritage left to us by Kolmogorov

  • Rather than present detailed proofs, the main ideas are described.

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  • ISBN: 978-3-540-36351-4
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Softcover Book USD 109.99
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Table of contents (15 chapters)

  1. Front Matter

    Pages I-VIII
  2. Some aspects of the probabilistic work

    • Loïc Chaumont, Laurent Mazliak, Marc Yor
    Pages 41-66
  3. Infinite dimensional Kolmogorov equations

    • Giuseppe Da Prato
    Pages 67-96
  4. Kolmogorov’s ε-entropy and the problem of statistical estimation

    • Mikhail Nikouline, Valentin Solev
    Pages 109-137
  5. Kolmogorov and topology

    • Victor M. Buchstaber
    Pages 139-150
  6. Kolmogorov and population dynamics

    • Karl Sigmund
    Pages 177-186
  7. Resonances and small divisors

    • Étienne Ghys
    Pages 187-213
  8. The KAM Theorem

    • John H. Hubbard
    Pages 215-238
  9. Kolmogorov Complexity

    • Bruno Durand, Alexander Zvonkin
    Pages 281-299

About this book

A.N. Kolmogorov (Tambov 1903, 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.

Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. The authors present here his contributions, 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 modern prospects.

This book can be read by anyone with a master's (or even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than presenting detailed proofs, the main ideas are described, and a bibliography for those who wish to understand the technical details.

Keywords

  • Division
  • Fourier series
  • Kolmogorov equations
  • Probability
  • complexity
  • dynamical systems
  • proof

Reviews

From the reviews:

"Andrei N. Kolmogorov (1903-1987) was one of the most prolific and influential mathematicians of the twentieth century. … this collection would be read by those who hold only a bachelor’s degree in mathematics, computer science or physics, and more generally, by those interested in mathematical ideas. … This impressive collection gives the reader an understanding of the depth and breadth of Kolmogorov’s contributions to mathematics. Each chapter includes a substantial list of references that invite further reading." (Elena Anne Marchisotto, MathDL, December, 2007)

"The object of Kolmogorov’s Heritage in Mathematics is to enable the general mathematical reader (educated to master’s level) to grasp something of Kolmogorov’s achievements. … I can judge, it is successful in its aim. … those mathematicians with a sense of history, who wish to place themselves within the general culture of mathematics, will find this book a worthy memorial to a great man." (T. W. Korner, SIAM reviews, Vol. 50 (4), December, 2008)

Editors and Affiliations

  • Institut de Mathématiques, Université Bordeaux 1, 351 cours de la Libération, France

    Éric Charpentier

  • Laboratoire de Physique Théorique de la Matiére Condensée, Université Pierre et Marie Curie, 4 Place Jussieu, France

    Annick Lesne

  • Institut des Hautes Études Scientifiques Le Bois-Marie, France

    Annick Lesne

  • Institut de Mathématiques, Université Bordeaux 1, 351 cours de la Libréation, France

    Nikolaï K. Nikolski

Bibliographic Information

  • Book Title: Kolmogorov's Heritage in Mathematics

  • Editors: Éric Charpentier, Annick Lesne, Nikolaï K. Nikolski

  • DOI: https://doi.org/10.1007/978-3-540-36351-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Hardcover ISBN: 978-3-540-36349-1Published: 29 August 2007

  • Softcover ISBN: 978-3-642-07165-2Published: 14 October 2010

  • eBook ISBN: 978-3-540-36351-4Published: 13 September 2007

  • Edition Number: 1

  • Number of Pages: VIII, 318

  • Number of Illustrations: 38 b/w illustrations

  • Additional Information: Original French edition published by Éditions Belin, 2004

  • Topics: Mathematical Logic and Foundations, Probability Theory, Dynamical Systems, Fourier Analysis, Topology

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-36351-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 109.99
Price excludes VAT (USA)
Hardcover Book USD 109.99
Price excludes VAT (USA)