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Algorithms: Main Ideas and Applications

  • Vladimir Uspensky
  • Alexei Semenov

Part of the Mathematics and Its Applications book series (MAIA, volume 251)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Vladimir Uspensky, Alexei Semenov
      Pages 1-2
  3. Notation and Terminology

    1. Vladimir Uspensky, Alexei Semenov
      Pages 3-4
  4. Fundamental Discoveries of the General Theory of Algorithms

    1. Front Matter
      Pages 5-6
    2. Vladimir Uspensky, Alexei Semenov
      Pages 17-21
    3. Vladimir Uspensky, Alexei Semenov
      Pages 22-30
    4. Vladimir Uspensky, Alexei Semenov
      Pages 31-44
    5. Vladimir Uspensky, Alexei Semenov
      Pages 45-45
    6. Vladimir Uspensky, Alexei Semenov
      Pages 46-47
    7. Vladimir Uspensky, Alexei Semenov
      Pages 48-57
    8. Vladimir Uspensky, Alexei Semenov
      Pages 58-65
    9. Vladimir Uspensky, Alexei Semenov
      Pages 66-67
    10. Vladimir Uspensky, Alexei Semenov
      Pages 70-72
    11. Vladimir Uspensky, Alexei Semenov
      Pages 73-76
    12. Vladimir Uspensky, Alexei Semenov
      Pages 77-79
    13. Vladimir Uspensky, Alexei Semenov
      Pages 80-83
    14. Vladimir Uspensky, Alexei Semenov
      Pages 98-107
    15. Vladimir Uspensky, Alexei Semenov
      Pages 110-114
    16. Vladimir Uspensky, Alexei Semenov
      Pages 115-117
  5. Mathematical Applications of the Theory of Algorithms

    1. Front Matter
      Pages 119-120
    2. Vladimir Uspensky, Alexei Semenov
      Pages 121-136
    3. Vladimir Uspensky, Alexei Semenov
      Pages 137-140
    4. Vladimir Uspensky, Alexei Semenov
      Pages 145-153
    5. Vladimir Uspensky, Alexei Semenov
      Pages 154-165
    6. Vladimir Uspensky, Alexei Semenov
      Pages 166-178
    7. Vladimir Uspensky, Alexei Semenov
      Pages 184-187
    8. Vladimir Uspensky, Alexei Semenov
      Pages 188-193
  6. Back Matter
    Pages 195-269

About this book

Introduction

Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the­ oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci­ entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).

Keywords

Notation algorithms arithmetic boundary element method complexity design entropy form hardware information information theory logic mathematical logic randomness semantics

Authors and affiliations

  • Vladimir Uspensky
    • 1
  • Alexei Semenov
    • 1
  1. 1.Department of Mathematical Logic, Faculty of Mechanics and MathematicsMoscow Lomonosov UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8232-2
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4256-9
  • Online ISBN 978-94-015-8232-2
  • Buy this book on publisher's site
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