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Algorithms: Main Ideas and Applications

  • Book
  • © 1993

Overview

Authors:
  1. Vladimir Uspensky

    1. Department of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow Lomonosov University, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

  2. Alexei Semenov

    1. Department of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow Lomonosov University, Moscow, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (30 chapters)

  1. Fundamental Discoveries of the General Theory of Algorithms

    1. First steps in the invariant, or machine-independent, theory of complexity of computations

      • Vladimir Uspensky, Alexei Semenov
      Pages 108-109

    2. The theory of complexity and entropy of constructive objects

      • Vladimir Uspensky, Alexei Semenov
      Pages 110-114

    3. Convenient computational models

      • Vladimir Uspensky, Alexei Semenov
      Pages 115-117

  2. Mathematical Applications of the Theory of Algorithms

    1. Front Matter

      Pages 119-120
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    2. Investigations of mass problems

      • Vladimir Uspensky, Alexei Semenov
      Pages 121-136

    3. Applications to the foundations of mathematics: constructive semantics

      • Vladimir Uspensky, Alexei Semenov
      Pages 137-140

    4. Applications to mathematical logic: formalized languages of logic and arithmetic

      • Vladimir Uspensky, Alexei Semenov
      Pages 141-144

    5. Computable analysis

      • Vladimir Uspensky, Alexei Semenov
      Pages 145-153

    6. Numbered structures

      • Vladimir Uspensky, Alexei Semenov
      Pages 154-165

    7. Applications to probability theory: definitions of a random sequence

      • Vladimir Uspensky, Alexei Semenov
      Pages 166-178

    8. Applications to information theory: the algorithmic approach to the concept of quantity of information

      • Vladimir Uspensky, Alexei Semenov
      Pages 179-183

    9. Complexity bounds for particular problems

      • Vladimir Uspensky, Alexei Semenov
      Pages 184-187

    10. Influence of the theory of algorithms on algorithmic practice

      • Vladimir Uspensky, Alexei Semenov
      Pages 188-193

  3. Back Matter

    Pages 195-269
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Keywords

About this book

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]).

Authors and Affiliations

  • Department of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow Lomonosov University, Moscow, Russia

    Vladimir Uspensky, Alexei Semenov

Bibliographic Information

  • Book Title: Algorithms: Main Ideas and Applications

  • Authors: Vladimir Uspensky, Alexei Semenov

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-015-8232-2

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1993

  • Hardcover ISBN: 978-0-7923-2210-8Published: 31 March 1993

  • Softcover ISBN: 978-90-481-4256-9Published: 07 December 2010

  • eBook ISBN: 978-94-015-8232-2Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: XII, 270

  • Additional Information: Originally published in Russian

  • Topics: Mathematical Logic and Foundations, Theory of Computation, Logic

  • Industry Sectors: IT & Software

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