Grundlehren der mathematischen Wissenschaften

Enumerability, Decidability, Computability

An Introduction to the Theory of Recursive Functions

Authors: Hermes, Hans

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About this book

The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im­ portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc­ cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-662-11686-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Enumerability, Decidability, Computability
Book Subtitle
An Introduction to the Theory of Recursive Functions
Authors
Translated by
Herman, G.T., Plassmann, O.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
127
Copyright
1965
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-11686-9
DOI
10.1007/978-3-662-11686-9
Series ISSN
0072-7830
Edition Number
1
Number of Pages
X, 245
Additional Information
Title of the original German edition: Aufzählbarkeit, Entscheidbarkeit, Berechenbarkeit
Topics