Enumerability · Decidability Computability: An Introduction to the Theory of Recursive Functions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1965
|
| Schriftenreihe: | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete
127 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (X, 245 p) |
| ISBN: | 9783662116869 9783662116883 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-11686-9 |
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Datensatz im Suchindex
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-11686-9 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:13Z |
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| isbn | 9783662116869 9783662116883 |
| issn | 0072-7830 |
| language | English |
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| series2 | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Hermes, Hans 1912-2003 Verfasser (DE-588)117712302 aut Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes Berlin, Heidelberg Springer Berlin Heidelberg 1965 1 Online-Ressource (X, 245 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete 127 0072-7830 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 Mathematics Mathematics, general Mathematik Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Algorithmentheorie (DE-588)4200409-3 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Aufzählbarkeit (DE-588)4800450-9 gnd rswk-swf Rekursive Funktion (DE-588)4138367-9 gnd rswk-swf Entscheidbarkeit (DE-588)4152398-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Rekursive Funktion (DE-588)4138367-9 s 2\p DE-604 Algorithmentheorie (DE-588)4200409-3 s 3\p DE-604 Algorithmus (DE-588)4001183-5 s 4\p DE-604 Berechenbarkeit (DE-588)4138368-0 s 5\p DE-604 Entscheidbarkeit (DE-588)4152398-2 s 6\p DE-604 Aufzählbarkeit (DE-588)4800450-9 s 7\p DE-604 https://doi.org/10.1007/978-3-662-11686-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hermes, Hans 1912-2003 Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions Mathematics Mathematics, general Mathematik Berechenbarkeit (DE-588)4138368-0 gnd Algorithmentheorie (DE-588)4200409-3 gnd Algorithmus (DE-588)4001183-5 gnd Aufzählbarkeit (DE-588)4800450-9 gnd Rekursive Funktion (DE-588)4138367-9 gnd Entscheidbarkeit (DE-588)4152398-2 gnd |
| subject_GND | (DE-588)4138368-0 (DE-588)4200409-3 (DE-588)4001183-5 (DE-588)4800450-9 (DE-588)4138367-9 (DE-588)4152398-2 (DE-588)4151278-9 |
| title | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_auth | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_exact_search | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_full | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_fullStr | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_full_unstemmed | Enumerability · Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_short | Enumerability · Decidability Computability |
| title_sort | enumerability decidability computability an introduction to the theory of recursive functions |
| title_sub | An Introduction to the Theory of Recursive Functions |
| topic | Mathematics Mathematics, general Mathematik Berechenbarkeit (DE-588)4138368-0 gnd Algorithmentheorie (DE-588)4200409-3 gnd Algorithmus (DE-588)4001183-5 gnd Aufzählbarkeit (DE-588)4800450-9 gnd Rekursive Funktion (DE-588)4138367-9 gnd Entscheidbarkeit (DE-588)4152398-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Berechenbarkeit Algorithmentheorie Algorithmus Aufzählbarkeit Rekursive Funktion Entscheidbarkeit Einführung |
| url | https://doi.org/10.1007/978-3-662-11686-9 |
| work_keys_str_mv | AT hermeshans enumerabilitydecidabilitycomputabilityanintroductiontothetheoryofrecursivefunctions |