東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

The foundations of computability theory

Robic, Borut.

Linked to FindBook

Google Book

Amazon

博客來

The foundations of computability theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	The foundations of computability theory/ by Borut Robic.
Author:	Robic, Borut.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2015.,
Description:	xx, 331 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Further Reading -- App. A, Mathematical Background -- References -- Index.
Contained By:	Springer eBooks
Subject:	Computable functions. -
Online resource:	http://dx.doi.org/10.1007/978-3-662-44808-3
ISBN:	9783662448083

The foundations of computability theory
Robic, Borut.

The foundations of computability theory[electronic resource] /by Borut Robic. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - xx, 331 p. :ill., digital ;24 cm.

Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Further Reading -- App. A, Mathematical Background -- References -- Index.

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

ISBN: 9783662448083

Standard No.: 10.1007/978-3-662-44808-3doiSubjects--Topical Terms:

559829
Computable functions.

LC Class. No.: QA9.59

Dewey Class. No.: 511.352

The foundations of computability theory
LDR:02750nmm a2200337 a 4500 001 2013145
003 DE-He213
005 20160428114006.0
006 m d
007 cr nn 008maaau
008 160518s2015 gw s 0 eng d
020 $a 9783662448083 $q (electronic bk.)
020 $a 9783662448076 $q (paper)
024 7 $a 10.1007/978-3-662-44808-3 $2 doi
035 $a 978-3-662-44808-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9.59
072 7 $a UY $2 bicssc
072 7 $a UYA $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a COM031000 $2 bisacsh
082 0 4 $a 511.352 $2 23
090 $a QA9.59 $b .R654 2015
100 1 $a Robic, Borut. $3 2162478
245 1 4 $a The foundations of computability theory $h [electronic resource] / $c by Borut Robic.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2015.
300 $a xx, 331 p. : $b ill., digital ; $c 24 cm.
505 0 $a Introduction -- The Foundational Crisis of Mathematics -- Formalism -- Hilbert's Attempt at Recovery -- The Quest for a Formalization -- The Turing Machine -- The First Basic Results -- Incomputable Problems -- Methods of Proving the Incomputability -- Computation with External Help -- Degrees of Unsolvability -- The Turing Hierarchy of Unsolvability -- The Class D of Degrees of Unsolvability -- C.E. Degrees and the Priority Method -- The Arithmetical Hierarchy -- Further Reading -- App. A, Mathematical Background -- References -- Index.
520 $a This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.
650 0 $a Computable functions. $3 559829
650 0 $a Computer science $x Mathematics. $3 532725
650 1 4 $a Computer Science. $3 626642
650 2 4 $a Theory of Computation. $3 892514
650 2 4 $a Mathematics of Computing. $3 891213
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-662-44808-3
950 $a Computer Science (Springer-11645)