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The foundations of computability the...

Robič, Borut.

The foundations of computability theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The foundations of computability theory // by Borut Robič.
Author:	Robič, Borut.
Published:	Berlin, Heidelberg :Springer, : 2015.,
Description:	xx, 331 p. :ill. ; : 24 cm.;
Subject:	Computable functions. -
ISBN:	9783662448076 (hbk) :

The foundations of computability theory /
Robič, Borut.

The foundations of computability theory /by Borut Robič. - Berlin, Heidelberg :Springer,2015. - xx, 331 p. :ill. ;24 cm.

Includes bibliographical references and index.

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: 9783662448076 (hbk) :NT2425Subjects--Topical Terms:

677058
Computable functions.

LC Class. No.: QA9.59 / .R654 2015

Dewey Class. No.: 511.352

The foundations of computability theory /
LDR:02326cam a2200181 a 4500 001 876752
008 171122s2015 gw a b 001 0 eng d
020 $a 9783662448076 (hbk) : $c NT2425
020 $a 9783662448083 (electronic bk.)
035 $a 9766248083
040 $a GP $b eng $c GP $c NFU
050 # 4 $a QA9.59 $b .R654 2015
082 0 4 $a 511.352 $2 23
100 1 $a Robič, Borut. $3 1127748
245 1 4 $a The foundations of computability theory / $c by Borut Robič.
260 # $a Berlin, Heidelberg : $b Springer, $c 2015.
300 $a xx, 331 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references and index.
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 677058
650 # 0 $a Computer science $x Mathematics. $3 528496