國立虎尾科技大學 |

Special topics in mathematics for computer scientists = sets, categories, topologies and measures /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Special topics in mathematics for computer scientists/ by Ernst-Erich Doberkat.
Reminder of title:	sets, categories, topologies and measures /
Author:	Doberkat, Ernst-Erich.
Published:	Cham :Imprint: Springer, : 2015.,
Description:	xx, 719 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Category Theory, Homological Algebra. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-22750-4
ISBN:	9783319227504

Special topics in mathematics for computer scientists = sets, categories, topologies and measures /
Doberkat, Ernst-Erich.

Special topics in mathematics for computer scientistssets, categories, topologies and measures /[electronic resource] :by Ernst-Erich Doberkat. - Cham :Imprint: Springer,2015. - xx, 719 p. :ill., digital ;24 cm.

Preface -- 1 The Axiom of Choice and Some of Its Equivalents -- 2 Categories -- 3 Topological Spaces -- 4 Measures for Probabilistic Systems -- List of Examples -- References -- Index.

This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs and various examples, the author systematically introduces the Axiom of Choice, explains Banach-Mazur games and the Axiom of Determinacy, discusses the basic constructions of sets and the interplay of coalgebras and Kripke models for modal logics with an emphasis on Kleisli categories, monads and probabilistic systems. The text further shows various ways of defining topologies, building on selected topics like uniform spaces, Godel's Completeness Theorem and topological systems. Finally, measurability, general integration, Borel sets and measures on Polish spaces, as well as the coalgebraic side of Markov transition kernels along with applications to probabilistic interpretations of modal logics are presented. Special emphasis is given to the integration of (co-)algebraic and measure-theoretic structures, a fairly new and exciting field, which is demonstrated through the interpretation of game logics. Readers familiar with basic mathematical structures like groups, Boolean algebras and elementary calculus including mathematical induction will discover a wealth of useful research tools. Throughout the book, exercises offer additional information, and case studies give examples of how the techniques can be applied in diverse areas of theoretical computer science and logics. References to the relevant mathematical literature enable the reader to find the original works and classical treatises, while the bibliographic notes at the end of each chapter provide further insights and discussions of alternative approaches.

ISBN: 9783319227504

Standard No.: 10.1007/978-3-319-22750-4doiSubjects--Topical Terms:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA76.9.M35

Dewey Class. No.: 004.0151

Special topics in mathematics for computer scientists = sets, categories, topologies and measures /
LDR:03086nam a2200325 a 4500 001 838173
003 DE-He213
005 20160425104913.0
006 m d
007 cr nn 008maaau
008 160616s2015 gw s 0 eng d
020 $a 9783319227504 $q (electronic bk.)
020 $a 9783319227498 $q (paper)
024 7 $a 10.1007/978-3-319-22750-4 $2 doi
035 $a 978-3-319-22750-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA76.9.M35
072 7 $a UYA $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a COM051010 $2 bisacsh
082 0 4 $a 004.0151 $2 23
090 $a QA76.9.M35 $b D633 2015
100 1 $a Doberkat, Ernst-Erich. $3 1069175
245 1 0 $a Special topics in mathematics for computer scientists $h [electronic resource] : $b sets, categories, topologies and measures / $c by Ernst-Erich Doberkat.
260 $a Cham : $c 2015. $b Imprint: Springer, $b Springer International Publishing :
300 $a xx, 719 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- 1 The Axiom of Choice and Some of Its Equivalents -- 2 Categories -- 3 Topological Spaces -- 4 Measures for Probabilistic Systems -- List of Examples -- References -- Index.
520 $a This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs and various examples, the author systematically introduces the Axiom of Choice, explains Banach-Mazur games and the Axiom of Determinacy, discusses the basic constructions of sets and the interplay of coalgebras and Kripke models for modal logics with an emphasis on Kleisli categories, monads and probabilistic systems. The text further shows various ways of defining topologies, building on selected topics like uniform spaces, Godel's Completeness Theorem and topological systems. Finally, measurability, general integration, Borel sets and measures on Polish spaces, as well as the coalgebraic side of Markov transition kernels along with applications to probabilistic interpretations of modal logics are presented. Special emphasis is given to the integration of (co-)algebraic and measure-theoretic structures, a fairly new and exciting field, which is demonstrated through the interpretation of game logics. Readers familiar with basic mathematical structures like groups, Boolean algebras and elementary calculus including mathematical induction will discover a wealth of useful research tools. Throughout the book, exercises offer additional information, and case studies give examples of how the techniques can be applied in diverse areas of theoretical computer science and logics. References to the relevant mathematical literature enable the reader to find the original works and classical treatises, while the bibliographic notes at the end of each chapter provide further insights and discussions of alternative approaches.
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a Mathematical Logic and Formal Languages. $3 670059
650 1 4 $a Computer Science. $3 593922
650 0 $a Algebra, Homological. $3 672614
650 0 $a Categories (Mathematics) $3 580337
650 0 $a Logic, Symbolic and mathematical. $3 527823
650 0 $a Computer science. $3 573171
650 0 $a Computer science $x Mathematics. $3 528496
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22750-4
950 $a Computer Science (Springer-11645)