國立虎尾科技大學 |

Special Topics in Mathematics for Computer Scientists = Sets, Categories, Topologies and Measures /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Special Topics in Mathematics for Computer Scientists/ by Ernst-Erich Doberkat.
其他題名:	Sets, Categories, Topologies and Measures /
作者:	Doberkat, Ernst-Erich.
面頁冊數:	XX, 719 p. 124 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical logic. -
電子資源:	https://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. - 1st ed. 2015. - XX, 719 p. 124 illus. in color.online resource.

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, Gödel’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:

810627
Mathematical logic.

LC Class. No.: QA8.9-10.3

Dewey Class. No.: 005.131

Special Topics in Mathematics for Computer Scientists = Sets, Categories, Topologies and Measures /
LDR:03455nam a22003975i 4500 001 967574
003 DE-He213
005 20200703130436.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319227504 $9 978-3-319-22750-4
024 7 $a 10.1007/978-3-319-22750-4 $2 doi
035 $a 978-3-319-22750-4
050 4 $a QA8.9-10.3
072 7 $a UYA $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a UYA $2 thema
082 0 4 $a 005.131 $2 23
100 1 $a Doberkat, Ernst-Erich. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $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.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XX, 719 p. 124 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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, Gödel’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 0 $a Mathematical logic. $2 bicssc $3 810627
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 1 4 $a Mathematical Logic and Formal Languages. $3 670059
650 2 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a Category Theory, Homological Algebra. $3 678397
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319227511
776 0 8 $i Printed edition: $z 9783319227498
776 0 8 $i Printed edition: $z 9783319368696
856 4 0 $u https://doi.org/10.1007/978-3-319-22750-4
912 $a ZDB-2-SCS
912 $a ZDB-2-SXCS
950 $a Computer Science (SpringerNature-11645)
950 $a Computer Science (R0) (SpringerNature-43710)