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Special topics in mathematics for computer scientists[electronic resource] :sets, categories, topologies and measures /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	004.0151
書名/作者:	Special topics in mathematics for computer scientists : sets, categories, topologies and measures // by Ernst-Erich Doberkat.
作者:	Doberkat, Ernst-Erich.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xx, 719 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Computer science - Mathematics.
標題:	Computer science.
標題:	Logic, Symbolic and mathematical.
標題:	Categories (Mathematics)
標題:	Algebra, Homological.
標題:	Computer Science.
標題:	Mathematical Logic and Formal Languages.
標題:	Mathematical Logic and Foundations.
標題:	Category Theory, Homological Algebra.
ISBN:	9783319227504
ISBN:	9783319227498
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-22750-4

Special topics in mathematics for computer scientists[electronic resource] :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 :Springer International Publishing :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:

382369
Computer science
--Mathematics.

LC Class. No.: QA76.9.M35

Dewey Class. No.: 004.0151

Special topics in mathematics for computer scientists[electronic resource] :sets, categories, topologies and measures /
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