000 03731nam a22004815i 4500
001 978-3-319-22750-4
003 DE-He213
005 20200420220220.0
007 cr nn 008mamaa
008 151116s2015 gw | s |||| 0|eng d
020 _a9783319227504
_9978-3-319-22750-4
024 7 _a10.1007/978-3-319-22750-4
_2doi
050 4 _aQA8.9-QA10.3
072 7 _aUYA
_2bicssc
072 7 _aMAT018000
_2bisacsh
072 7 _aCOM051010
_2bisacsh
082 0 4 _a005.131
_223
100 1 _aDoberkat, Ernst-Erich.
_eauthor.
245 1 0 _aSpecial Topics in Mathematics for Computer Scientists
_h[electronic resource] :
_bSets, Categories, Topologies and Measures /
_cby Ernst-Erich Doberkat.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXX, 719 p. 124 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- 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 _aThis 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, G�odel'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 _aComputer science.
650 0 _aMathematical logic.
650 0 _aCategory theory (Mathematics).
650 0 _aHomological algebra.
650 1 4 _aComputer Science.
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aCategory Theory, Homological Algebra.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319227498
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-22750-4
912 _aZDB-2-SCS
942 _cEBK
999 _c51858
_d51858