000 03803nam a22004215i 4500
003 DE-He213
005 20231104114222.0
007 cr nn 008mamaa
008 151116s2015 gw | s |||| 0|eng d
020 _a9783319227504
_z978-3-319-22750-4
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 _aUYA
_2thema005.131
_223
100 1 _aDoberkat, Ernst-Erich.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpecial Topics in Mathematics for Computer Scientists :
_bSets, Categories, Topologies and Measures /
_cby Ernst-Erich Doberkat.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _a1 online 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, 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 _aComputer science.
650 0 _aLogic, Symbolic and mathematical.
650 0 _aAlgebra.
650 1 4 _aMathematical Logic and Formal Languages.
_0http://scigraph.springernature.com/things/product-market-codes/I16048
650 2 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
650 2 4 _aCategory Theory, Homological Algebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11035
710 2 _aSpringerLink (Online service)
856 4 0 _uhttps://doi.org/10.1007/978-3-319-22750-4
_3Springer eBooks
_zOnline access link to the resource
912 _aZDB-2-SCS
999 _c200433812
_d52024
942 _2lcc
_cEBK
041 _aeng