Special Topics in Mathematics for Computer Scientists (Record no. 51858)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03731nam a22004815i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-319-22750-4 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200420220220.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 151116s2015 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783319227504 |
| -- | 978-3-319-22750-4 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 005.131 |
| 100 1# - AUTHOR NAME | |
| Author | Doberkat, Ernst-Erich. |
| 245 10 - TITLE STATEMENT | |
| Title | Special Topics in Mathematics for Computer Scientists |
| Sub Title | Sets, Categories, Topologies and Measures / |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XX, 719 p. 124 illus. in color. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 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 ## - SUMMARY, ETC. | |
| Summary, etc | 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, 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. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-319-22750-4 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2015. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical logic. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Category theory (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Homological algebra. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Science. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical Logic and Formal Languages. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical Logic and Foundations. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Category Theory, Homological Algebra. |
| 912 ## - | |
| -- | ZDB-2-SCS |
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