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Special Topics in Mathematics for Computer Scientists - Sets, Categories, Topologies and Measures by Ernst-Erich Doberkat(pradyutvam2)[CPUL]{TRUE PDF}[2015]

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Description

 							
  
  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.
  
  Hardcover: 719 pages
 
Publisher: Springer; 1st ed. 2015 edition (November 19, 2015)
  Language: English
  ISBN-10: 3319227491
 
ISBN-13: 978-3319227498
  Product Dimensions: 9.2 x 6.1 x 1.6 inches
  
   						

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