Special Topics in Mathematics for Computer Scientists - Sets, Categories, Topologies and Measures (Paperback, Softcover reprint of the original 1st ed. 2015)

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, Goedel'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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Release date:	August 2016
First published:	2015
Authors:	Ernst-Erich Doberkat
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	719
Edition:	Softcover reprint of the original 1st ed. 2015
ISBN-13:	978-3-319-36869-6
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Mathematical foundations > General Promotions
LSN:	3-319-36869-9
Barcode:	9783319368696

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!