Special Topics in Mathematics for Computer Scientists

Special Topics in Mathematics for Computer Scientists

Special Topics in Mathematics for Computer Scientists: Sets, Categories, Topologies and Measures
Springer | Mathematics | November 19, 2015 | ISBN-10: 3319227491 | 719 pages | pdf | 8.7 mb

by Ernst-Erich Doberkat (Author)
Provides a systematic and accessible treatment of useful topics for theoretical computer scientists
Displays the mathematical techniques with carefully constructed and rigorous approaches
Includes a variety of examples from diverse fields of mathematics and computer science
Features case studies to provide methods for research problems
Classroom tested exposition of the content

From the Back Cover
This textbook addresses the mathematical descrion 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.

About the Author
Ernst-Erich Doberkat:
- doctorate degree in mathematics from the University of Paderborn
- habilitation in computer science from the University of Hagen
- associate professor of mathematics and computer science at Clarkson University in Potsdam, NY
- full professor of software technology and adjunct professor of mathematics at various universities in Germany between 1985 and 2014
- lectures given at universities in Germany, Italy, China and the US

Number of Illustrations and Tables
124 in colour
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Category Theory, Homological Algebra

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