Special Topics in Mathematics for Computer Scientists : Sets, Categories, Topologies and Measures / by Ernst-Erich Doberkat.

Format:

Book

Author/Creator:

Doberkat, Ernst-Erich, author.

Contributor:

SpringerLink (Online service)

Series:

Computer Science (Springer-11645)

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Categories (Mathematics).

Algebra, Homological.

Mathematical Logic and Formal Languages.

Mathematical Logic and Foundations.

Category Theory, Homological Algebra.

Local Subjects:

Mathematical Logic and Formal Languages.

Mathematical Logic and Foundations.

Category Theory, Homological Algebra.

Physical Description:

1 online resource (XX, 719 pages) : 124 illustrations in color

Edition:

First edition 2015.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

978-3-319-22750-4

9783319227504

Access Restriction:

Restricted for use by site license.