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Mathematical Foundations of Advanced Informatics

Volume 1: Inductive Approaches

  • Bernhard Steffen
  • Oliver Rüthing
  • Michael Huth

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 1-18
  3. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 19-65
  4. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 67-117
  5. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 119-159
  6. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 161-208
  7. Bernhard Steffen, Oliver Rüthing, Michael Huth
    Pages 209-218
  8. Back Matter
    Pages 219-228

About this book

Introduction

The books in this trilogy capture the foundational core of advanced informatics. The authors make the foundations accessible, enabling students to become effective problem solvers.

This first volume establishes the inductive approach as a fundamental principle for system and domain analysis. After a brief introduction to the elementary mathematical structures, such as sets, propositional logic, relations, and functions, the authors focus on the separation between syntax (representation) and semantics (meaning), and on the advantages of the consistent and persistent use of inductive definitions. They identify compositionality as a feature that not only acts as a foundation for algebraic proofs but also as a key for more general scalability of modeling and analysis. A core principle throughout is invariance, which the authors consider a key for the mastery of change, whether in the form of extensions, transformations, or abstractions.

This textbook is suitable for undergraduate and graduate courses in computer science and for self-study. Most chapters contain exercises and the content has been class-tested over many years in various universities.

Keywords

Propositions Sets Relations Functions Induction Inductive Proofs Pragmatics System Analysis Domain Analysis Syntax Semantics Compositionality

Authors and affiliations

  • Bernhard Steffen
    • 1
  • Oliver Rüthing
    • 2
  • Michael Huth
    • 3
  1. 1.Fakultät für InformatikTechnical University of DortmundDortmundGermany
  2. 2.Fakultät für InformatikTechnical University of DortmundDortmundGermany
  3. 3.Department of ComputingImperial College LondonLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-68397-3
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-68396-6
  • Online ISBN 978-3-319-68397-3
  • Buy this book on publisher's site