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Modelling Computing Systems

Mathematics for Computer Science

  • Textbook
  • © 2013

Overview

Authors:
  1. Faron Moller

    1. Department of Computer Science, Swansea University, Swansea, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  2. Georg Struth

    1. Dept. Computer Science, University of Sheffield, Sheffield, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  • Provides an elementary introduction to the mathematics and modelling of computing systems
  • Explores concepts of games and strategies to provide a paradigm for understanding the nature of computation
  • Develops a foundation for computational thinking and problem solving
  • Presents the topics in a clear and comprehensive style
  • Introduces bisimulation, Hennessy-Milner logic, and the relationship between them, at an introductory level
  • Includes supplementary material: sn.pub/extras

Part of the book series: Undergraduate Topics in Computer Science (UTICS)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Introduction

    • Faron Moller, Georg Struth
    Pages 1-14

  3. Mathematics for Computer Science

    1. Front Matter

      Pages 15-15
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    2. Propositional Logic

      • Faron Moller, Georg Struth
      Pages 17-55

    3. Sets

      • Faron Moller, Georg Struth
      Pages 57-86

    4. Boolean Algebras and Circuits

      • Faron Moller, Georg Struth
      Pages 87-108

    5. Predicate Logic

      • Faron Moller, Georg Struth
      Pages 109-129

    6. Proof Strategies

      • Faron Moller, Georg Struth
      Pages 131-154

    7. Functions

      • Faron Moller, Georg Struth
      Pages 155-178

    8. Relations

      • Faron Moller, Georg Struth
      Pages 179-199

    9. Inductive and Recursive Definitions

      • Faron Moller, Georg Struth
      Pages 201-222

    10. Proofs by Induction

      • Faron Moller, Georg Struth
      Pages 223-250

    11. Games and Strategies

      • Faron Moller, Georg Struth
      Pages 251-275

  4. Modelling Computing Systems

    1. Front Matter

      Pages 277-277
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    2. Modelling Processes

      • Faron Moller, Georg Struth
      Pages 279-307

    3. Distinguishing Between Processes

      • Faron Moller, Georg Struth
      Pages 309-332

    4. Logical Properties of Processes

      • Faron Moller, Georg Struth
      Pages 333-356

    5. Concurrent Processes

      • Faron Moller, Georg Struth
      Pages 357-379

    6. Temporal Properties

      • Faron Moller, Georg Struth
      Pages 381-403

  5. Back Matter

    Pages 405-500
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Keywords

About this book

This engaging text presents the fundamental mathematics and modelling techniques for computing systems in a novel and light-hearted way, which can be easily followed by students at the very beginning of their university education. Key concepts are taught through a large collection of challenging yet fun mathematical games and logical puzzles that require no prior knowledge about computers. The text begins with intuition and examples as a basis from which precise concepts are then developed; demonstrating how, by working within the confines of a precise structured method, the occurrence of errors in the system can be drastically reduced. 

Features: demonstrates how game theory provides a paradigm for an intuitive understanding of the nature of computation; contains more than 400 exercises throughout the text, with detailed solutions to half of these presented at the end of the book, together with numerous theorems, definitions and examples; describes a modelling approach based on state transition systems.

Reviews

“This book by UK academics Moller (Swansea Univ.) and Struth (Univ. of Sheffield) is designed to serve as a textbook for first-year university students in computer science. The volume contains 15 chapters, divided in two parts. … libraries may wish to acquire it for the benefit of advanced undergraduates. Summing Up: Recommended. Only comprehensive academic mathematics and computer science collections.” (B. Borchers, Choice, Vol. 51 (7), March, 2014)

“This book contains essential mathematics and modelling techniques for computing systems for which a presentation style suitable for first year undergraduate students has been chosen. … The book contains more than 200 exercises throughout the text and provides complete solutions at the back of the book on more than 80 pages.” (Gudula Rünger, zbMATH, Vol. 1278, 2014)

Authors and Affiliations

  • Department of Computer Science, Swansea University, Swansea, United Kingdom

    Faron Moller

  • Dept. Computer Science, University of Sheffield, Sheffield, United Kingdom

    Georg Struth

About the authors

Prof. Faron Moller is a Professor of Computer Science at Swansea University, UK.

Dr. Georg Struth is a Reader in Computer Science at the University of Sheffield, UK.

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