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Guide to Discrete Mathematics

An Accessible Introduction to the History, Theory, Logic and Applications

  • Textbook
  • © 2016

Overview

Authors:
  1. Gerard O'Regan

    1. SQC Consulting , Mallow, Ireland

    View author publications

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  • Presents a broad and accessible introduction to discrete mathematics
  • Provides an introduction to logic, covering historical developments
  • Presents a strong focus on applications to coding and graph theory, formal methods, databases, and software reliability
  • Offers such pedagogical features as key topics, chapter summaries, review questions, a glossary and index
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computer Science (TCS)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. Mathematics in Civilization

    • Gerard O’Regan
    Pages 1-24

  3. Sets, Relations and Functions

    • Gerard O’Regan
    Pages 25-51

  4. Number Theory

    • Gerard O’Regan
    Pages 53-74

  5. Mathematical Induction and Recursion

    • Gerard O’Regan
    Pages 75-84

  6. Sequences, Series and Permutations and Combinations

    • Gerard O’Regan
    Pages 85-97

  7. Algebra

    • Gerard O’Regan
    Pages 99-116

  8. Automata Theory

    • Gerard O’Regan
    Pages 117-126

  9. Matrix Theory

    • Gerard O’Regan
    Pages 127-139

  10. Graph Theory

    • Gerard O’Regan
    Pages 141-153

  11. Cryptography

    • Gerard O’Regan
    Pages 155-170

  12. Coding Theory

    • Gerard O’Regan
    Pages 171-183

  13. Language Theory and Semantics

    • Gerard O’Regan
    Pages 185-206

  14. Computability and Decidability

    • Gerard O’Regan
    Pages 207-218

  15. A Short History of Logic

    • Gerard O’Regan
    Pages 219-233

  16. Propositional and Predicate Logic

    • Gerard O’Regan
    Pages 235-261

  17. Advanced Topics in Logic

    • Gerard O’Regan
    Pages 263-281

  18. Software Engineering Mathematics

    • Gerard O’Regan
    Pages 283-297

  19. Formal Methods

    • Gerard O’Regan
    Pages 299-318

  20. Z Formal Specification Language

    • Gerard O’Regan
    Pages 319-334
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Keywords

About this book

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. 


Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.


Reviews

“This book is … an encyclopedic overview of topics of and related to discrete mathematics in the broad sense, including many topics from computer science and software engineering. … Each chapter has a summary and a list of review question which help the reader to recapitulate the contents … . for each topic the reader is able to grasp the specific flavor and can move forward to more specific and advanced literature.” (Dieter Riebesehl, zbMATH 1358.68004, 2017)

Authors and Affiliations

  • SQC Consulting , Mallow, Ireland

    Gerard O'Regan

About the author

Dr. Gerard O'Regan is a CMMI software process improvement consultant with research interests including software quality and software process improvement, mathematical approaches to software quality, and the history of computing. He is the author of such Springer titles as Introduction to the History of Computing, Pillars of Computing, Introduction to Software Quality, Giants of Computing, and Mathematics in Computing.

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