Guide to Discrete Mathematics

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

  • Gerard O'Regan

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Gerard O’Regan
    Pages 1-24
  3. Gerard O’Regan
    Pages 25-51
  4. Gerard O’Regan
    Pages 53-74
  5. Gerard O’Regan
    Pages 75-84
  6. Gerard O’Regan
    Pages 99-116
  7. Gerard O’Regan
    Pages 117-126
  8. Gerard O’Regan
    Pages 127-139
  9. Gerard O’Regan
    Pages 141-153
  10. Gerard O’Regan
    Pages 155-170
  11. Gerard O’Regan
    Pages 171-183
  12. Gerard O’Regan
    Pages 185-206
  13. Gerard O’Regan
    Pages 207-218
  14. Gerard O’Regan
    Pages 219-233
  15. Gerard O’Regan
    Pages 235-261
  16. Gerard O’Regan
    Pages 263-281
  17. Gerard O’Regan
    Pages 283-297
  18. Gerard O’Regan
    Pages 299-318
  19. Gerard O’Regan
    Pages 319-334
  20. Gerard O’Regan
    Pages 335-360
  21. Back Matter
    Pages 361-368

About this book


This stimulating textbook/reference 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.

Topics and 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, covering simultaneous and quadratic equations, and the laws of logarithms and indices, in addition to such structures in abstract algebra as monoids, groups, rings, integral domains, fields, and vector spaces
  • 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 such advanced topics as fuzzy logic, temporal logic, intuitionistic logic, undefined values, theorem provers, and the applications of logic to AI
  • Examines the important field of software engineering, describing formal methods, including the Z specification language
  • Investigates probability and statistics, covering discrete random variables, probability distributions, sample spaces, variance and standard deviation, and hypothesis testing

This engaging and clearly written work offers an invaluable overview of discrete mathematics for undergraduate computer science students, and to students of mathematics interested in the rich applications of discrete mathematics to the field of computing.


Discrete mathematics Theorem proving Propositional logic Formal methods Relations and functions

Authors and affiliations

  • Gerard O'Regan
    • 1
  1. 1.SQC Consulting MallowIreland

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science Computer Science (R0)
  • Print ISBN 978-3-319-44560-1
  • Online ISBN 978-3-319-44561-8
  • Series Print ISSN 1868-0941
  • Series Online ISSN 1868-095X
  • Buy this book on publisher's site
Industry Sectors
IT & Software