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Mathematics in Computing

An Accessible Guide to Historical, Foundational and Application Contexts

  • Gerard O’Regan
Textbook

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

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Gerard O’Regan
    Pages 1-11
  3. Gerard O’Regan
    Pages 13-29
  4. Gerard O’Regan
    Pages 31-60
  5. Gerard O’Regan
    Pages 61-75
  6. Gerard O’Regan
    Pages 77-98
  7. Gerard O’Regan
    Pages 99-115
  8. Gerard O’Regan
    Pages 131-140
  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 185-207
  13. Gerard O’Regan
    Pages 209-220
  14. Gerard O’Regan
    Pages 221-233
  15. Gerard O’Regan
    Pages 235-245
  16. Gerard O’Regan
    Pages 247-273
  17. Gerard O’Regan
    Pages 275-291
  18. Gerard O’Regan
    Pages 293-302
  19. Gerard O’Regan
    Pages 303-318
  20. Gerard O’Regan
    Pages 319-332
  21. Gerard O’Regan
    Pages 333-354
  22. Gerard O’Regan
    Pages 355-371
  23. Gerard O’Regan
    Pages 373-382
  24. Gerard O’Regan
    Pages 383-392
  25. Gerard O’Regan
    Pages 393-410
  26. Gerard O’Regan
    Pages 411-424
  27. Gerard O’Regan
    Pages 425-444
  28. Gerard O’Regan
    Pages 445-448
  29. Back Matter
    Pages 449-458

About this book

Introduction

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems.

Topics and features:

  • Includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary
  • Describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann
  • Introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices
  • Explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory
  • Reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking
  • Covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving
  • Presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus

This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Keywords

Calculus Coding Theory Cryptography Discrete Mathematics Formal Methods Graph Theory Group Theory and Ring Theory History of Mathematics Matrix Theory Number Theory Probability and Statistics Software Engineering Software Reliability Z Specification Language

Authors and affiliations

  • Gerard O’Regan
    • 1
  1. 1.SQC ConsultingMallowIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-34209-8
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-030-34208-1
  • Online ISBN 978-3-030-34209-8
  • Series Print ISSN 1863-7310
  • Series Online ISSN 2197-1781
  • Buy this book on publisher's site
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