Mathematics in Computing

An Accessible Guide to Historical, Foundational and Application Contexts

  • Gerard O’Regan

Table of contents

  1. Front Matter
    Pages 1-1
  2. Gerard O’Regan
    Pages 1-22
  3. Gerard O’Regan
    Pages 23-41
  4. Gerard O’Regan
    Pages 43-70
  5. Gerard O’Regan
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  6. Gerard O’Regan
    Pages 89-108
  7. Gerard O’Regan
    Pages 109-122
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    Pages 123-140
  9. Gerard O’Regan
    Pages 141-154
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  16. Gerard O’Regan
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  17. Gerard O’Regan
    Pages 267-275
  18. Back Matter
    Pages 18-18

About this book

Introduction

From the earliest examples of computation to the digital devices that are ubiquitous in modern society, the application of mathematics to computing has underpinned the technology that has built our world.

This clearly written and enlightening textbook/reference provides a concise, introductory guide to the key mathematical concepts and techniques used by computer scientists. Spanning a wide range of topics – from number theory to software engineering – the book demonstrates the practical computing applications behind seemingly abstract ideas. The work of important figures such as Alan Turing and Robert Floyd are also discussed, highlighting how the theory has been informed by historical developments.

Topics and features:

  • Ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary
  • Places our current state of knowledge within the context of the contributions made by early civilizations, such as the ancient Babylonians, Egyptians and Greeks
  • Examines the building blocks of mathematics, including sets, relations and functions
  • Presents an introduction to logic, formal methods and software engineering
  • Explains the fundamentals of number theory, and its application in cryptography
  • Describes the basics of coding theory, language theory, and graph theory
  • Discusses the concept of computability and decideability
  • Includes concise coverage of calculus, probability and statistics, matrices, complex numbers and quaternions

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.MallowIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4534-9
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-4471-4533-2
  • Online ISBN 978-1-4471-4534-9
  • About this book