Mathematics in Computing An Accessible Guide to Historical, Foundati
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/refe
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Gerard O’Regan
Mathematics in Computing An Accessible Guide to Historical, Foundational and Application Contexts
2123
Gerard O’Regan Mallow, Ireland
ISBN 978-1-4471-4533-2 ISBN 978-1-4471-4534-9 (eBook) DOI 10.1007/978-1-4471-4534-9 Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2012951294 © Springer-Verlag London 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my siblings Mary Rose, Donal, Francis and Marguerita
Preface
Overview The objective of this book is to give the reader a flavour of mathematics used in the computing field. The goal is to show how mathematics is applied in computing, rather than the study of mathematics for its own sake.
Organization and Features The first chapter discusses the contributions made by early civilisations to computing. This includes work done by the Babylonians, Egyptians and Greeks. The Egyptians applied mathematics to solve practical problems such as the construction of pyramids. The Greeks made a major contribution to mathematics and geometry, and most students are familiar with the work of Euclid. Chapter 2 provides an introduction to fundamental building blocks in mathematics including sets, relations and functions. A set is a collection of well-defined objects and it m
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