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CLOCKS
PROBLEM SOLVING FOR UNDERGRADUATES
William Briggs
University of Colorado at Denver
Denver, Colorado
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Society for Industrial and Applied Mathematics
Philadelphia
Copyright © 2005 by the Society for Industrial and Applied Mathematics.
109876543 21
All rights reserved. Printed in the United States of America. No part of this book may
be reproduced, stored, or transmitted in any manner without the written permission
of the publisher. For information, write to the Society for Industrial and Applied
Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.
MATLAB® is a registered trademark of The MathWorks, Inc. For MATLAB product information
please contact The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA,
508-647-7000, Fax: 508-647-7101, info@, /.
Library of Congress Cataloging-in-Publication Data
Briggs, William L.
Ants, bikes, and clocks : problem solving for undergraduates / William Briggs.
p. cm.
Includes bibliographical references and index.
ISBN 0-89871-574-1 (pbk.)
1. Problem solving. I. Title.
2005
510-dc22 2004058720
513JTL is a registered trademark.
Contents
1 Introduction 1
Exercises 4
Hints and Answers 6
2 A Problem-Solving Framework 7
Polya's Method 7
Exercises 12
Hints and Answers 14
3 Problem-Solving Strategies 17
Exercises 30
Hints and Answers 32
4 How Do You Do It? 35
Exercises 38
Hints and Answers 40
5 Parts of the Whole 43
Basic Uses of Percentages 43
Assorted Problems 46
Exercises 48
Hints and Answers 51
6 A World of Change 53
Exercises 57
Hints and Answers 60
7 At Any Rate 63
Exercises 68
Hints and Answers 70
8 Difference Equations 73
Background 73
Exercises 82
Hints and Answers 84
V
vi Contents
9 Insight puting 87
P61ya's Method puting 87
Root Finding