Seduced by Mathematics: The Enduring Fascination of Mathematics

225 Pages·2022·10.818 MB·English

by  James D. Stein

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Problem Solving in Mathematics and Beyond
Print ISSN: 2591-7234
Online ISSN: 2591-7242
Series Editor: Dr. Alfred S. Posamentier
Distinguished Lecturer
New York City College of Technology - City University of New York
There are countless applications that would be considered problem solving in
mathematics and beyond. One could even argue that most of mathematics in one
way or another involves solving problems. However, this series is intended to be of
interest to the general audience with the sole purpose of demonstrating the power
and beauty of mathematics through clever problem-solving experiences.
Each of the books will be aimed at the general audience, which implies that the
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o writing level will be such that it will not engulfed in technical language — rather
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ds primary purpose of this series is to approach the topic of mathematics problem-
orl solving in a most appealing and attractive way in order to win more of the
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Vol. 28 Seduced by Mathematics: The Enduring Fascination of Mathematics
by James D Stein
Vol. 27 Mathematics: Its Historical Aspects, Wonders and Beyond
by Alfred S Posamentier and Arthur D Kramer
Vol. 26 Creative Secondary School Mathematics: 125 Enrichment Units
for Grades 7 to 12
by Alfred S Posamentier
Vol. 25 Geometry in Our Three-Dimensional World
by Alfred S Posamentier, Bernd Thaller, Christian Dorner,
Robert Geretschläger, Guenter Maresch, Christian Spreitzer
and David Stuhlpfarrer
For the complete list of volumes in this series, please visit www.worldscientific.com/series/psmb
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Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Control Number: 2022017162
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
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o Problem Solving in Mathematics and Beyond — Vol. 28
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c. SEDUCED BY MATHEMATICS
ntifi The Enduring Fascination of Mathematics
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ci Copyright © 2023 by World Scientific Publishing Co. Pte. Ltd.
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orl All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ww system now known or to be invented, without written permission from the publisher.
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w For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
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D Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy

is not required from the publisher.
ISBN 978-981-125-546-5 (hardcover)
ISBN 978-981-125-635-6 (paperback)
ISBN 978-981-125-547-2 (ebook for institutions)
ISBN 978-981-125-548-9 (ebook for individuals)
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/12812#t=suppl
Desk Editors: Balasubramanian Shanmugam/Rok Ting Tan
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
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b4628  Seduced by Mathematics
Preface — Just What Does
She See in Him, Anyway?
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ed fr she see in him, anyway?”
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nlo “Just what do you see in math, anyway?” is a familiar question for
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encounter someone who doesn’t share their feelings. Of course, it’s
not just math. If you are a jazz aficionado or an American who likes
soccer, you’ve probably heard something similar.
So what do you do? If you’re a jazz aficionado, you find the most
universally appealing jazz you can find and play it for your friend. If
you like soccer, you find videos of incredible goals. But what do you do
if you are me, and feel the way I do about math?
That’s easy. You write this book.
This book would not have been written had I not encountered
several people along the way who made critical contributions. First
up is my wife, Linda. She and her mother visited Taiwan in early
January 2020, and when she returned I contracted pneumonia.
Despite my saying, “I’m sure it’s just a cold,” she made sure I got
proper medical attention, including 6 weeks of caring for me when
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b4628  Seduced by Mathematics
vi Seduced by Mathematics: The Enduring Fascination of Mathematics
I literally couldn’t do anything. Covid was putting in an appearance at
the time, and I’m pretty sure that had she not done what she did,
I wouldn’t be here to write this book.
Next are John Bachar and Ken Warner, two good friends and col-
leagues from California State University, Long Beach. Mathematicians
are grouped in families in much the same way as real people are. Ken’s
thesis advisor at UCLA was Angus Taylor, who was also the thesis
advisor for Bill Bade, who was my thesis advisor. John’s thesis advisor
was Phil Curtis, who co-authored many brilliant and insightful papers
with Bill. Bill talked Phil into hiring me at UCLA, and John and Ken
were instrumental in seeing that I was hired at CSULB and that
m I received tenure. I’m grateful to have this opportunity to express my
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ntifi Oh, yes, without John and Ken, I would not be married to the
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worl dent at CSULB. So, I owe them more than just a career.
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scholar — and there are damned few of us left.” I know John and Ken
fall into that category, and I’d bet large sums that Al does, too.
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b4628  Seduced by Mathematics
About the Author
m James D. Stein
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de University of California at Berkeley. He has pub-
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fixed points, but has also published several papers in physics and
mathematics education. He taught courses at both undergraduate and
graduate levels but specialized in teaching courses in mathematics
education and calculus, real analysis and functional analysis. He
served as a Content Review Expert for the textbook adoption for the
State of California in both 2000 and 2013. He is also the author of
The Fate of Schrodinger's Cat
approximately a dozen books on mathematics and science for the
general public, including , published by
World Scientific Publishing. In retirement, he does podcasts with
authors of books on mathematics and science for New Books Network.
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B1948 Governing Asia
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b4628  Seduced by Mathematics
Contents
m Preface — Just What Does SheSee in Him, Anyway?
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orld Introduction: Seduced by Mathematics vi1i
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w Chapter 1 Seduced by Numbers 9
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o Chapter 4 Seduced by Analytic Geometry 67
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Chapter 5 Seduced by Mathematical Induction
(and How to Avoid It) 85
Chapter 6 Seduced by Calculus I 99
Chapter 7 Seduced by Complex Numbers 113
Chapter 8 Seduced by Infinite Series 129
Chapter 9 Seduced by Probability 147
Chapter 10 Seduced by Infinity 163
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