How the Other Half Thinks: Adventures in Mathematical Reasoning [Hardcover]

Sherman K. Stein (Author)

Book Description

ISBN-10: 007137339X | ISBN-13: 978-0071373395 | Publication Date: June 21, 2001 | Edition: 1st

Maths enthusiasts aren't necessarily the number-crunching geeks we tend to assume. In fact, they know that maths is about much more than numbers; it is a profoundly philosophical endeavour, as well as a stimulating mental exercise. In "How the Other Half Thinks", Sherman Stein emphasizes the creative elements of mathematics by exploring some significant mathematical discoveries through simple, intuitive manipulations. With an ingenious technique that uses no algebra or trigonometry, and only a minimum of arithmetic, Stein takes us through the thought process behind some of math's great discoveries and applications. Each chapter begins with a simple question about strings made up of the letters "a" and "b", which leads to other, more profound questions. Along the way, we become familiar with concepts from such fields as topology and probability, and learn how they have led to applications such as codes and radar, computing and even baseball statistics. Recreational and instructive, "How the Other Half Thinks" should appeal to die-hard maths enthusiasts (of which there are many) as well as those "right-brainers" who are looking for a way to understand and enjoy maths.

Editorial Reviews

From the Back Cover

Some topics in advanced mathematics require nothing more than arithmetic and common sense. How the Other Half Thinks makes use of this phenomenon to offer both the mathematically adept and mathematical beginner eight fascinating illustrations of the mathematical way.

Each chapter starts with a question about strings made up of nothing more than two letters. This question in turn suggests thought-provoking problems. After these problems are explored and solved, the author shows how the related mathematics has been applied in areas as varied as computers, cell phones, measurement of astronomical distances, and cell growth.

An experienced educator, prize-winning expositor, and researcher, Stein engagingly presents each concept. The leisurely pace allows a reader to move slowly through each chapter, omitting no steps. This approach makes complex concepts like topology, set theory, and probability accessible and exciting. The book creates a bridge across the gulf between the two cultures: humanities and the sciences.

Stein shows how the mathematical style of thinking is one that everyone can use to understand the world. This charming book speaks to both those who employ the intuitive, creative right half of the brain, and to those who rely more on the analytical, numerical left half. How the Other Half Thinks is for the novice and the skilled, the poet and the scientist, the left-brained and the right-brained. When you read this book, you are immersed in the world of mathematics, not as a spectator, but as an involved participant.

"Occasionally, in some difficult musical compositions there are beautiful, but easy parts­­"so simple a beginner could play them. So it is with mathematics as well. There are some discoveries in advanced mathematics that do not depend on specialized knowledge, not even on algebra, geometry, or trigonometry. Instead they may involve, at most, a little arithmetic, such as 'the sum of two odd numbers is even,' and common sense. As I wrote, I kept in mind two types of readers: those who enjoyed mathematics until they were turned off by an unpleasant episode, usually around fifth grade; and mathematics aficionados, who will find much that is new throughout the book."
­­"Sherman Stein

About the Author

Sherman Stein, received his Ph.D. from Columbia University. After a one-year instructorship at Princeton University, he joined the faculty at the University of California, Davis, where he taught until 1993. His main mathematical interests are in algebra, combinatorics, and pedagogy. He has been the recipient of two MAA awards; the Lester R. Ford Award for Mathematical Exposition, and the Beckenbach Book Prize for Algebra and Tiling (with Sandor Szabo). He also received The Distinguished Teaching Award from the University of California, Davis, and an honorary Doctor of Humane Letters from Marietta College. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Hardcover: 177 pages
• Publisher: McGraw-Hill Companies; 1st edition (June 21, 2001)
• Language: English
• ISBN-10: 007137339X
• ISBN-13: 978-0071373395
• Product Dimensions: 8.6 x 5.8 x 0.7 inches
• Shipping Weight: 12.8 ounces
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,375,536 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

31 of 32 people found the following review helpful:

5.0 out of 5 stars A Welcome Addition, September 9, 2001

By 

Penelope W. Yaqub "Fawzi M. Yaqub" (Fredonia, NY, U.S.A.) - See all my reviews
(REAL NAME)   

This review is from: How the Other Half Thinks: Adventures in Mathematical Reasoning (Hardcover)

This is a well written and much needed book. Of all disciplines, mathematics continues to be the least understood by the general public. Even among the scientists who use mathematics daily in their work, many are not fully aware of the true nature of the subject. One of the main reasons for this lack of familiarity is the absence of books that illustrate the mathematical way of thinking in a way that non-mathematicians can easily comprehend. In this book, Sherman Stein leads the reader through a number of genuine mathematical problems whose statements and solutions are presented in a way that requires no more than the use of common sense and, possibly, a few facts from elementary arithmetic. By reading this book, readers will have a chance to see how mathematicians think and what processes they go through before solving a mathematical problem.
The book consists of eight chapters, each starts with a simple question that leads to others, and from the discussion of these a general question arises and an answer is developed. This question then is often related to others asked by other mathematicians or scientists and, on a number of occasions, some applications are pointed out. Although the eight chapters are basically independent and can be read in any order, there is similarity in the type of questions they treat. The best way to get a flavor of the book--the type of questions it discusses and how the material is handled--is to read the first chapter, where a question that seems so simple at first glance leads to an interesting and unexpected solution. This spirit continues throughout the entire book. I believe that the author's choice of topics and the clear and interesting way in which he discusses them make this book truly accessible to any intelligent member of the "other half." The book also has something of interest to professional mathematicians as well; they will find that many of the problems it discusses are new to them.

Fawzi M. Yaqub
Professor Emeritus of mathematics
SUNY College at Fredonia

8 of 9 people found the following review helpful:

5.0 out of 5 stars "Real math" for the layman, August 28, 2003

By 

Steve Stowers (Springfield, Illinois USA) - See all my reviews

This review is from: How the Other Half Thinks: Adventures in Mathematical Reasoning (Hardcover)

In his preface, the author does a good job of explaining what he set out to do in this book; then, in the rest of the book, he does a good job of doing it! Stein has attempted to present examples of real mathematical reasoning that (unlike some of the most beautiful parts of math) DON'T require any math background to understand or appreciate--and in my opinion, he succeeds brilliantly. If you love a well-reasoned, clearly explained argument but never even took algebra or geometry, you will enjoy this book. On the other hand, even mathematically sophisticated readers are likely to find some things here that they hadn't seen before, so they should enjoy the book too.

5 of 21 people found the following review helpful:

1.0 out of 5 stars Would be better named "How to put the other half to sleep", December 2, 2003

By 

G. Varghese "gvarghese" (NJ, USA) - See all my reviews
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This review is from: How the Other Half Thinks: Adventures in Mathematical Reasoning (Paperback)

Being of a non-mathematical nature and "the other half", I was forced to read this book for my college math course and do an essay on it. My teacher told me the book discusses how non-mathematical minds think. I figured it would be something worth looking into and might help me understand math better. The book did no such thing. All it basically did was put me to sleep. It discusses how a mathematical mind would approach a problem and that's all well and wonderful, but I'm not of the mathematical mind and neither are most of the people who would read this. Before you get the wrong idea, I love puzzles and analyzing things like real problem solving, but I've never been so bored in my life (and I read 1500+ page books for computer programming with ease) as I was when I read this book. Writing college papers is not difficult, but writing one that's more than a page that a math teacher will like on this book is damn near impossible. A mathematics professor or even a math major might find this useful, but in my opinion, for other people who are like me it's going to be relatively useless because it left me even more confused and with a stronger dislike for math.