How the Other Half Thinks: Adventures in Mathematical Reasoning 1st Edition by Sherman K. Stein (PDF)

Description

With its ingeniously intuitive approach, How the Other Half Thinks will appeal to those enthusiasts who are charmed by mathematics and its style of thinking, as well as those more tentative readers who would like to find out why advanced mathematics casts a spell over so many of its followers. At once an entertaining, interactive mathematical exercise and an innovative exploration of mathematical reasoning, it will appeal to the enthusiast and the novice, the scientist and the humanist, and the left-brained and the right-brained.

User’s Reviews

Editorial Reviews: From the Back Cover “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.”–Sherman Stein from the IntroductionSome topics in advanced mathematics simply require arithmetic and common sense. How the Other Half Thinks by Sherman Stein uses this phenomenon to offer both the adept and the beginner eight fascinating illustrations of the mathematical way. With a leisurely pace, Stein guides readers through each mathematical problem. His approach makes complex concepts like topology, set theory, and probability accessible and exciting. After the problem is solved, Stein shows how the related mathematics are applied in areas such as computers, measurement of astronomical distances, and cell growth. The mathematical style of thinking is one that everyone can use to understand the world, whether they use the creative right half of the brain, or rely more on the analytical left half. How the Other Half Thinks is for the novice and the skilled, the poet and the scientist–who can each be immersed in the mathematical world, not as a spectator, but as a participant. About the Author Sherman Stein, Ph.D., has taught at the University of California at Davis. He is the recipient of the Lester R. Ford Award for Mathematical Exposition and the B eckenback Book Prize for Algebra and Tiling (with S. Szabó). He also received the Distinguished Teaching Award at his campus and was awarded an Honorary Doctorate of Humane Letters from Marietta College.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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. YaqubProfessor Emeritus of mathematicsSUNY College at Fredonia

⭐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.

⭐The author poses a series of mathematical puzzles and then shows how to solve them, primarily using infinite series. Very very clever. It all makes sense when you read the solutions but you’d never have thought of them yourself.

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