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

A great book

Since it does provide much of the foundation for modern societies and the applications are commonly covered with very effective disguises, mathematics is both a pillar and a whipping post. More misunderstood and hence feared than any other subject, it is the only one where it is fashionable and acceptable to profess ignorance. The only solution to this problem is to gently explain how valuable it is and let the economic realities of mathematical knowledge take control. In this book, Stein puts forward many valuable points concerning how necessary mathematics is.
While I do endorse the book, there is one negative point that must be made. The title should be different. One of the points in the book is that mathematics is much more than just number manipulation. Although this is well-known to mathematicians, it is a very common misconception. Therefore, the emphasis on numbers present in the title is unfortunate, but probably necessary for marketing purposes.
Now that the ranting is complete, it is time to praise the interior of the book. All of the points are significant and well made. Stein writes very well, explaining topics in a manner that keeps understanding within the range of the target audience, which is the intelligent layperson. His multiple explanations as to why the product of two negative numbers is positive is excellent. In my career, I have encountered several very educated people in technical fields who really did not understand why this is so. They had simply accepted it because they knew it worked, but had always been afraid of raising the question for fear of embarrassment.
Another point that cannot be emphasized enough is the sudden appearance of a "miracle"(reviewer word) number. These are numbers that are put forward to justify a point and are not subject to critical review. After that, they are accepted at a level that makes the belief in them an act of faith. Honestly, is nature so inefficient in anything that humans really use only 10% of their brains? This is an absurd number that has been repeated so many times that it is accepted as gospel. Stein does his part to help clear up some of these problems. However, it would have been better if more time had been spent in this area.
While there is some strength in numbers, the real power lies in the effective use of them, which is the realm of the underlying mathematics. This book contains many valuable lessons on why mathematics, rather than money, makes the world go round.

I can use the book to indirectly persuade youngsters, who think Math. is nothing but number and boring, to take it more seriously. It's hard for me to come up with more logical and more convincing than what already there in the book.

Professor Stein's book is an amazing read. It's humorous, insightful, and educational. A couple of those "great mysteries" from our math classes in school are solved and you will slap your forehead and say,"Well, they could have taught me THAT years ago!"

I highly recommend this book to all levels of math students AND math teachers.

I have been doing calculus for a very long time and I am appalled by the ugly approach to mathematics by these two authors. Math is so beautiful because it is not phoney and the outcome is useful, exciting, tangible, palpable. But not here. The authors simply love wasting time and energy with useless stuff like proving limits that are instinctively so obvious. What next, prove that 1+1=2? You might get sick of math reading this book, but it's not maths fault, really.

This book has helped me come into a firm understanding of some heavy calculus, and I now do well in my calculus classes. Thank you to Newton, for coming up with this stuff (and hijacking Liebniz' notes), and to the two authors, who made calculus easy to understand and very powerful as a tool of the future.

I used this book for three semesters and found it to be nothing less than excellent. Thorough demonstrated examples and tons of practice exercises allows the student to develop a comprehensive foundation in calculus. This book is my math Bible. I find it so valuable, I have kept to this day and still reference it when needed. A must for any serious math student.

McGraw Hill's 'Calculus and Analytic Geometry' is an excellent calc book in itself, and this guide is an excellent resource for any student using that book. It contains solutions for all of the problems in the textbook, step by step in an easy to understand manner. I definitely recommend this book and it deserves 5 stars, but I'm only giving it 4 stars because the price is a bit steep.