| What Is Mathematics? An Elementary Approach to Ideas and Methods
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"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."--Albert Einstein (on the first edition)For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not to real understanding or greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.
Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.
Formal mathematics is like spelling and grammar: a matter of the correct application of local rules. Meaningful mathematics is like journalism: it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature: it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is a marvelously literate story: it opens a window onto the world of mathematics for anyone interested to view.
A 1996 revision of a timeless classic originally published in 1941. Highly recommended for any serious student, teacher or scholar of mathematics.
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- ISBN13: 9780195105193- Condition: USED - Very Good
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By S. Chien
Everything is in good condition as said. I am happy of doing business with the seller.
TKS.
By Olifante (Lisbon, Portugal)
The book is littered with mangled formulas, mostly due to the fact the minus sign is missing from most formulas. This is completely unacceptable in any math book, but particularly so in a book aimed at beginners, who will probably feel bewildered by the huge amount of nonsensical formulas.
Adding insult to injury, the poor layout of Kindle edition makes the book hard to enjoy. Section headings often appear as orphans at the bottom of pages and many formulas are displayed as small, low-quality images. The low image quality is especially visible when reading the book on a Kindle 2 as opposed to for example the Kindle Mac app. Inlining formula images with running text is particularly annoying, since it deforms the text layout.
I was so annoyed by these problems that I tried to return this book, only to discover that returns are not allowed for digital books.
Do NOT buy the Kindle edition of this book.
By flickfreak (USA)
For those who love mathematics, I can't praise this work highly enough. It's not designed so much to help the reader solve math problems as it is to impart a solid understanding of the fundamentals of the subject. Anyone who finds mathematics endlessly intriguing will be glad to own this book.
By Methaya Sirichit (Bangkok Thailand)
This book is so beautifully written that it epitomises an ideal of mathematics education. Everything is presented and explained clearly, which makes it suitable for the layman. The contents covered are also ambitious and wide-range. Topics are presented in a logical and satisfying manner. Natural numbers and the concept of induction are introduced early. Then a more thorough discussion of number system follows in Chapter 2 which concludes the background in arithmatic. After that the book shifts its focus to the opposite pole of mathematics where geometry (both euclidian and beyond) are presented in a way that algebra is employed to give greater understanding and appreciation of the topic and to allow the readers to understand the key role of algebra which helps bringing arithmetic and geometry together in a coherent manner.
Although I believe that the book is suited for lay people, we must not expect that the authors will hold you hand-in-hand while introducing you to the beauty of mathematics. The authors make clear that they want you to think. And think hard you will, if you want to get the best out of this book. By this, we have come to the greatest merit of this tome: sure, everything is clearly explained, however the most important messages are written not conspicuously but between the lines (and much of them in the exercises). We can only come to appreciate what the authors want to say when we commit ourselves in the required thinking part and discover for ourselves what the authors want us to know but didn't say. I think the book succeeds triumphantly in its writing style and is therefore difficult to be out done in this respect. Mathematics will continue to progress but this book will never become obsolete.
I do strongly encourage everyone who reads this book to do all the exercises in every chapter. You have no idea what you miss if you skip them; the are the crown-gem of this book. Don't be deterred if you cannot solve over a third of the problems. Just by thinking about them (albeit unable to solve) will move you closer to real understanding of the topics being discussed. Don't be appalled to know that answers are not provided in the back of the book. You know it when you solve it; this only heigthens the satisfaction of doing math.
I know many math-degree holders who hesitate to refer to themselves as mathematicians (they would just say "well, I had/did a degree in math."). I think that is because while they know a lot of mathematical facts and techniques, they never really understand or appreciate it in a fundamental way. This shows what is missing in our math education. This book is the ideal antidote.
Also check out books by John Stillwell. Most of his books are as good as this volume.
By Peter J. Mitas
Basic Math Quick Reference Handbook
This thorough coverage of so many aspects of mathematics forms a threshold that separates the interested enthusiast from the professional mathematician.
Couldn't be better.
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