| View Larger Image | What Is Mathematics? An Elementary Approach to Ideas and Methods | Paperbackby Richard Courant (Author), Herbert Robbins (Author), Ian Stewart (Editor)
| List Price: | $24.95 | | Price: | $16.47 | | You Save: | $8.48 (34%) | | | Available: | Usually ships in 24 hours |
| | Binding: | Paperback | | Publisher: | Oxford University Press, USA | | Edition: | 2nd Edition | | Page Count: | 592 Pages | | Publication Date: | July 18, 1996 | | Sales Rank: | 15,613th |
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FEATURES | - ISBN13: 9780195105193
- Condition: NEW
- Notes: Brand New from Publisher. No Remainder Mark.
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EDITORIAL REVIEWS |
Product Description
"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. |
Amazon.com Review
A 1996 revision of a timeless classic originally published in 1941. Highly recommended for any serious student, teacher or scholar of mathematics. |
CUSTOMER REVIEWS (Average Customer Rating: 5.0 based on 31 reviews)
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Incredibly thorough by Peter J. Mitas  5 Stars
April 17, 2009
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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Rescued me from years of math despair by J. M. Eriksson 5 Stars
January 23, 2009
I always liked math as a child and was quite talented, but I absolutely hated the way math was taught in school. For a long time I could always grasp the necessary concepts intuitively, and so I didn't have to bother with the books we were supposed to be working with (my teachers were frustrated over my not doing any "exercises", but I got away with it since I aced the exams). But when it came to high school and a bit more demanding math (mainly calculus), I couldn't do it all by pure intuition and since I couldn't deal with the math textbooks, I fell behind. Eventually I developed an outright aversion for math, confusing my life-long love for the subject with my intense dislike of how it was taught in school.
I kept looking for a better way to learn math - I just knew there had to be one. University textbooks was often better structured, but they presumed a lot of skills that I didn't have yet. Far too many years later I randomly came upon this book, and in it I found everything I had been looking for all along, namely clear and concise discussions of mathematical concepts.
In school, the focus was always on exercises, with no clear explanation of the concepts involved. In fact, discussion of mathematical concepts was clearly avoided, even when it would have seemed quite natural. The general idea seemed to be to get kids to use mathematical concepts more or less blindly, and thereby "learning" them without having to think about them. For me this was just utterly perverse and unspeakably frustrating. Being intensely interested in understanding things, but strongly averse to mindless repetition, more than anything I felt like I was being punished, expected to learn how to use math, but deviously kept from actually understanding what I was doing. In practice, I could absolutely not do the exercises without first grasping the concepts, and once I knew the concepts, the type of exercises provided were meaningless.
When I found the book by Courant, I knew after only a few pages that I was home. Here were rigorous explanations and discussions of all the basic concepts of math, beginning on the first page with a discussion of the concept of number, moving on through the book to include the foundations of number theory, geometry, topology and calculus. There are also some exercises in this book, but they are not in any way the main focus, and they are quite well devised. Despite struggling with an almost pathological aversion to exercises in mathematical textbooks, I quite enjoyed them!
If you are an intelligent person who has given up on math, despite having a vague sense that you really should be enjoying it, perhaps you should take a look at this book. Doing so is very easy since large parts of it are viewable for free through Google Books.
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What is "What is Mathematics"??? by Ioannis Sarras 5 Stars
October 12, 2008
It's a lucid presentation of the ideas that govern the different domains of Mathematics. Clear but not too easy, it needs commitment by the reader in order to understand its essence to the full. Courant (as his mentor Hilbert) shows how important and useful it is to demystify the cumbersome technicalities that often dominate the subject.
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Review by Undergraduate Math Major by bluemountain98 (Meadville, PA) 5 Stars
July 06, 2008
As an above average undergraduate math major(by no means exceptional) I always had some nagging questions in the back of my mind. Questions like: what is the connection between e, pi, 1/x? Why does the Taylor series expansion work? How did we come across complex numbers? I found a lot of good answers in this book. This book is totally worth the price - I think I can speak for (and speak to) all who have at least an undergraduate preparation in math (and have some knawing questions).
Overall a great, broad overview of the discipline. Spread the word.
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It's incredible (when read carefully with a controlled imagination) by A Reader (California USA) 5 Stars
January 17, 2008
Nevertheless, this book does in fact deserve 5 stars. I wanted to be the first to give it less than 4 stars, but the quality of the presentation of ideas is just too damn good.
An engineer or physicist would be quite happy with this book, which makes sense given Courant's career focus on applied mathematics. Still, a lot of "pure" mathematicians obviously enjoy it too. lol.
(By the way, this review really refers to original. No doubt Ian Stewart crapped it up a bit.)
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