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What Is Mathematics? An Elementary Approach to Ideas and Methods
Binding: Paperback
Author: Richard Courant
Manufacturer: Oxford University Press, USA
Availability: Usually ships in 24 hours
Features:
Average Rating: 5.0
Total Customer Reviews: 33
List Price: $24.95
Our Price: $16.47
Sales Rank: 10166
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.
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Users Product Reviews: |
Product Review Summary: A fascinating book. 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.
Product Review Summary: Math education at its best and most beautiful. 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. Let 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.
Product Review Summary: Incredibly thorough 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.
Product Review Summary: Rescued me from years of math despair 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.
Product Review Summary: What is "What is Mathematics"??? 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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