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What Is Mathematics?: An Elementary Approach to Ideas and Methods (Oxford Paperbacks) Paperback – 5 Sep 1996


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Product details

  • Paperback: 592 pages
  • Publisher: OUP USA; 2 edition (5 Sept. 1996)
  • Language: English
  • ISBN-10: 0195105192
  • ISBN-13: 978-0195105193
  • Product Dimensions: 22.9 x 2.7 x 15.4 cm
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (22 customer reviews)
  • Amazon Bestsellers Rank: 130,152 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

Can...be read with great profit by anyone desiring general mathematical literacy. (Mathematics Abstracts)

A great book. (Ludwig Otto, Paul Quinn College)

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)

Without doubt, the work will have great influence. It should be in the hands of everyone, professional or otherwise, who is interested in scientific thinking. (The New York Times)

A work of extraordinary perfection. (Mathematical Reviews)

It contains an excellent selection of material for students who have no desire to develop mathematical skills but who may be willing to look briefly into this field of intellectual activity....For the inquiring student who wishes to know what real mathematics is about, or for the trained engineer or physicist who has some interest in the justification of procedures he uses, it should prove a source of great pleasure and satisfaction. (Journal of Applied Physics)

This book is a work of art. (Marston Morse)

This is not a book in philosophy; but there are probably few philosophers who can not gain instruction and clarification from it. It succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods."

It is a work of high perfection, whether judged by aesthetic, pedagogical or scientific standards. It is astonishing to what extent (Herman Weyl)

Still a book that all prospective mathematics teachers should read and experience. A rare book that has retained its "freshness" and readability for more than 50 years....Very readable. (Stephen Krulik, Temple University)

About the Author

The late Richard Courant, headed the Department of Mathematicas at New York University and was Director of the Institute of Mathematical Sciences—which has subsequently renamed the Courant Institute of Mathematical Sciences. His book Mathematical Physics is familiar to every physicist, and his book Differential and Integral Calculus is acknowledged to be one of the best presentations of the subject written in modern times. Herbert Robbins is New Jersey Professor of Mathematical Statistics at Rutgers University. Ian Stewart is Professor of Mathematics at the University of Warwick, and author of Nature's Numbers and Does God Play Dice?. He also writes the "Mathematical Recreations" column in Scientific American.

Inside This Book (Learn More)
First Sentence
Number is the basis of modern mathematics. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews

9 of 9 people found the following review helpful By Palle E T Jorgensen on 16 April 2003
Format: Paperback
Einstein writes..."Easily understandable." And Herman Weyl,..."It is a work of high perfection." It is both for
beginners and for scholars. The first edition by Courant and Robbins, has been revised, with love and care, by Ian Stewart.
Of the sciences, math stands out in the way some central ideas and tools are timeless. Key math ideas from our first mathematical experiences, perhaps early in life, often have more permanence this way. While the fads do change in math, there are some landmarks that remain, and which inspire generations. And they are as useful now as they were at their inception, the fundamentals of numbers, of geometry, of calculus and differential equations. The authors are ambitious in trying to cover the essetials within the span of 500 plus pages. You find the facts, presented in clear and engaging prose, and with lots of illustrations.
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32 of 34 people found the following review helpful By A Customer on 7 Feb. 2001
Format: Paperback
A wide-ranging overview of pure mathematics, first published in the 1940s, now re-issued and brought up to date with an additional chapter by Ian Stewart, this book is at the level of a capable student at the higher end of high school mathematics (A-level in the UK) or the beginning of a mathematics degree.
The scope of this book is awesome, covering number theory, geometry, topology, calculus, and much more. The chapter on projective geometry is a real treat, as it explores a beautiful topic that has dropped out of the modern maths syllabus. The only noticeable omission is group theory, which gets only a passing mention.
The style is clear, although the pace is rapid, and the reader is expected to fill in some details. There is an emphasis throughout on rigour - where this is relaxed for the sake of brevity, this is clearly signalled.
An appendix of problems and exercises (without answers) encourages further exploration of each topic.
A true classic and an enhancement to any mathematician's bookshelf.
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6 of 6 people found the following review helpful By Enigma on 12 Oct. 2010
Format: Paperback
I was searching for the perfect book in my first year of a 2 year BA Hons in Mathematics Education to really help me to extend my mathematical knowledge but in a readable format.
This was recommended to me by my Geometry lecturer as the bible to which he would always return and when I read it I could see why. Fantastically clear explanations which really get back to the roots of things like differentiation. I am sure that the fact the author used his (then)teenage son to help him in formulating understandable explanations shines through. This book might have first been written many decades ago, but it has certainly stood the test of time. I cant recommend it highly enough.
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5 of 5 people found the following review helpful By Paul P. Mealing on 4 Nov. 2012
Format: Paperback Verified Purchase
This is a book for scholars. If you want to learn some mathematics instead of just reading about it, then this is the book for you. It combines exposition with worked examples in just the right balance, giving mathematical explanations in diverse fields like topology, Euclidean geometry, number theory, Boolean algebra, calculus, complex algebra and mathematical induction (not a complete list). You can dip into it anywhere or read it cover to cover. It's refreshing to read a text on mathematics where, at the end of the day, you accomplish a deeper understanding and a confidence to apply it.

Elvene
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4 of 4 people found the following review helpful By M. F. Cayley on 5 April 2011
Format: Paperback Verified Purchase
The book covers a broad range of topics in (mainly pure) maths. It should be comprehensible to anyone who has done the equivalent of UK "A" Level maths. To get the most out of it, you need to be willing to concentrate hard - explanations are clear but sometimes at a breathless pace - and to tackle some of the exercises. The most technical parts are clearly flagged up as optional reading. For anyone wanting to go beyond school maths, or about to embark on a maths course at university, the book will be invaluable.

If I have a quibble, it is that the exercises and some parts of the book are printed in smallish type which my (ageing) eyes had difficulty coping with, especially when it came to subscripts and superscripts, some of which I could not decipher. In places the notation - for instance some symbols used in relation to sets - is outmoded, but this is not a significant problem.
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9 of 10 people found the following review helpful By A Customer on 24 July 1998
Format: Paperback
So Einstein thought this book "easily understandable" ? Well, if you are a beginner at calculus you will not find it "easily understandable", for that would mean you didn't learn a single new thing! Calculus is perhaps the most profound and far-reaching discovery of the millenium, and is certainly not trivial. However, this magical book is the best possible introduction. It is written so that your perplexities will always be accompanied by so beautiful results or promises of results, that you will be more than ready to do the necessary efforts. These come, for instance, in the form of exercises and in the details of the demonstrations, which are all there. There is no cheating. Well, the book is not only about calculus. There are many previous chapters on theory of numbers, geometry, algebra, topology. But I think it culminates with calculus, and the preceding chapters serve as steps of a staircase leading to it. The new edition has the collaboratio! n of Ian Stewart, an inspired writer.
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2 of 2 people found the following review helpful By Jamie B. on 2 Nov. 2009
Format: Paperback
What Courant and Robbins have managed to do is to write a book that not only introduces to some of the most fascinating aspects of mathematics, in a beautiful, challenging way, but also encourages you to think beyond the confines of the question. Perhaps Einstein was rather overoptimistic when he called it easily understandable, but nonetheless, I think it is the challenge that makes it exciting, because where would the fun be if you could it all in 5 minutes? And, it is usually in thinking about something like this that you gain a more intimate understanding of and deeper appreciation for it.
Covering everything from Number Theory to Constructive and Projective Geometry, Limits and Topology, this is well worth the price.
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