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What Is Mathematics? An Elementary Approach to Ideas and Methods (Oxford Paperbacks) Paperback – 18 Jul 1996

4.5 out of 5 stars 29 customer reviews

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Product details

  • Paperback: 592 pages
  • Publisher: Oxford University Press, U.S.A.; 2 edition (18 July 1996)
  • Language: English
  • ISBN-10: 0195105192
  • ISBN-13: 978-0195105193
  • Product Dimensions: 22.9 x 2.7 x 15.4 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (29 customer reviews)
  • Amazon Bestsellers Rank: 79,629 in Books (See Top 100 in Books)
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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."Journal of Philosophy

It is a work of high perfection, whether judged by aesthetic, pedagogical or scientific standards. It is astonishing to what extent What is Mathematics? has succeeded in making clear by means of the simplest examples all the fundamental ideas and methods which we mathematicians consider the life blood of our science. (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)

From the Back Cover

Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Brought up to date with a new chapter by Ian Stewart, this 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.

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Top Customer Reviews

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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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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Format: Kindle Edition Verified Purchase
What Is Mathematics is such a great book but the kindle edition is awful.

I am a young Mathematician not as good as many readers which may find more mistakes, nonetheless I've found many many mistakes. I may be the only one with this issues...

I've found (and sent corrections but haven't been fixed although a download a newer verson which was available): Subindexes that do not match (Pos 938 during the proof of the uniqueness factorization of any integer N) what is that q_8?, the word cöordinates along the book is miswritten. Empty set symbol used instead of 0. The infinity symbol is represented by "oo". Really? Can't this be any better?

I'm willing to enjoy this book but the kindle version is horrible.

If could go back to October, belive me i wouldn't buy this book for the kindle, I'd buy the paperback edition
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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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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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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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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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