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on 7 February 2001
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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on 11 December 2014
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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on 16 April 2003
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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on 4 November 2012
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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on 12 October 2010
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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on 5 April 2011
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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on 8 May 2013
This book was great! It covered a huge range of mathematical ideas, and pushed past anything learned in school or college. The algebra is well laid out, and it is well-written. The only fault I can give is that it is quite a dense book. At times, pushing through one chapter could take hours, but if you have the time and the inclination, then I thoroughly recommend this as a recreational and educational Mathematics book!
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on 10 July 2005
Forgiving my blasphemy above, this is an unsurpassably great maths book. This book is about beautiful maths beautifully written: it epitomises the romance and magnetism of mathematics. You will learn some fundamental maths supplemented with techniques as powerful as they are elegent. I'm a theorist, and I think all academics and amateurs should have this book - not just my (socially retarded) brothers, the mathematicians.
This book aquaints you with the pure fundamentals in the calculus, topology, limits and convergence, the number system........just buy this book, ok. If you're here, and thus considering buying this book, let me assure you that it is well worth it.
If you love mathematics, you will love this book; and if you love this book, you're in love with mathematics.
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on 24 July 1998
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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on 2 November 2009
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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