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What Is Mathematics? An Elementary Approach to Ideas and Methods (Oxford Paperbacks) Paperback – 18 Jul 1996
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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.See all Product description
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Top customer reviews
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.
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
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.
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.
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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