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What Is Mathematics? An Elementary Approach to Ideas and Methods 2nd Edition

by Richard Courant (Author), Herbert Robbins (Author), Ian Stewart (Editor)
4.6 4.6 out of 5 stars 487 ratings
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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 does not lead to real understanding or to 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 like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.
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  1. ISBN-10
    0195105192
  2. ISBN-13
    978-0195105193
  3. Edition
    2nd
  4. Publisher
    Oxford University Press
  5. Publication date
    July 18, 1996
  6. Language
    English
  7. Dimensions
    9.02 x 6.05 x 1.06 inches
  8. Print length
    592 pages
  9. See all details
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Editorial Reviews

Amazon.com Review

A 1996 revision of a timeless classic originally published in 1941. Highly recommended for any serious student, teacher or scholar of mathematics.

Review

*Praise for the previous edition:

"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

"Should prove a source of great pleasure and satisfaction."--Journal of Applied Physics

"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

Product details

  • Publisher ‏ : ‎ Oxford University Press; 2nd edition (July 18, 1996)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 592 pages
  • ISBN-10 ‏ : ‎ 0195105192
  • ISBN-13 ‏ : ‎ 978-0195105193
  • Item Weight ‏ : ‎ 1.8 pounds
  • Dimensions ‏ : ‎ 9.02 x 6.05 x 1.06 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 487 ratings

About the author

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Ian Stewart

Ian Stewart

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Ian Stewart FRS is Emeritus Professor of Mathematics at the University of

Warwick and a leading popularizer of mathematics. He is author or coauthor of

over 200 research papers on pattern formation, chaos, network dynamics, and

biomathematics. He has been a Fellow of the Royal Society since 2001, and has

served on Council, its governing body. He has five honorary doctorates.

He has published more than 120 books including Why Beauty is Truth, Professor

Stewart's Cabinet of Mathematical Curiosities, Calculating the Cosmos,

Significant Figures, and the four-volume series The Science of Discworld with

Terry Pratchett and Jack Cohen. He has also written the science fiction novels

Wheelers and Heaven with Jack Cohen, and The Living Labyrinth and Rock Star with

Tim Poston.

He wrote the Mathematical Recreations column for Scientific American from 1990

to 2001. He has made 90 television appearances and 450 radio broadcasts, most of

them about mathematics for the general public, and has delivered hundreds of

public lectures on mathematics.

His awards include the Royal Society’s Faraday Medal, the Gold Medal of the

Institute of Mathematics and Its Applications, the Zeeman Medal (IMA and London

Mathematical Society), the Lewis Thomas Prize (Rockefeller University), and the

Euler Book Prize (Mathematical Association of America).

Customer reviews

4.6 out of 5 stars
487 global ratings

Customers say

Customers find the book's content excellent and accessible to many levels. They also say it's an easy read with exercises. However, some customers feel it'd be better for math enthusiasts and others say it isn't a casual read.

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ContentReadability
22 customers mention "Content"17 positive5 negative

Customers find the book's content excellent for math enthusiasts, teaching advanced concepts and theorems. They also say it's simple to read, provides clear examples, and covers almost all the topics. Readers also appreciate the exercises throughout the reading and find the author touches almost all topics.

"...This book will teach you advanced concepts and theorems. It does not have the wording of an average textbook...." Read more

"...It reveals the beauty of Mathematics and the inconceivable nature of this imperfect world that follows its perfect laws." Read more

"...It is simple to read and gives hundreds of clear examples on solving mathematical problems and great insights into the history of mathematics...." Read more

"This is like a mathematics bible!!! It touches on subjects that I have learned as a math major throughout my college career...." Read more

11 customers mention "Readability"7 positive4 negative

Customers are mixed about the readability. Some mention that it's an easy read and contains exercises. They also appreciate the great clarity of the book. However, some customers say that it is not a casual read.

"...Well written, decently paced given the subject matter, and enlightening...." Read more

"If you love mathematics, you will love this book. It is simple to read and gives hundreds of clear examples on solving mathematical problems and..." Read more

"...and the smaller size type kind of blots together which makes it difficult to read...." Read more

"...It is also an easy read and I love how it contains exercises throughout the reading...." Read more

Top reviews from the United States

Dave
5.0 out of 5 stars Not just a book but an intellectual discussion
Reviewed in the United States on April 11, 2024
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This book is like discussing with an old friend about mathematics. Whenever I come back to this book, I learn something new and I understand math a little better. This book will teach you advanced concepts and theorems. It does not have the wording of an average textbook. It feels like you are having an intellectual debate. Trivia: Albert Einstein read the first edition of this book.
One person found this helpful
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levk1234
5.0 out of 5 stars The perfect eternal classic! A must study for any educated person.
Reviewed in the United States on March 10, 2024
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I was already kind of old when I learned about this book, but it still influenced every aspect of my life.
These kinds of books teach wisdom, not just the subject in the title. It reveals the beauty of Mathematics and the inconceivable nature of this imperfect world that follows its perfect laws.
One person found this helpful
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Chad H.
5.0 out of 5 stars The book that does it all.
Reviewed in the United States on June 15, 2020
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Excellent read, I had always wondered; and now I know.

It’s a total nerd book, if you love math at the conceptual level, enjoy history, and the engineering aspect of how things came to be- this is a great book. I’m a network engineer, wife turned me on to this book from her college days - she was a math major. Well written, decently paced given the subject matter, and enlightening.

If none of the above interests you, the book may also be used as a soporific.
22 people found this helpful
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Angel Ortiz
4.0 out of 5 stars What is Mathematics? An Elementary Approach to Ideas and Methods
Reviewed in the United States on July 30, 2013
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If you love mathematics, you will love this book. It is simple to read and gives hundreds of clear examples on solving mathematical problems and great insights into the history of mathematics. This book is helping me understand and appreciate mathematics. It is excellent for those students interested in continuing exploring the world of mathematics. It is definitely a work of art.
2 people found this helpful
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Yali
5.0 out of 5 stars Mathematics Bible!
Reviewed in the United States on July 4, 2020
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This is like a mathematics bible!!! It touches on subjects that I have learned as a math major throughout my college career. It is also an easy read and I love how it contains exercises throughout the reading. If you are looking for a math book to refresh your mind on some content, then this is the book for you as well!!!
5 people found this helpful
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William B. Zimmerly
5.0 out of 5 stars A Timeless and Unforgettable Introduction to Higher Math
Reviewed in the United States on December 4, 2010
Verified Purchase
After reading this:

"It doesn't matter what mathematical things are: it's what they do that counts. Thus mathematics hovers uneasily between the real and the not real; its meaning does not reside in formal abstractions, but neither is it tangible. This may cause problems with philosophers who like tidy categories, but it is the great strength of mathematics -- what I have elsewhere called its 'unreal reality.' Mathematics links the abstract world of mental concepts to the real world of physical things without being located completely in either." - Ian Stewart, What is Mathematics?

...I was hooked and after reading it several times, I still can't put it down! Great job to all who contributed to creating this masterpiece.
18 people found this helpful
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boredtojeff
3.0 out of 5 stars Great content, bad physical copy
Reviewed in the United States on August 28, 2016
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Content: 5/5
Physical copy: 1/5

I own the paperback 1996 second edition from Oxford University Press, which was $15. Though the price is awesome for the amount of knowledge you get in this book, the print quality is not. It appears that the book is simply photocopied from an earlier edition. The margins are crooked from page to page, the weight of the font varies between lines, and the smaller size type kind of blots together which makes it difficult to read. Most importantly, I've found several places where small parts of notation are missing or cut off, probably from the photocopy not picking it up.

Overall, this is a wonderful book for anyone curious about serious math. It's cheap though, perhaps too cheap. It's due for a new typesetting in a new edition, even if it raises the price to $25-30. It might be better to look for an old hardcover of the book, even if it costs more than a new paperback.
47 people found this helpful
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Danae
5.0 out of 5 stars This book has it all! Very comprehensive
Reviewed in the United States on April 9, 2017
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I'm really excited to have gotten this book. I used to hate math, and as a college student, I got lucky enough to have a great teacher who helped me appreciate the subject. This book has everything! The basics all the way through calculus. It's accessible to many levels too. When I finish school and begin teaching, I will be using this book to create lesson plans. Out toy like math at all, or want to learn, this is a great book.
11 people found this helpful
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Top reviews from other countries

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José Marcelo Medina Camacho
5.0 out of 5 stars Uno de los mejores libros, con autor de lujo
Reviewed in Mexico on December 28, 2023
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El libro es estupendo pero, la tipografía no es muy legible, principalmente donde hay ecuaciones, no se si los reescribieron, en algunos lados pésimamente interpretados confunden el 8 con una s, en fín creo que deberia de haberlo comprado empastado, in clusive el kindle deforma mucho este tipo de documentos matemáticos, les recomiendo comprar mejor la edición empastada.
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Arnab Chaudhuri
5.0 out of 5 stars Great book
Reviewed in Canada on June 7, 2022
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Great book
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Nicolas
5.0 out of 5 stars Muy completo
Reviewed in Spain on July 27, 2021
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Gran libro para los que nos gusta la matematica.
One person found this helpful
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Pritam Sarkar
5.0 out of 5 stars A great classic.
Reviewed in India on April 21, 2021
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This book is like a textbook. It covers almost all topics of pure mathematics.
One person found this helpful
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Docpappy
5.0 out of 5 stars All time favourite
Reviewed in the United Kingdom on August 11, 2018
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This book is probably my all time favourite mathematics text for introducing undergraduate mathematics. The author is a prolific writer and very engaging. The breadth of topics covered is impressive.
2 people found this helpful
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