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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A 1996 revision of a timeless classic originally published in 1941. Highly recommended for any serious student, teacher or scholar of mathematics.
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
"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
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Number is the basis of modern mathematics. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Number is the basis of modern mathematics. Read the first page
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3 of 3 people found the following review helpful
Format:Paperback
Courant's 500-page text is not entirely suitable for the layman. Its target audience includes those who enjoy reading and studying mathematics and have a good background through precalculus or higher. "What is Mathematics?" is a mathematics book, not a book about mathematics.
"What is Mathematics?" is not a new book. It was first published in 1941. New editions appeared in 1943, 1945, and 1947. My soft cover fourth edition by Oxford University Press is in its 12 printing.
The authors indicate that it is no means necessary to "plow through it page by page, chapter by chapter". I fully agree. I have skipped around, jumping to chapters of particular interest, but I have now read nearly every chapter.
I initially skipped to page 165 and delved directly into projective geometry (chapter IV), proceeded to topology (chapter V), and then jumped backwards to the beginning to explore the theory of numbers. After moving to geometry, I finally returned to the later chapters on functions and limits, maxima and minima, and the calculus.
Courant engages the reader in discussions on mathematical concepts rather than focusing on applications and problem solving. "What is Mathematics?" is a great textbook for students that have completed a year or more of calculus and wish to pull all of their mathematical learning together before moving on to more advanced studies. I suspect that it would even be welcomed by students that have completed an undergraduate degree in mathematics.
I cannot resist quoting Albert Einstein's comment on What is Mathematics? - "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable."
Richard Courant was a highly respected mathematician. He taught in Germany and in Cambridge and was director of the Institute of Mathematical Sciences at New York University (now renamed the Courant Institute of Mathematical Sciences). Courant has authored other widely acclaimed mathematical texts including Methods of Mathematical Physics (co-authored with David Hilbert) and his popular Differential and Integral Calculus.
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, and more. Much of it is presented with an eye to applications. The book is a classic and a masterpiece. The co-authors are ambitious (and remarkably sucessful)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. The book has been used by generations of readers, and it still points to the future.
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, and more. Much of it is presented with an eye to applications. The book is a classic and a masterpiece. The co-authors are ambitious (and remarkably sucessful)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. The book has been used by generations of readers, and it still points to the future.
By "kangaru"
Format:Paperback
This is an interesting and wide ranging book. In the main it presents, develops and explains it's ideas very well, although I did not always find it, as one reviewer, a mister Albert Einstein described it, "easily understandable". I have two minor complaints about this book:
1) Print quality
For no apparent reason the text size varies occasionally, and in places the printing is slightly blurred, so that sometimes the subscripts and superscripts on formulae are illegible. Perhaps they skimped on typesetting costs by photoreproducing formulae from the original printing?
2) Incompleteness
If you bought this book because the front cover says "...representation of the fundamental concepts and methods of the whole field of mathematics" (another A.E. quote) you may be disappointed to find this is not the case. Trigonometry, for example, is not discussed, except where it crops up in other topics such as applying calculus to trig functions.
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4.6 out of 5 stars
Most recent customer reviews
4.0 out of 5 stars
Not an 'easy' read
This is a demanding book. One cannot read it listening to Bach. [a clash of complexities]. The construction of he book is 'old style' [which is every seeming possible variation is... Read more
Published on Aug 21 2003 by newton fisher
5.0 out of 5 stars
A book on mathematical ideas to look beyond the formalism
A very interesting exposition of some of the main branches and ideas of mathematics. This is a book for beginners and experts, students and professors. Read more
Published on Sep 6 2002 by Gustavo de Oliveira
5.0 out of 5 stars
For mature thinking in mathematics
A "closer" look at mathematics: Book ends where all other books on Mathematics start. With this book, you look at all of basic mathematics much more deeply. Read more
Published on Jan 31 2002 by Alok Govil
5.0 out of 5 stars
Lucid!!!
The title suggests a topic more on the philosophy
of math rather than math proper, but it's all real math, and superbly
done!
of math rather than math proper, but it's all real math, and superbly
done!
Published on Dec 26 2001 by a reader
5.0 out of 5 stars
A classic that will challenge and inspire.. A MUST HAVE!!
This book will give you a superb introduction to basic mathematics culminating in the CALCULUS. The topics and manner of presentations are excellent. Read more
Published on Sep 11 2001 by Kersi Von Zerububbel
5.0 out of 5 stars
classic
I give this book 5 stars because it is a classic. I believe, however, that it is too sketchy to be useful for the beginner as it is advertised. Read more
Published on Aug 3 2001 by Antonio Villarroel
5.0 out of 5 stars
Inspirational
Like other reviewers, I first read this book between high school and college, and my experience was the same - wonder, challenge, appreciation. Read more
Published on Sep 15 2000 by Judith H. Klitgaard
5.0 out of 5 stars
A Masterpiece
If you start to read "What is Mathematics?" in order to find a direct answer to the title's issue, forget it! Read more
Published on Jun 24 2000 by Ary Armando Perez Jr.
5.0 out of 5 stars
Inspiring
Although I was always good in math in high school, I never really appreciated it. One summer I found this book in a dusty little corner of a bookshelf and I started reading it. Read more
Published on Oct 24 1999
5.0 out of 5 stars
Masterpiece of mathematical exposition
I read this book while in high school, before enrolling in college. I was captured by the beauty of the subject. Read more
Published on May 21 1999 by Giuseppe A. Paleologo
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