Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.

  • Apple
  • Android
  • Windows Phone
  • Android

To get the free app, enter your mobile phone number.

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

4.5 out of 5 stars 69 customer reviews
ISBN-13: 978-0195105193
ISBN-10: 0195105192
Why is ISBN important?
ISBN
This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The 13-digit and 10-digit formats both work.
Scan an ISBN with your phone
Use the Amazon App to scan ISBNs and compare prices.
Have one to sell? Sell on Amazon
Buy used On clicking this link, a new layer will be open
$11.31 On clicking this link, a new layer will be open
Buy new On clicking this link, a new layer will be open
$14.65 On clicking this link, a new layer will be open
More Buying Choices
62 New from $10.00 60 Used from $7.11
Free Two-Day Shipping for College Students with Prime Student Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student


The Amazon Book Review
The Amazon Book Review
Author interviews, book reviews, editors picks, and more. Read it now
$14.65 FREE Shipping on orders with at least $25 of books. In Stock. Ships from and sold by Amazon.com. Gift-wrap available.
click to open popover

Frequently Bought Together

  • What Is Mathematics? An Elementary Approach to Ideas and Methods
  • +
  • Concepts of Modern Mathematics (Dover Books on Mathematics)
  • +
  • Mathematics: Its Content, Methods and Meaning (3 Volumes in One)
Total price: $55.08
Buy the selected items together

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


If you buy a new print edition of this book (or purchased one in the past), you can buy the Kindle edition for only $2.99 (Save 70%). Print edition purchase must be sold by Amazon. Learn more.
For thousands of qualifying books, your past, present, and future print-edition purchases now lets you buy the Kindle edition for $2.99 or less. (Textbooks available for $9.99 or less.)
  • Thousands of books are eligible, including current and former best sellers.
  • Look for the Kindle MatchBook icon on print and Kindle book detail pages of qualifying books. You can also see more Kindle MatchBook titles here or look up all of your Kindle MatchBook titles here.
  • Read the Kindle edition on any Kindle device or with a free Kindle Reading App.
  • Print edition must be purchased new and sold by Amazon.com.
  • Gifting of the Kindle edition at the Kindle MatchBook price is not available.
Learn more about Kindle MatchBook.


The latest book club pick from Oprah
"The Underground Railroad" by Colson Whitehead is a magnificent novel chronicling a young slave's adventures as she makes a desperate bid for freedom in the antebellum South. See more

Product Details

  • Paperback: 592 pages
  • Publisher: Oxford University Press; 2 edition (July 18, 1996)
  • Language: English
  • ISBN-10: 0195105192
  • ISBN-13: 978-0195105193
  • Product Dimensions: 9 x 1 x 6.1 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (69 customer reviews)
  • Amazon Best Sellers Rank: #69,026 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Michael Wischmeyer on August 3, 2003
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 by Oxford University Press in 1941 with later editions in 1943, 1945, and 1947. Good quality soft cover copies are still in print as Oxford Paperbacks.

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.
Read more ›
Comment 220 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
This book genuinely has more mathematical content, for around $15-$25, than most, maybe all, "bridge" texts for college math majors, costing 5 or 10 times as much.

This book was written by a master, for an intelligent person knowing only 1950's style high school mathematics (some trig, algebra, and geometry).

When I fiorst tried to read it as a youngster however I was not used to books that required actually thinking about each statement, before proceeding to the next. Hence I could not read it at the pace I thought normal.

So this is not a breezy read, but is an outstanding one. It has literally no competitor to my knowledge at the present time, in quantity of material, quality of material, and quality of exposition.

Even experts may learn something here about the most familiar topics. E.g. in presenting the proof of the well known fact that all integers greater than one have unique prime factorizations, the authors show how a clever use of induction avoids developing the characterization of a gcd, which usually precedes this theorem. I had never seen that before.

If you are looking for a miracle book that treats the reader like a baby, and still covers calculus, this is not it. But if you have the prerequisites of a good high school course of elementary math, and are willing to spend time on the arguments, there is no better book for beginners and intelligent laypersons.
Comment 112 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
By A Customer on October 23, 1999
Format: Paperback
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. I still remember how for the first time, I was inspired by the subject while reading this book. I couldn't stop reading it, until I finished it. At the time, I didn't really know Calculus or any advanced subject and I had never read any math books other than the high school textbooks. This book literally changed my life. I might have forgotten who my first love was, but I remember very well this book after 25 years!
4 Comments 79 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
If you start to read "What is Mathematics?" in order to find a direct answer to the title's issue, forget it! I would like to adapt a piece of "My Brain is Open", by Bruce Schechter, in the following way: "Asking a mathematician to explain exactly what is mathematics is a little like asking a poet what a poem is, or a musician what jazz is. Asked this last question, Louis Armstrong replied, `Man, if you gotta ask, you'll never know.'" On the other hand, if you start to read just to go deeper and deeper in the beautiful, and sometimes magic, structure of Math than I say: Go ahead! Because this book is a perennial source of pleasure. Of course it demands a lot of work to solve some of its problems (at least for me!), but as Courant says, you cannot learn music only by listening! I have reproduced almost all the calculations of this book and I know that it demands a lot of effort, but it is one of the few books I know where each small piece of calculation has its own reward! This book is my definition of perfect guide to Math style! Try it!
Comment 42 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
I always liked math as a child and was quite talented, but I absolutely hated the way math was taught in school. For a long time I could always grasp the necessary concepts intuitively, and so I didn't have to bother with the books we were supposed to be working with (my teachers were frustrated over my not doing any "exercises", but I got away with it since I aced the exams). But when it came to high school and a bit more demanding math (mainly calculus), I couldn't do it all by pure intuition and since I couldn't deal with the math textbooks, I fell behind. Eventually I developed an outright aversion for math, confusing my life-long love for the subject with my intense dislike of how it was taught in school.

I kept looking for a better way to learn math - I just knew there had to be one. University textbooks was often better structured, but they presumed a lot of skills that I didn't have yet. Far too many years later I randomly came upon this book, and in it I found everything I had been looking for all along, namely clear and concise discussions of mathematical concepts.

In school, the focus was always on exercises, with no clear explanation of the concepts involved. In fact, discussion of mathematical concepts was clearly avoided, even when it would have seemed quite natural. The general idea seemed to be to get kids to use mathematical concepts more or less blindly, and thereby "learning" them without having to think about them. For me this was just utterly perverse and unspeakably frustrating. Being intensely interested in understanding things, but strongly averse to mindless repetition, more than anything I felt like I was being punished, expected to learn how to use math, but deviously kept from actually understanding what I was doing.
Read more ›
6 Comments 35 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse

Most Recent Customer Reviews

Set up an Amazon Giveaway

What Is Mathematics? An Elementary Approach to Ideas and Methods
Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway
This item: What Is Mathematics? An Elementary Approach to Ideas and Methods

Pages with Related Products. See and discover other items: complex numbers, geometry textbook