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Book Recommendation – What is Mathematics?

Neil RobertsonJune 20, 20224 comments

What is Mathematics is a classic, lucidly written survey of mathematics by Courant and Robbins.  The first edition was published in 1941!  I have only read a portion of it, mainly the chapter on calculus.  One page of Courant is worth about five pages of my old college calculus textbook, and it’s a lot more fun to read.

The reader of this book should already be familiar with algebra and trigonometry.  For engineers, some worthwhile sections of the book are:

Chapter 2, section 5, Complex Numbers.

Chapter 6, Functions and Limits.

Chapter 8, The Calculus.

As the author states, “… Chapters VI and VIII together form a self-contained presentation of the calculus with emphasis on understanding rather than routine”.  The book does not discuss linear algebra.  Chapters 1 – 8 are a reproduction of the 1947 edition, while Chapter 9, Recent Developments, was written by Ian Stewart for this 1996 edition.  The book is available new in paperback from Amazon and other outlets.

Richard Courant and Herbert Robbins, What is Mathematics?  An Elementary Approach to Ideas and Methods, 2nd Edition, Oxford University Press, 1996.

Courant also wrote a textbook, Introduction to Calculus and Analysis.



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Comment by kazJune 21, 2022

What might be missing... free pdf download.


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Comment by neiroberJune 21, 2022

Indeed, such are available.

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Comment by Rick LyonsJune 28, 2022

Regarding the book; "In the sixty years during which Courant and Robbins, as the book is often called, has been in print, several distinguished scholars have had the opportunity to sing its praises. Reviewing the first edition, E. T. Bell described the work as “inspirational collateral reading.” Hermann Weyl thought it “a work of high perfection.” For Marston Morse it was simply “a work of art.” Even Albert Einstein chimed in with high praise."

https://www.ams.org/notices/200111/rev-blank.pdf


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Comment by neiroberJune 28, 2022

Rick,

Thanks for this interesting book review from 2001.  The book was "sixty years" old then.  I hope it will still be in print in another 21 years!

Neil


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