What Is Mathematics? An Elementary Approach to Ideas and Methods
By Richard Courant, Herbert Robbins
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Richard Courant and Herbert Robbins set out an elementary approach to the ideas and methods of mathematics. It first appeared in 1941, and a later new edition aimed to restore meaning to mathematics in place of rote memorization.
In his essay Undergraduation, Paul Graham named it among other highly recommended books, together with Hilbert and Cohn-Vossen's Geometry and the Imagination.
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Other highly recommended books: What is Mathematics?, by Courant and Robbins; Geometry and the Imagination by Hilbert and Cohn-Vossen.
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Richard Courant, Herbert Robbins