Can anyone suggest a book that a lot of visualization into real analysis, like the book Proof Without Words by Nelsen.

  • $\begingroup$ Most good books have pictures. I don't see the point or thepossibility of giving proofs without.words of results of real.analysis $\endgroup$ – Pedro Tamaroff Dec 27 '13 at 15:02
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    $\begingroup$ I am not expecting the proofs to be devoid of words, but can you suggest some books that provide good insight behind the theorems, so I can practically visualize the different concepts. $\endgroup$ – QED Dec 27 '13 at 15:06
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    $\begingroup$ Spivak's Calculus, Apostol's Calculus, and Abbott's "Understanding Analysis". The latter has started to be my favourite. $\endgroup$ – Pedro Tamaroff Dec 27 '13 at 15:11
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    $\begingroup$ @PedroTamaroff I've leafed through all three. None of them present coloured pictures, and as many pictures, as Stewart's Calculus though this isn't a book for real analysis. $\endgroup$ – NNOX Apps May 20 '18 at 21:56

I really like James Callahan's Advanced Calculus: A Geometric View. Only after reading this book did I really understand what was going on with the change of variables formula when doing integration. There are many nuggets of intuition in this book, and they are explained with plenty of diagrams. Also, consider it to be a supplementary textbook for whichever main book you might be using to learn real analysis.


I have always been looking for good mathematics books that build intuition through visualization.

I recently found Mathematical Analysis I by Claudio Canuto and Anita Tabacco.

The book really uses a lot of graphics to convey the meaning of mathematical formulas. More than other textbook I've looked at. It's not proofs without words because it does contain lots of words, but it's clearly "illustrated concepts" in mathematical analysis.

Here are some examples. The book contains many more.

The effect of scaling

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A classical result about convergence

enter image description here

Taylor polynomials

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Domain and mappings

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