Book Recommendations – Big List of Serious but Fun ‘Unusual’ Books

big-listbook-recommendationeducationreference-requestsoft-question

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems)

  • in "recreational mathematics";
  • in any other field (but from a perspective that is not presented in standard university courses).

For example, I would appreciate some references to books by Martin Gardner and John Conway.

I really liked the answers given to this related question and to this, in particular:

  • On Numbers and Games, by John Conway (which was not an answer actually);
  • Generatingfunctionology, by Herbert Wilf;
  • The Symmetries of Things, by John Conway;
  • The Sensual (Quadratic) Form, by John Conway.

But I would like to know other opinions on the books proposed in these threads and on other books (also newly published ones).

Best Answer

Here are some more books which are informative and also provide fun!

Combinatorics

If you like Generatingfunctionology by Herbert Wilf then of course you will also like

With respect to the authors, especially Donald E. Knuth no comments are necessary to this book from my side besides, this is a wonderful book - this is an informative book - this book is pure reading fun. It's extremely valuable if you're interested in combinatorics and as Wilf's GF is a perfect starter this book is a great follow-up to deepen the knowledge. One of many amusing ideas was to dedicate the margin to comments of some of his student's:

From the Preface: Students always know better than their teachers, so we have asked the first students of this material to contribute their frank opinions, as graffiti in the margins. Some of these marginal markings are merely corny, some are profound; some of them warn about ambiguities or obscurities, others are ...

Note: I've answered this question about specific books in combinatorics and it was (and is) a problem for me to restrict myself to the most concise information and therefore decided not to mention this brilliant book.

Experimental Mathematics

This relatively new, exciting and challenging discipline provides us with fascinating mathematics. Leading experts in this discipline are the Borwein Brothers Jonathan and Peter. I strongly recommend all of their books, especially:

If you take a look at the table of contents of the referenced link, maybe you will also find it funny, exciting and informative. It's interesting, since they often share with us the way how they found deep and interesting results and this is pure fun for me! In the same spirit are their follow-ups:

The material in these books is most of the time accessible and not too hard, but to get an impression of the art of these guys and their beautiful math you may have a look at this article: Ramanujan, Modular Equations and Approximations to Pi or How to Compute One Billion Digits of Pi by the Borwein Brothers and D.H. Bailey.

Of course, Ramanujan and beautiful math is often strongly connected :-)

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