Big list of serious but fun "unusual" books
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).
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
- Concrete Mathematics by Graham, Knuth & Patashnik.
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:
- Mathematics by Experiment - Plausible Reasoning in the $21^{\text{st}}$ Century by Jonathan Borwein and David Bailey.
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 Computer as Crucible: An Introduction to Experimental Mathematics and some more.
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 :-)
Here's a few off the top of my head.
- Experiments in Topology, Stephen Barr
- On Knots, Louis Kauffman
- Gödel, Escher, Bach: an Eternal Golden Braid, Douglas Hofstadter
- 1,2,3, infinity, George Gamow
I've made this community wiki, so other people can feel free to edit this post and add to the list.
Good examples are:
- Havil: Gamma
- Aigner, Ziegler: Proofs from THE BOOK
- Schroeder: Number Theory in Science and Communication
- Arnold: Catastrophe Theory
- Tabachnikov: Geometry and Billiards
- Markowich: Applied Partial Differential Equations
- Pesic: Abel's Proof
- Harel: Computers Ltd.
Every book by Edmund Landau is certainly interesting to look at. Wiener used to say about his style that "His books read like a Sears-Roebuck catalogue." Personally, I've read his Zahlentheorie and his two books on introductory calculus and foundations of analysis. Wikipedia has a small list (the three books I mentioned and their corresponding ISBNs). There are further publications, but not in english. His Lectures on Number Theory continue for 3 or 4 more volumes, I think.