* Dan Asimov <dasimov@earthlink.net> [Feb 23. 2012 07:40]:
A bright friend of mine just turned 15. They are rather advanced in math for their age and a good chess-player.
At age 12 I was ecstatic to receive the first book in Martin Gardner's series of collected columns, around 1959. My friend has not seen anything by Gardner yet, so those are the first thing that comes to mind. Yet I wonder if at this point they might seem somewhat dated.
All suggestions and opinions welcome.
--Dan
(Others have already suggested Conway/Guy "Book of Numbers" and Graham/Knuth/Patashnik "Concrete Math", which would have been me immediate answers). J.\ M.\ Borwein, P.\ B.\ Borwein: {Pi and the AGM} Wiley, (1987) H.-D.\ Ebbinghaus, H.\ Hermes, F.\ Hirzebruch, M.\ Koecher, K.\ Mainzer, J.\ Neukirch, A.\ Prestel, R.\ Remmert: {Zahlen}, second edition, Springer-Verlag, (1988). English translation: {Numbers}
From the "pretty pics" department there is Mandelbrot and also Heinz-Otto Peitgen, Hartmut J\"{u}rgens, Dietmar Saupe: {Chaos and Fractals}, Springer-Verlag, (1992) (and at least one two titles of the same-ish authors)
John B.\ Fraleigh: {A first course in abstract algebra}, sixth edition, Addison-Wesley, (2000) %% there should be a newer edition Instead of a (closed-source, eek!) program: Thomas H.\ Cormen, Charles E.\ Leiserson, Ronald L.\ Rivest, Clifford Stein: {Introduction to Algorithms}, MIT Press, second edition, (2001) %% there may be a newer edition Joachim von zur Gathen, J\"{u}rgen Gerhard: {Modern Computer Algebra}, Cambridge University Press, second edition, (2003).