Gamma: a recommendation

Julian Havil's Gamma: exploring Euler's constant is a charming mathematics book filled with interesting results on every page. A good calculus course will prepare you for most of the material.

One of the things I particularly like about the book is that at the end he presents a very elegant and accessible account of the Prime Number Theorem and the Riemann Hypothesis. On top of that he gives the necessary background in complex function theory required for the Riemann Hypothesis in an appendix. I have never seen a better brief.

So if you looking for a really good math book on summer vacation, and you like playing with numbers, then check this one out.