Recommended reading for a 15-year-old hopeful university mathematics student. I am in the UK, studying GCSE, if that means anything to you.
What would you recommend to me, to further my understanding of mathematics, of my current level or further?
Thanks.
 A: I would recommend a two-pronged approach!
Strengthening your algebra and problem solving skills beyond what is covered in GCSE would be very valuable. Books such as 'Student Problems from the Mathematical Gazette', ISBN 0 906588 49 9, available from the Mathematical Association, would provide good challenges for you. 
For general appreciation of Mathematics (which should whet your appetite for your future maths education) there are many good and popular books - for example '17 equations that changed the world' by Ian Stewart.
A: I recommend that you find a book that is both enjoyable and challenging but not too challenging. If it generates curiosity in mathematics everything else should be doable. I'm not saying easy, some things will come easily to you, others will be hard work but with curiosity you will persist and overcome. One view of math is that it is the art of solving problems so my suggestions will biased that way. Here are some suggestions; they may be a little on the old side. I'm sure there are newer books that I'm not as familiar with, on the other hand you may find inexpensive copies in second bookstores such as those run by Oxfam.

How to Solve It by G. Polya
Problem books by Martin Gardner
The Lore of Large Numbers by Philip J. Davis
Countdown by Steve Olson (This book is more about competitive math problem solving than the math per se. The math is only about 30% (rough) of the book.)
The Mathematical Experience by Philip J. Davis and Rueben Hersh (The math may be only about 10% but there are many short essays that are fun to dip into.)  

I will add to this list if I think of anything else. Other users may add newer books or completely disagree with me.
