Math book for an eager learner with non-mathematical background I was reading answers to How do you explain the concept of logarithm to a five year old?
 and realized that I really don't understand mathematics. Okay, I lied when I said that I had no mathematical background, but it is as bad as that. I did learn mathematics throughout my education (I am a graduate) as part of my curriculum, but either due to my lack of interest or due to poor instructors in this part of the continent, I never really quite understood it. I became a programmer and started liking mathematics. I mean I see some solutions on project euler and I am really fascinated by them. Can someone point me to a resource/book/approach which will teach me mathematics from grounds up with a focus on understanding what goes under the hood? Not just ability to solve problems, but an in general solid understanding of mathematics which will make appreciate the concepts and then I guess the problem solving will come slowly. I have no time frame to learn anything, I just want to really learn and understand mathematics.

The Prime Number Theorem, by G. J. O. Jameson is an excellent book for self-study.
