I'm about halfway through college and have just begun to realize that my understanding of mathematics is rather dismal. This may sound obvious but I know that I can do math because, in high school, once I finally understood a process (which I did in about average time) I could apply it to specific examples. Unfortunately, I don't feel like I learned anything but a random assortment of specific procedures from pre-Algebra to pre-Calculus and nothing like a foundational understanding of why math works or how its connected. So now, when I go on Wikipedia to look up another a math term, the definition is basically in another language. Being taught by coaches was probably not a huge help either, lol.

What I'm looking for, then, are two things. First, I'd like a list of mathematical subject areas (like arithmetic(?), pre-algebra, algebra, geometry, etc) that I need to know, hopefully in a rather hiearchical structure, so that I can move from a basic topic to its extension. Second, if anyone has any ideas on a book or textbook for any of these areas, I'd also appreciate that. (Maybe one textbook covers multiple basic ideas). Either of these things - or references to them - would be really appreciated.

Thanks in advance!