I just started to read Basic Mathematics by Serge Lang because I feel that my mathematics foundations are not strong and solid and frequently I get sloppy at reasoning while solving some problem.
op, start with this for a strong foundation (preferably in order):
-precal and calculus
plenty of pdf's online
to not get off on a rocky start, search for pdf lecture notes
Cool. I'm reading a first course on calculus by serge lang, too. I've been reading for two days so far and I've already covered conic sections. I don't do the problems or anything because I know how to solve them but I'm trying to figure out why the fuck so much time was wasted teaching math in high school. The concepts aren't hard and we waste HOURS teaching them in public school. All the more reason to homeschool I guess.
Lang was my first encounter with calc. Though I can now appreciate just how shit that book is, at 15 it gave me a welcome "here's content, and guess what: you can actually just read it and learn it in a coherent manner" to contrast with the ack-basswards "discovery" and "investigation" paradigm of high school math (rest assured these were misnomers)