I have currently finished AS maths (British curriculum), but the problem with the British curriculum is that it misses out the basis of maths; it misses out a focus on functions. When I look at other curriculum, I feel like there is a huge gap in my understanding of maths because I'm not as good with functions. I'm now going off to Uni to study medicine, but I want to also learn maths in my spare time, so I want to start right from the beginning and go all the way to the top: to understanding complex proofs about complex topics and to also be able to write my own proofs. HOWEVER, my MAIN focus is to learn new topics in maths before I get good at proofs. I'm asking because when I come to learn chemistry in Uni, I will not really need maths as much, but I will indeed be a much better interpreter of the universe around me if I can understand studies which are done on a high mathematical basis.
So please, can anyone guide me towards some topics to start with? And give me a rough idea of the different types of things that I would learn? Also, please recommend BOOKS (can't learn without them :)). Please help me with this because I really do love maths and want to learn it; all of it. Thank you very much in advance :)
[Note: I couldn't find an appropriate tag, so I had to put the one below.]