Complete course of self-study I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study mathematics.
I request people to tell me what topics an undergraduate may/must study and the books that you highly recommend (please do not ask me to define an undergraduate).  
Background:


*

*Single variable calculus from Apostol's book Calculus;

*I have started IN Herstein's topics in algebra;

*I have a limited knowledge of linear algebra: I only know what a basis is, a dimension is, a bit of transpose, inverse of a matrix, determinants defined in terms of co-factors, etc., but no more;

*absolutely elementary point set topology. I think open and closed balls, limit points, compactness, Bolzano-Weirstrass theorem (I may have forgotten this topology bit);

*binomial coefficients, recursions, bijections;

*very elementary number theory: divisibility, modular arithmetic, Fermat's little theorem, Euler's phi function, etc.
I asked a similar question (covering less ground than this one) some time back which received no answers and which I deleted. Even if I do not manage to get into a good university, I wish to self-study mathematics. I thanks all those who help me and all those who give me their valuable criticism and advice.
P.S.: Thanks all of you. Time for me to start studying.

I would suggest some mathematical modeling or other practical application of mathematics. Also Finite automata and graph-theory is interesting as it is further away from "pure math" as I see it, it has given me another perspective of math.
