TITLE: Is there a correct order to learning maths properly?
QUESTION [9 upvotes]: I am a high school student but I would like to self-learn higher level maths so is there a correct order to do that?
I have learnt pre-calculus, calculus, algebra, series and sequences, combinatorics, complex numbers, polynomials and geometry all at high school level.
Where should I go from here? Some people recommended that I learn how to prove things properly, is that a good idea? What textbooks do you recommend?

REPLY [5 votes]: I'm not mathematician. I hold degree in management both bachelor's and master's degree. Anyway, to my knowledge, if you want to learn math from scratch, the order will be 
college algebra, algebra & trigonometry, precalculus, calculus, linear algebra, differential equation, intro to analysis (or advanced calculus), functional analysis, real analysis, probability theory
There're some books I recommend

College Algebra by Henry Burchard Fine
Fundamentals of Algebra & Trigonometry by Earl Swokowski
Precalculus by Sheldon Axler
Calculus vol.1&2 by Tom M. Apostol
Introduction to Linear Algebra by Gilbert Strang
Mathematical Analysis by Tom M. Apostol
Introductory Functional Analysis with Applications by Erwin Kreyszig

Supplement: How to Prove It by Daniel J. Velleman. You need this book to learn how to do rigorous proofs for mathematical theorems.