/sci/ - Science & Math

How do I stop being a mathlet-mid and start to approach professional math-fag level?
For example, what do I need to read or learn in order to solve almost any solvable equation put in front of me (and how can I know that it is solvable)?
Real, imaginary, algebraic, transcendental, summation, product, etc., it doesn't matter, I really just want to get past the number crunching filter.
I want to master the methods used to solve equations, calculate numbers, and perform manipulations so a book on just one specific and broad area of mathematics doesn't help (yes, obviously I should start with algebra but I want to focus specifically on solving methods.) I want to get this computational shit out of the way before I dive deep into theory (or more likely, read theory and the practical methods at the same time). I don't want to be one of those guys who can teach a class on category theory but has forgotten how to do polynomial division.