>There is also the usual problem of self study, in that you don't have a roadmap and can waste time easily.Can you expand on what you mean by "roadmap"?
To me, a roadmap is very easy to get and can be arrived at from different angles.
method 1) Pick up an "Advanced Mathematics" book and start at page 1. The sequential chapters of that book would start a roadmap. If page 1 looks incomprehensible, look at the preface/introduction to see what the author lists as prerequisites. Seek out the book(s) on the prerequisites and start on page 1 of that book. If that prerequisite looks like gibberish, then look at that book's prequisite. And so on.
method 2) Google "advanced mathematics study roadmap" and look at various answers from math.stackexchange.com, reddit.com, blogs, etc.
method 3) Look at the undergrad curriculum of math courses for degree requirements (e.g. Bachelor of Mathematics, Bsc Electrical Engineering, etc) published by universities. (e.g. go to http://mit.edu).
It seems like a "roadmap" for self-study is readily accessible for anyone curious.