>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.
The usual problem in self study (of any subject) is that you go towards what is easily accessible from where you are right now, which means you might miss out on useful avenues visible to someone who already has a good view of that "lay of the land", so to speak. You may also lack the discipline to push through something that is difficult for you when you can't see they payoff - an outside influence could convince you it will be worthwhile. Depending on the type of student you are, you can also spend too much time inefficiently on things that are comfortable.
You can try and do something like recapitulate the core curriculum of a math degree, say, but there are constraints there you aren't aware of and it won't be the right path for everyone.
method 2 expanded to "actually ask questions at some of these locations" is actually a good way to inject some outside direction. So it's a mitigation for this problem.
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.