I've stopped studying mathematics ever since graduating high school four years ago...

Is there a huge difference in the quality of education you get and the kind of people you get to work with, between elite PhD STEM departments (Stanford, MIT, Caltech) and tier 2 departments? The facilities and endowment should be better but is there more to it?
Same question for master's.

The best introductory book is the one Stroustrup wrote.

Sure, if it is some kind of fraudulent paper mill where they are just pumping out shit publications for the sake of looking busy/grabbing grant money. The best way is to use sci-hub to go through journals in whatever field you are doing, and find the most interesting research, find out where those people are and apply to that grad program. Failing that, look up the supervisors of the PhD program(s) individually and follow their students to see what schools they end up.For example say you want to get into a CMU grad program to specialize in Type Theory with all their prominent researchers there. You can't get in so you discover one of their best protege students now teaches at CT dlicata.web.wesleyan.edu/pubs.html and it may even be a better option than CMU, as in a smaller less 'elite' university you will prob have more access to the supervisor of your program, have opportunities to co-author papers with them instead of them just auditing your work and rubber stamping their name on it, ect. This person will also have connections, so can land you a nice postdoc position using all their ivy league/elite school network.

For the most part you don't have to pay for a PhD either, that is usually covered by some grant they receive and then hire you with it as basically an apprentice to learn their field.

Stroustrup's book is shit m8. You're better off with youtube vids.

>youtube vids
Any recommendations?

>You're better off with youtube vids
Implied that the book was even worse than videos. Doesn't mean that videos are a good way to learn.