Question

Learning specifics or general ideas first

Answer 1

Make sure to understand *examples*.  If you can't identify the concepts your studying in the context of examples, you're going to have a much harder time being able to follow what is happening.

Answer 2

Personally I often need to go back and forth, make a pause of some days/weeks and come back to the topic.

But I would advice going linearly first to have a general idea of what is going on, and, of course, in 99.99% of cases you will not understand a lot of things, but thats normal. Then you can read again and take more time on details to figure out things.

Answer 3

It depends. Pretty much all topics can be understood with either approach. If you follow a course, pay attention to the lecturer on day 1, they’ll surely say what their approach to the course is. If you follow a book or a set of notes, read the intro or preface to see what the author had in mind.

Going linearly from start to finish is more and more complicated the more advanced the subject is, because often there is no finish, and it’s hard to find the start. That is why it’s not a bad idea to understand the examples that motivated the theory. Mark my words, theories stem from specific examples. Understanding a few models gives you some advantage in understanding the theory at some point. Well, these words are not mine, but you know what I mean.

Answer 4

Whatever comes easiest at a given time. I usually try to digest new math in the most abstract form I know of and resort to examples when I need clarification. I do like abstraction for abstractions sake though, YMMV.