When do you are finished with a book that you are learning

[samspotting]

Lectures don't teach everything, and learning on your own you skim through a lot of theorems. Sure you understand them, but if you were showed them a few days later and you needed to prove them, then you might not be able to do so.

Do you try and remedy with another pass through the book, or just go on to another one.

 

[Hurkyl]

Lectures don't teach everything, and learning on your own you skim through a lot of theorems. Sure you understand them

No you don't. You simply know of them. Understanding requires knowledge and experience.


The ability to prove theorems is not needed for understanding -- but it is usually a consequence of understanding, since a great many theorems are straightforward applications of the basic ideas at hand. (But it won't seem straightforward until you understand the material!)