> never abandon a book you have chosen without working all the way through it
Extremely bad idea, and I learned it the hard way. A lot (most?) textbooks have more details than you need to know. It's better to find out the most important material in the book, focus on that first, and then go to the next tier of important material in the book, and so on. At some level (perhaps after the first), feel free to try other books without completing the current one.
Unfortunately, it's not easier to know which material in the textbook is important and which are merely detailed examples on your own. You need someone with mastery to tell you that.
> If you face difficulties, do not give up but instead go back twenty times if that should prove necessary and only then allow yourself to investigate another mathematician's solution
Partially agree. Pick an N that is large enough, but not too large. Another mistake I would make is refusing to move on until I've solved the problem. A more practical approach is to give it N times over M hours/days, and then move on and/or look up the solution. You'll learn more this way.
Extremely bad idea, and I learned it the hard way. A lot (most?) textbooks have more details than you need to know. It's better to find out the most important material in the book, focus on that first, and then go to the next tier of important material in the book, and so on. At some level (perhaps after the first), feel free to try other books without completing the current one.
Unfortunately, it's not easier to know which material in the textbook is important and which are merely detailed examples on your own. You need someone with mastery to tell you that.
> If you face difficulties, do not give up but instead go back twenty times if that should prove necessary and only then allow yourself to investigate another mathematician's solution
Partially agree. Pick an N that is large enough, but not too large. Another mistake I would make is refusing to move on until I've solved the problem. A more practical approach is to give it N times over M hours/days, and then move on and/or look up the solution. You'll learn more this way.