When you're taking a mathematics class, you usually know exactly what sections of a book you need to know, and you can focus your time on these important sections.
However, when studying by myself, even when I'm trying to study the book as thoroughly as possible, I often feel tempted to skip sections of material (maybe a subsection of a chapter, a proof, or an exercise set). Yet at the same time, I don't want to skip it, fearing that what I want to skip might be something really important. Some reasons you might want to skip are:
- You might feel that you already know it well enough
- The proof or the exercises might be too difficult or boring
- The section might seem not very important
For instance, when self-studying from Apostol's Calculus, I felt the need to skip the section on calculating errors of the taylor series for the log function because it seemed unimportant, and the 'rigorous' proof of the FTC which seemed completely unmotivated.
What are your strategies for studying material in a thorough, complete way? When is it best to skip -- and how should you determine if the material you're skipping is important or not?