In (1.1.2) Modeling and abstraction, I describe the box can be stacked in the fields of mathematics. So the author of a mathematics book assumes that the reader build blocks up the exactly correct way. So it is impossible to pile up the knowledge which cherry-picked roughly. We need to invest sufficient time to lay a solid foundation.
Especially mathematical books use the contents defined earlier in the book to compress subsequent parts.
In such a book, you can not understand the subsequent parts by looking roughly. To understand the second half, you must understand the first half firmly. Although it seems paradoxical, reading it with effort reduces the whole effort.
It is not limited to mathematics. If you can not understand a book when you read roughly, you need to read firmly. If you read it with your eyes and you can not understand it, you need to use your hands.
Reading with hands takes more time than just reading it with your eyes. So, you need to think about how you can make it more efficient. First, you should focus on what you need for your purpose. If you do not know what you need, use hands to grasp the whole picture. If you can not do either, you have to read with hands from one end.
However, while doing that, you should think about how to make it efficient. Here are some examples:
- Can I summarize only essential points?
- Can I make a phrase that appears many times into a symbol or an abbreviation?
- Which is efficient to describe the concept in words or a diagram?