[nohaydeprobleme]

This is a great comment. To add on to a point that really aligns with my experiences:

> "Review from time to time but don't let a hard first couple chapters prevent you from ever learning the concepts."

This is a very good approach, and I wish I started doing this earlier. Even in my university math courses, the professors sometimes skipped ahead to have students focus on a few later chapters before coming back, or told the class to skip several pages in the book. I also found that working on later exercises in a textbook would sometimes help me better understand concepts introduced in earlier chapters.

Lastly—though this may not be completely relevant to studying mathematics—I've explicitly been taught in various language courses (explicitly for audio courses and implicitly for in-person university courses) that it's okay to move ahead if I know at least 80% of the material. The percentage may be higher for studying math topics, but especially for someone self-learning out of interest or for a specific application, it's much more preferable to move forward and revisit earlier exercises as needed, instead of quit the book. If you find yourself getting lost in later chapters, there is no problem with revisiting earlier chapters. You'd also likely be no worse off (possibly even better) than many undergraduates studying the textbook for a course for the first time.

The most important thing is just to not quit the habit of consistent study. Perfectionism in understanding is a pitfall for self-directed studies, which consistency in studying beats every time.

[physicles]

All great points.

> it's okay to move ahead if I know at least 80% of the material.

One of the worst feelings is moving on in a textbook and realizing you are indeed totally lost.

Here’s my own list of necessary but not sufficient conditions for deep learning:

- Motivation. Easy to overlook; hard to get if you don’t already have it.

- Frequent experience of “I have no idea how to solve this,” followed by hours or days of playing with the problem, followed by a eureka moment. You can’t be sure you’ve learned the thing unless you’ve constructed the solution yourself. Builds confidence too.

- Seeing the same material in different contexts or presented in different ways. It’s like looking at an object from different angles.

And for bonus points:

- Teach the concept to a curious friend. Their questions will lead you to deeper understanding.