I am looking to find advice on the most optimal and efficient way to properly and deeply study a mathematics textbook, such that I completely understand everything and thus giving me good foundations for future study of more advanced mathematics. However, I want to change my ways of studying, such that I am not wasting my time using woefully inefficient methods, which I believe I may be using currently in my studies.

Currently I am reading and self studying a basic high-school level algebra textbook. However, I am taking much longer than I want to and feel I should be taking.

Mathematics is cumulative knowledge, and so I fear, should I not make sure I understand everything in the textbook 100%, I will fail in the future when I try to study further advanced mathematics, because I might have gaps in my knowledge and understanding of more foundational mathematics. Such as basic algebra.

Therefore, I have acquired a bad habit of highlighting, underlining anything and everything I deem even remotely important that I might read in a page in the textbook. In every single page of my textbook, some portion of text is underlined or highlighted. I have fear that if I don't write down what I've just learned and understood, on a page, I will forget it in the future and won't be able to understand mathematics anymore.

But I actually feel this may be counter productive. Instead maybe I should read a page, make sure I completely understand it mentally, then instead of writing down notes and highlighting things in the textbook, I should actually just tackle the problems in the book about the topic I just learned, which will then actually consolidate my knowledge, understanding and memory of the topic I just read and learned from in the textbook, rather than making notes before I do the problems.

I may simply read that a+b = b+a for instance, and I'd highlight it. Then I might write something in the margins of the pages in the textbook about the new information I just read of, a+b = b+a. I'd think about it a little longer and come up with a new way to think about it or visualize it more intuitively and then I'd instead write a new stream of consciousness into my actual note book and potentially write a page, 2 pages or 3 pages to explain my new way of visualizing or thinking about something I just learned in the textbook. I usually never ever read these notes again that I've written and I feel like they are a waste of time almost. But I'm obsessed with making sure I completely 100% understand everything I read in a textbook in mathematics such that I don't have any possible gaps in my knowledge. I am scared I will not be able to learn or understand more advanced mathematics in the future, if I don't make sure to understand everything now, to give myself solid foundation knowledge of mathematics.

I am wondering whether, instead, to read a mathematics textbook efficiently, should I: Read the page in the textbook, think about it, make sure I understand it. Then when I've made sure I completely understand what I've just read/learned in the textbook, I will then solve the set of problems in the textbook to consolidate my knowledge and understanding. After that, I'll simply move on to the next page/topic in the textbook and repeat the same process.

Instead of taking many notes, writing in the margins of the book, highlighting and underlining everything. Then after all those notes, I would only then actually attempt to solve the problems in the book. But maybe, I should just read, make sure I understand what I've just read/learned, then attempt the problems in the book. Rather than, read the book, highlight and underline information, then make sure I understand, write notes, then do the problems. This process I feel like takes me 4 or 5 times longer than it would if I were to just read the book, make sure I understand the topic, do the problems and move on to the next page/topic in the textbook.

I feel like, if I understand something currently as I am reading it, if I don't write it down in the form of notes on the book and in my note book, I will forget it in the future. But I think that, by instead, making sure I understand it after reading it, but not writing any notes, instead keeping it in my brain, then doing the problems, will actually consolidate my knowledge much better than writing many notes?