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## Main Question or Discussion Point

I recently have been trying, with various levels of success to self-study some physics and mathematics texts. I've been trying a variety of things to improve my outcomes, but I would like to pose a question to the PF community about how they go about learning physics and maths (I don't mean which texts you use, but how you use them).

Obviously everyone will have a slightly different way of learning that works for them, but I'm hoping by getting some perspective anyone can improve their study habits.

As for myself, I tend to get just one set of lecture notes or a book on the subject of interest, start at page one, work through every example in detail, until the very end of the book. While I think this is good in principle, you get a thorough understanding of all the material, it doesn't actually work for me in practice. For larger texts, after a certain depth I begin to lose interest and get bored, and end up with a lot of half-read texts.

To contrast, Ian Stewart wrote in Letters to a Young Mathematician that he likes to flick through a mathematics text until he finds something interesting, then works his way back through the necessary sections so he can understand it.

Generally as I work through a text I write a lot, I think this is important in gaining understanding of a complicated work, unraveling the details yourself, working through the exercises - this is where the vast majority of my learning takes place. My habit is to write it all roughly on pad paper, which I subsequently throw out. As I learn more I am starting to regret this, I have kept my notes from formal lecture courses and I find myself referring back to them continually- I wonder how many potentially useful problems and notes I have discarded. At the same time a line has to be drawn with how much paper you keep.

An interesting technique I'm trying now is to draw summaries of notes, rather than listing them out - that is to try to capture abstract concepts and methodologies pictorially, giving a different perspective - a sort of image mind map.

How do you do it?

Obviously everyone will have a slightly different way of learning that works for them, but I'm hoping by getting some perspective anyone can improve their study habits.

As for myself, I tend to get just one set of lecture notes or a book on the subject of interest, start at page one, work through every example in detail, until the very end of the book. While I think this is good in principle, you get a thorough understanding of all the material, it doesn't actually work for me in practice. For larger texts, after a certain depth I begin to lose interest and get bored, and end up with a lot of half-read texts.

To contrast, Ian Stewart wrote in Letters to a Young Mathematician that he likes to flick through a mathematics text until he finds something interesting, then works his way back through the necessary sections so he can understand it.

Generally as I work through a text I write a lot, I think this is important in gaining understanding of a complicated work, unraveling the details yourself, working through the exercises - this is where the vast majority of my learning takes place. My habit is to write it all roughly on pad paper, which I subsequently throw out. As I learn more I am starting to regret this, I have kept my notes from formal lecture courses and I find myself referring back to them continually- I wonder how many potentially useful problems and notes I have discarded. At the same time a line has to be drawn with how much paper you keep.

An interesting technique I'm trying now is to draw summaries of notes, rather than listing them out - that is to try to capture abstract concepts and methodologies pictorially, giving a different perspective - a sort of image mind map.

How do you do it?