I read math for personal enjoyment, so note that I don’t have many checks on my understanding, besides my ability to read more math and feel like I understand.
As I read the book I mentally keep track of how difficult it feels and how much things make sense. If things feel more difficult than I’ll make notes as I go through. The notes are more for the purpose of moving slowly through each statement—otherwise I might skip sentences. I’ll draw pictures and label everything in the picture and maybe do a really simple example.
A lot of my focus is on creating mental visualizations and creating a mapping from the definition to the visualization, or from the written proof to the visualization. I’m not sure how to describe it, but different aspects of the visual might seem ‘looser’ and ambiguous or ‘tighter’ and well defined, and this guides my thinking. I’ll go back and forth trying to work out an example on paper and figuring out how the picture changes until it seems well defined. For example, I’ve been doing some topology lately, and have been constructing different pictures of lines or shapes and imaginary manifolds and removing different size pieces of them to get an idea of what is considered connected and what is not connected.
Previously I used to do lots of exercises, but I’ve found the above thing seems to help me learn better and make the exercises easier when I do them, so I’ve been doing fewer exercises. With exercises where I can look through the book and find a proof that use a similar method and modify it to solve the problem, and then I feel like I’ve just copied it instead of learning anything, so I often skip these types of problems. For something I’m learning to use for something else (I’m learning math to understand physics better) I do the simple check-your-understanding exercises and move on.
At the end of a chapter of few, I make a ‘note sheet’ where I add definitions and examples to a single (or several) sheet of paper, as though I was in college and preparing for an exam.
What I haven’t figured out is that sometimes I come across small things that I’m not able to understand. Sometimes I ask questions on stack exchange, but find this really breaks up my routine, so if they seem like confusions with minimal impact I move on.
I read math for personal enjoyment, so note that I don’t have many checks on my understanding, besides my ability to read more math and feel like I understand.
As I read the book I mentally keep track of how difficult it feels and how much things make sense. If things feel more difficult than I’ll make notes as I go through. The notes are more for the purpose of moving slowly through each statement—otherwise I might skip sentences. I’ll draw pictures and label everything in the picture and maybe do a really simple example.
A lot of my focus is on creating mental visualizations and creating a mapping from the definition to the visualization, or from the written proof to the visualization. I’m not sure how to describe it, but different aspects of the visual might seem ‘looser’ and ambiguous or ‘tighter’ and well defined, and this guides my thinking. I’ll go back and forth trying to work out an example on paper and figuring out how the picture changes until it seems well defined. For example, I’ve been doing some topology lately, and have been constructing different pictures of lines or shapes and imaginary manifolds and removing different size pieces of them to get an idea of what is considered connected and what is not connected.
Previously I used to do lots of exercises, but I’ve found the above thing seems to help me learn better and make the exercises easier when I do them, so I’ve been doing fewer exercises. With exercises where I can look through the book and find a proof that use a similar method and modify it to solve the problem, and then I feel like I’ve just copied it instead of learning anything, so I often skip these types of problems. For something I’m learning to use for something else (I’m learning math to understand physics better) I do the simple check-your-understanding exercises and move on.
At the end of a chapter of few, I make a ‘note sheet’ where I add definitions and examples to a single (or several) sheet of paper, as though I was in college and preparing for an exam.
What I haven’t figured out is that sometimes I come across small things that I’m not able to understand. Sometimes I ask questions on stack exchange, but find this really breaks up my routine, so if they seem like confusions with minimal impact I move on.