This might read like confident advice, but it’s mostly just the strategy I’ve been using because it seems sensible to me.
For any of these topics with dedicated books (especially ones recommended as high quality), there will be proofs presented along the way while reading them. Don’t just read the proofs. Try pausing before you read/understand the proof and try to work out how you would prove it yourself. Then read (and maybe re-read) until you think you get it, and try to prove it again without looking back at the material.
Keeping a list of these exercises might be handy to test yourself with later.
Also keep notes as you go about anything you find remotely confusing. Follow up on the confusion.
This doesn’t tell you that you’ve “mastered the topic,” but mastery comes in building blocks of deliberate practice.
This might read like confident advice, but it’s mostly just the strategy I’ve been using because it seems sensible to me.
For any of these topics with dedicated books (especially ones recommended as high quality), there will be proofs presented along the way while reading them. Don’t just read the proofs. Try pausing before you read/understand the proof and try to work out how you would prove it yourself. Then read (and maybe re-read) until you think you get it, and try to prove it again without looking back at the material.
Keeping a list of these exercises might be handy to test yourself with later.
Also keep notes as you go about anything you find remotely confusing. Follow up on the confusion.
This doesn’t tell you that you’ve “mastered the topic,” but mastery comes in building blocks of deliberate practice.