I’ve never heard of Programmed Learning before, but I don’t think it is too different from going through a text and doing the exercises right away? Maybe following these procedures will give you the experience you want:
Try to prove every statement yourself, physically or mathematically.
When you prove something, rederive all its pre-requisites. If there are a great deal, then just sketch out the pre-requisites in your head or use some sort of heuristic proof.
Summarise parts of the book, including proofs, models etc. so it is easier to rederive stuff and link it to things (see 8).
For bonus points, try proving some stuff in a different way.
Try to anticipate what should be coming next on a page by page to section by section to chapter by chapter level
Try to predict what problems they’ll ask you in the exercises. If you can’t predict the first question, try predicting the next (again ties into 3).
Generate interesting questions if you think there aren’t enough.
Constantly link the ideas in the text to other bits of knowledge you have (this ties into the prior point), especially the earlier parts of the book. Note that this is a good way to prove old things in a novel manner. A way to reduce the complexity of this is to have a few scenarios you apply new ideas to. IIRC that’s what Atiyah did.
For definitions, think of some concrete models to fit the formalism into your native ontology. Then you can leverage your intuitions to figure out what the right sorts of questions to ask are and how to answer them.
In some sense, this is how you should be reading a maths/physics book.
I’ve never heard of Programmed Learning before, but I don’t think it is too different from going through a text and doing the exercises right away? Maybe following these procedures will give you the experience you want:
Try to prove every statement yourself, physically or mathematically.
When you prove something, rederive all its pre-requisites. If there are a great deal, then just sketch out the pre-requisites in your head or use some sort of heuristic proof.
Summarise parts of the book, including proofs, models etc. so it is easier to rederive stuff and link it to things (see 8).
For bonus points, try proving some stuff in a different way.
Try to anticipate what should be coming next on a page by page to section by section to chapter by chapter level
Try to predict what problems they’ll ask you in the exercises. If you can’t predict the first question, try predicting the next (again ties into 3).
Generate interesting questions if you think there aren’t enough.
Constantly link the ideas in the text to other bits of knowledge you have (this ties into the prior point), especially the earlier parts of the book. Note that this is a good way to prove old things in a novel manner. A way to reduce the complexity of this is to have a few scenarios you apply new ideas to. IIRC that’s what Atiyah did.
For definitions, think of some concrete models to fit the formalism into your native ontology. Then you can leverage your intuitions to figure out what the right sorts of questions to ask are and how to answer them.
In some sense, this is how you should be reading a maths/physics book.