I've wanted "expandable" math ebooks, which in some ways are similar to what you are describing.
The way these would work is that in their initial, unexpanded state, everything is presented the way it would be presented to an expert in the field. For instance, if you are interested in seeing how the prime number theory is proved, the unexpanded view would present the proof the way it would be presented if it were a new result being published in a top analytic number theory journal.
This would, of course, be over the head of most people--even most mathematicians who are not number theorists. This is where the "expandable" part comes in.
For any part of the proof, you would be able to expand it. There would be several kinds of expansion available.
1. Horizontal expansion. This keeps the argument at the same level, but fills in more steps.
2. Vertical expansion. This is for when you run into something you don't know. It expands to give you the necessary background to continue.
3. Calculation expansion (I need a better name for this). This would be used for things like evaluation of integrals or solving differential equations or similar things that show up in the proof. It's for when you know how to evaluate integrals or solve differential equations, but just aren't seeing the particular substitution or integration by parts or whatever that makes this particular calculation work.
The difference between calculation expansion and horizontal expansion is that calculation expansion is for where you need something expanded that is relatively elementary compared to the current level, whereas horizontal expansion is where you need more steps at the current level to follow the argument.
All of these expansions would in an ideal expandable ebook be applicable recessively, with vertical expansion going all the way down to high school math. The net result would be if you took, say, an expandable ebook on the prime number theorem, and did maximum vertical expansion, you'd end up with in effect a course of study that takes you from high school to understanding the proof of the prime number theorem--it would teach you all the number theory and calculus and complex analysis and so on that you need to understand that proof.
The way these would work is that in their initial, unexpanded state, everything is presented the way it would be presented to an expert in the field. For instance, if you are interested in seeing how the prime number theory is proved, the unexpanded view would present the proof the way it would be presented if it were a new result being published in a top analytic number theory journal.
This would, of course, be over the head of most people--even most mathematicians who are not number theorists. This is where the "expandable" part comes in.
For any part of the proof, you would be able to expand it. There would be several kinds of expansion available.
1. Horizontal expansion. This keeps the argument at the same level, but fills in more steps.
2. Vertical expansion. This is for when you run into something you don't know. It expands to give you the necessary background to continue.
3. Calculation expansion (I need a better name for this). This would be used for things like evaluation of integrals or solving differential equations or similar things that show up in the proof. It's for when you know how to evaluate integrals or solve differential equations, but just aren't seeing the particular substitution or integration by parts or whatever that makes this particular calculation work.
The difference between calculation expansion and horizontal expansion is that calculation expansion is for where you need something expanded that is relatively elementary compared to the current level, whereas horizontal expansion is where you need more steps at the current level to follow the argument.
All of these expansions would in an ideal expandable ebook be applicable recessively, with vertical expansion going all the way down to high school math. The net result would be if you took, say, an expandable ebook on the prime number theorem, and did maximum vertical expansion, you'd end up with in effect a course of study that takes you from high school to understanding the proof of the prime number theorem--it would teach you all the number theory and calculus and complex analysis and so on that you need to understand that proof.