> I've sometimes wondered about a WikiTextBook site which has definitive and progressive tutorials/lessons on topics that don't fit the 'pedia format, starting from pre-school all the way up to post-grad.
I've wanted something similar, but going the other way. That is, you start at post-grad level and can expand things to lower level as needed.
For instance, an article in this format on the prime number theorem would start out stating the theorem and presenting a proof at a level that you'd see if this was a proof from a mathematics journal. At any step in the proof you could expand the article in two ways.
1. Horizontal expansion. This fills in omitted steps, but stays at the same level.
2. Vertical expansion. This explains the step in terms of less advanced material.
Expanded material could further be expanded, both horizontally and vertically. So for instance suppose that in the top level proof of the prime number theorem an integral appeared and was evaluated. Expanding horizontally would fill in the details of how you evaluate that integral.
But suppose you have not studied calculus. You could expand that integral vertically, and keep expanding, until you get down to an explanation of calculus. That would give you essentially a course in calculus--but just the calculus needed to support the prime number theorem proof.
This could be the basis of an alternative way to teach math and physics (and other sciences). Pick a set of interesting, advanced results, chosen so that when you expand all of them the bottom level will have covered the complete undergraduate math and physics curriculum. I think this could be a good approach because it provides more motivation. Everything you learn at the bottom level is motivated because it is needed for that specific advanced result you are trying to learn. Contrast that to the current approach where you have long stretches of material that might not seem interesting but that you are learning because you are told you'll need in 3 or 4 years when you are finally getting to look at interesting stuff.