> So why do some learning resources designed for autodidacts—such as Math Academy, or the generally very good Execute Program—rely so heavily on dependency graphs?

I went to a university where the upper-division undergraduate math courses didn't have much in the way of prerequisites.

A foreseeable consequence of this approach is that the first several weeks of each ten-week class are spent covering material that's shared with other classes, because that material is relevant to both classes but isn't included in the lower-division prerequisites. This is very bad as a matter of curriculum design, but good if you're more interested in making sure students never have scheduling conflicts.

Another example of dependency graphs is that when my sister signed up for Portuguese classes, she took "Portuguese 1 for Spanish speakers" rather than "Portuguese 1". You can learn Portuguese from an English perspective, or you can learn it from a Spanish perspective, and those are both approaches that can work, but they're not approaches you'd want to combine. In this case, one of the approaches is clearly superior - if you can relate Portuguese to your knowledge of Spanish, that will work better than relating it to English - but even where no particular dependency structure is preferable to another, it remains true that the plan for going from A to B isn't the same as the plan for going from B to A, or the same as the plan for going from nothing to B. So the curriculum needs to rely on a dependency tree.