> 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?<p>I went to a university where the upper-division undergraduate math courses didn't have much in the way of prerequisites.<p>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.<p>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 <i>can</i> 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.