3 ms·

I'm not sure about abstract algebra specifically, but in other subjects that I have tried to take up on my own, I have found that the dependencies become obviou

I'm not sure about abstract algebra specifically, but in other subjects that I have tried to take up on my own, I have found that the dependencies become obvious once you realize you are in over your head. In fact, my preferred method of learning these days is to start with your goal, then traverse that so-called dependency graph to the dependent, and often simpler, concepts until you are able to work your way back to your original goal again.

sj4nz 12y ago
This is a nice way of priming your mind for the concepts you're interested in--and is probably another example of why the current educational system languishes under standardized testing for metrics: when the goal isn't in the students' direct interest, the system can only provide an indirect benefit for their minds. It's very inefficient. The class structure has grown out of the physical limitations of presenting course information to mass groups of people in physical classrooms. Take the MIT Modules, make them asynchronous and add accountability (limitations and commitments: something like, only 5 active modules at a time until you've completed them) and mentoring (which is your next module? If you struggled with X, maybe you should go back a couple dependencies?) and you could have a really effective system that creates even more amazing people--at the pace that suits them best.