I have also come to the same conclusion, and I believe it would be a very great idea to create a program that graph’s a topic’s “dependency courses”, perhaps with some must-read books for each subject.
I talk about applying the knowledge a lot because it is a wonderful constraint, it makes it so that you don't accidentally read things cover to cover, but do like a depth first search into the subject instead.
Just that if you need to understand differential equations, and you don't know calculus, the answer in this context isn't reading Spivak from start to finish (here I am assuming a working programmer / self-learner that wants to apply the knowledge - constrained by time and application much more heavily than a student of mathematics for example).
Like most algorithm courses are fairly abstract form of programming (writing a line of code) where as a working programmer is a software engineer constrained by time and resources. This means that for example this algorithm course, it teaches you to generalize your solutions but that's not always realistic goal, or even desirable goal, in software engineering, and you might find out this if you implement one of the algorithms to do something for you in a small program.
Applying what you've learned in some software project of yours constraints you nicely such that you can't waste your time reading stuff from cover to cover.