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.
It is not such a great idea, the dependency courses. Most prerequisites for a self-learner are kind of overblown IME. If you're applying the knowledge and / or you don't have time to go through them like a college student, your prerequisites have a different function for you (the least amount that makes you understand the main topic you want to understand in order to apply that knowledge, this might mean just literally skimming a paper or reading a subchapter of a chapter in some other book - you are not there for the prerequisites).
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.
The authors that can write a book such that you can understand it without previous knowledge are wonderful, but it is heavily dependent on the subject. It’s hard to talk about differential equations without first knowing calculus.
It is not possible and I didn't mean to imply that. There'll be endless prereqs. most of the time.
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).
Could you please expand on what you mean by applying knowledge? But sure, I don’t believe reading a book from cover to cover is necessary in most cases, and I seldom do so with scientific books.
I firmly believe you need a software problem / idea to go with your learning. When you run into problems fixing / making what you want, search for what might help you.
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.
