Mathematics doesn't really have dependencies. Everything can be thought of in terms of everything else: you need an in, which is usually arithmetic or geometry (but, for physicists, is often physics – and for programmers, is often concepts related to their favourite programming languages), and then everything can be defined in terms of something else.

However, many people find it easier if you have concrete anchors, rather than making everything an abstract ivory tower. A certain kind of musician might get Fourier series quite quickly by analogy to the behaviour of sound, and then pick up Taylor series by analogy to that; somebody like me might find it easier to translate the most general Fourier series to a Maclaurin series, then compare coefficients. All these approaches would give you an understanding of Fourier, Maclaurin and Taylor series', which then lets you learn things that build upon them.

The "separate courses" approach is doable (and the best I've come up with so far), but it doesn't scale: courses that cover the same things without providing further insight don't get merged together. It can't handle the combinations that, intuitively, I feel like there should be a way to handle. Human teachers can cope with it just fine!

One nitpick on trane-math: running `cargo test` will wipe out the .trane directory, if it exists. That seems not very good; perhaps there should be a way to point trane at a temporary directory, so you can test it better?