I've been trolling my wife's cookbooks.
There I find basic ingredients (e.g. make batter, making
eggs), main dishes (steak), and 7-course means (how to
choose side dishes, wines, etc). The 'cake' section, for
example, has option "subroutines" such as toppings.
The idea would be to develop a cookbook-style of presentation
for computational mathematics. Pick an algorithm, write a page.
When something is used that is not explained, there is a reference
to other sections (ala cakes that suggest "see the frostings")
Each entry would be an algorithm or idea, explained in at most one
2-sided loose-leaf paper. The algorithms would be gathered into
sections, e.g. "basic ingredients" like resultant, "main dishes"
like polynomial factorization, and "7-course meals" like solving
the heat equation (target is the physics class). The 'cake'
subroutines would involve choice of polynomial representation,
sparse, dense, distributed, recursive, etc.
I want to be able to "write in the small" (1 page) with a focus on
a single subject but "organize in the large" so I can shuffle these
subjects into groups by purpose. The analogy is that my wife has
a cookbook that only deals with pickles. I'd like a cookbook that
only deals with rings, composed of loose-leaf selections from the
overall collection. This would be assembled for a computational
mathematics class. The same material could be re-arranged and
re-selected for a different class.
The key focus is on providing explanation and motivation. Most
books that mention the resultant spend pages on the proof and
not a word about why or where to use it.
The 1 page / 2 sides focus is much easier to write than a whole
chapter and, since you're staring at a single routine, it is easier
to provide motivation for why it exists and what the tradeoffs are.
"How" is interesting but "Why" is vital.
I've drafted a 0th cut at the idea. See