The letter ℘: name and origin? (2017)

I have seen math textbooks that have a "table of symbols" or similar, by the table of contents or the index. It's really helpful. Also nice to have - a "map of the book" (I don't know a better name for this) which indicates graphically which sections of the book depend on which other sections. "Dependency graph", maybe?

I wish music books would do this too - I've been self-teaching myself a little classical guitar, and some of the scores I'm reading have various symbols that have taken me quite a while to figure out. I eventually determined that a bold III means to play in third position in some books, but these things aren't consistent between publishers.

Classical music is relatively standardized. Roman numerals to indicate position are standard practice for all string instruments (I remember learning this as a beginning bass player as a kid). You will sometimes see Roman numerals used as a means of identifying chords relative to the tonic of the current key, but that’s uncommon and the notation is a bit different than the position notation in how it’s placed on the staff (if it even appears on the staff and not in a harmonic analysis).¹ I’ve not seen the upper- and lower-case distinction in roman numeral notation I learned somewhere which uses cases to distinguish between major and minor in any classical music harmonization texts, but I may have just paid insufficient attention.

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1. I have a vague notion that it might show up in figured bass once in a great while, but I could be wrong.

This all seems right to me. As for your figured bass comment, you could have something like iii^6_4 for an e minor chord with the B in the bass, when the key is C major. But if you were writing it next to the staff you wouldn’t need to write the iii - it’s implied by the bass note and the figures, and classically figured bass writes the minimum it has to, for example just 6 instead of 63 for a first-inversion triad.

I've played lots of piano and wind music and took lessons for that stuff in school, but I've been self-teaching guitar / ukulele / bass / mandolin in a smattering of different styles, which is probably part of my issue. I go through cycles where I'll focus on one instrument and style for a few weeks - in the last year I've dabbled in bluegrass banjolele, Irish fiddle tunes on mandolin, jazz on bass and keys, rock electric ukulele, funk piano, rock organ... And that's not even an exhaustive list.