[sidlls]

My experience with the average programmer is...different from yours. The software development field is exceptionally bad in this regard. Physicists are mathematically sloppy sometimes (why, yes, I will just multiply both sides by `dy` and take as many liberties with operators, harmonics/series, and vector differential operations as I care to, thanks).

Mathematics, like any other academic field, has jargon (and this includes notation, customary symbols for a given application, etc.), and students of the field ought to learn the jargon if they wish to be proficient. On the other hand, textbooks meant to instruct ought to teach the jargon. It's been forever since I've opened a mathematics textbook; I don't recall any being terribly bad in this regard.