Does anyone know by chance a good guide on writing lecture notes for math courses, or in the general? I know eventually I’ll have to get back into teaching, and will be doing higher-level courses, but I myself have never made my own lecture notes and want to do good on my future students by starting now than waiting for later in a couple of years

I dunno if that’s a dumb question or not, I just know that understanding a field well is much, much different skill than teaching a field well, so I want to practice it early and do right

oh, hm. i would have slightly different answers depending on whether 'lecture notes' means notes for your own use only, or means material that you would share with students (i guess, at a minimum, i would suggest that these not be exactly the same thing, although for many people they are).

even then it is hard to have good advice without some idea of course materials (e.g. a textbook, if not a syllabus selecting material from a textbook). one big adjustment one has to make from studying for oneself is that the "best" approach to the material in terms of one or more fixed internal objectives, might not be the best for a course. particularly if the course is largely based on one textbook.

e.g. in a class that has a single assigned textbook, it will not do to replace the textbook's proofs with "better" proofs whenever possible, or to otherwise offer "alternatives" to the book whenever it is might be possible. you have to be really selective about how much you reference the world outside of a book.

and my view on that isn't specific to classes for non-majors (although it definitely applies there). unless you are teaching at the graduate level, your choice of textbook should almost entirely determine what you cover, and largely determine how you cover it.