Several styles of writing about mathematics are appropriate in different contexts.
- A mathematician writes something to be read by other mathematicians.
- A mathematician writes something to be read by students at some specified level.
- A student writes something in order to demonstrate that the student knows something.
- A student writes a question addressed to an instructor.
Whoever writes an explicit account of the norms and standards governing the each of these or governing the choice among them, will disagree in some things with everyone else who writes such a thing. But that doesn't mean it's not worth doing.
Quite a lot has been written about the first bullet point.
I will be surprised if no one's written about the second.
I have an impression that the third is relatively neglected. And the fourth. But right now I'm mainly wondering about the third, and less so about the second. The third is something that possibly ought to be included in undergraduate math courses.
What has been published on the third item?