one of the most frustrating tasks is writing the problem set for the first homework assignment:
there's usually very little content from which to ask any interesting [1] problems;
for the student who lack self-awareness, it's best to have a few hard, interesting problems early on, if only so that they are not deluded into thinking that this will be an easy class [2] ..!
the problems shouldn't be impossible, either, otherwise done students will panic, expect everything to be hard, and won't be able to do as well as they could otherwise!
[1] from experience, if i think a problem is interesting then often it will be too hard for the students ..
[2] the trouble with teaching maths is that we always teach topics that we know with great certainty .. which means, without experience, it is very difficult to tell what is easy for the students and what is not. for one thing, i'm recently becoming aware that students never know linear algebra as well as i'd want them to know it..
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