I'm wondering why lecturers at university select the problems they select in the problem sets? I don't understand why those problems have to be selected and not any others.

I'm sure no one would get upset if you did more than the allotted set. My perception is that most lecturers here in the states have a predefined set of learning objectives (put forth by the department or a curriculum committee), and they have to try to adhere to that for the material. So, they probably pick and choose based on that, and speculatively, that they don't want to get bad ratings for giving too much "extraneous" work.

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