This is a soft question for which there is no objective right answer. I am wondering about how many exercise questions at the end of a chapter in a pure math upper division undergraduate to graduate level book one "should" do in order to sufficiently understand the material, and how can I choose the most "appropriate" set of questions (i.e. one that would maximize my learning without being repetitive exercises)? Of course, there is no "should" in the objective sense, hence the quotation mark. The way to go about this can be as follows:
- Find some publicly available university course website about the same subject you are studying, and if it has a list of weekly homework assignments, do them, and possibly check the answer online.
- If the book has solutions for some select problems at the end of a book, do them
- avoid doing hundreds of mechanical rote calculation problems
However, I am wondering how my answer would be answered if 1 and 2 are not available. Even for 2, the select problems may consist of many questions that question the reader similar things. In general, how do professors choose their homework assignments to give to students, i.e. if you are a pure math professor, what makes you determine that certain questions would be 'good' for your students and certain others would be not quite necessary? I understand that this last question depends on professors, but what principles do math professors use in general to pick exercises?