Post Made Community Wiki by Scott Morrison
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I haven't really made up my mind on this issue yet. I think writing up lecture notes beforehand has 2 big advantages over "winging it": 1) It allows you to be much more detailed and thoughtful in presenting material in your own voice then a spontaneous lecture could be. It also allows you to catch mistakes much more readily before they pass into the students' hands. 2) It creates drafts for future courses that can later be modified,expanded or rewritten however you choose with the possibility of eventual publication. Or not. Of course,the problem with this approach is the lectures become much more "rigid" i.e. it's harder to add material or change things as you go and you rethink things or your perspective changes. I think the best answer is a compromise: Write up careful drafts,but leave blank spaces on the notes for handwritten additions or revisions you come up with on the spur of the moment-especially those that result from student input. These changes can then be incorporated into the eternally evolving draft.