tag:blogger.com,1999:blog-3722233.post8486536773166358525..comments2021-05-16T09:01:42.816-05:00Comments on Computational Complexity: Teaching without a netLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3722233.post-48555175375426761322013-10-31T06:24:20.254-05:002013-10-31T06:24:20.254-05:00What was the subtlety and who was the original aut...What was the subtlety and who was the original author or is it a secret?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24661054382759429292013-10-27T07:44:13.878-05:002013-10-27T07:44:13.878-05:00One of the more interesting courses I had was a 1s...One of the more interesting courses I had was a 1st year Calculus. Our instructor was a distinguished and horribly overworked astronomer, who jumped in to substitute the assigned instructor. He obviously did not have time to prepare: he would come to class, ask us what was the last thing we did, and start proving the next theorem. He wrote out a hypothesis (like, "assume both second order partial derivatives of a 2-variable function exist") then proceeded to prove the theorem (in this case, that the two are the same function). He would jump back between proof and hypothesis (like, "well, assume for the moment also that they are continuous") and continue with the proof, with occasional stumbles. He would go back and erase some of the hypothesis when it seemed they were necessary--sometimes reintroducing them later, when it seemed like they were needed. At the end he would go back and try to reduce the number of hypotheses, and offer alternative proof strategies that would require fewer assumptions. <br />While this could be confusing, and a bit of an adventure (the "no net" feeling, as viewed by the students). It really gave a feeling for what hypothesis was used where, and more importantly, a feeling of how a mathematician thought. I thought it was great--some students HATED it....CSProfhttps://www.blogger.com/profile/07212822875614144307noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-739836152443755062013-10-23T09:41:53.218-05:002013-10-23T09:41:53.218-05:00I do work things out in advance BUT since these ar...I do work things out in advance BUT since these are NOW proofs they are sometimes<br />incorrect. This is rare- but the fact that it COULD gives every lecture the POTENTIAL to have something not work, and not be fixable.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-69572716125907957992013-10-22T07:31:13.209-05:002013-10-22T07:31:13.209-05:00I'm not sure I understand: you are working out...I'm not sure I understand: you are working out the proofs in advance of class (I assume?). So if you have the proof worked out in advance then your working assumption should be that it is correct. (Of course, it is always possible that you find a bug while teaching, but this should not be happening every time!) If you *don't* have the proof worked out in advance, then I think it's insufficient preparation, not something to be emulated.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3427581970468994272013-10-21T15:48:37.752-05:002013-10-21T15:48:37.752-05:00Actually I'm not worried, the course is going...Actually I'm not worried, the course is going well and I don't want to fumble TOO much.<br /><br />I have seen profs use a CARICTURE of what you are saying as an excuse to not prepare. <br /><br />I fully agree that its good for students to see mistakes--- when math is FIRST discovered the proofs are informal, not quite right. When it gets polished up it loses some of the excitement of discovery. I am, albeit not quite intentionally, restoring that.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90374448737849070512013-10-21T13:29:03.007-05:002013-10-21T13:29:03.007-05:00I don't understand what you are worried about....I don't understand what you are worried about.<br /><br />If I am not mistaken one of the main techniques of teaching, is by setting an example.<br />By teaching without a safety net you are setting a very good example especially if you make a mistake once in a while (unless you are like me and when you try to prove something you get it right on the first atttempt. Sadely this is not a good example for mear mortals, since it scares them away).<br /><br />I think the fact a teacher makes a mistake once in a while actually makes the lecture more exciting. It seems that people remember things better when something exciting and related happens, maybe it is some primordial trait.Anonymousnoreply@blogger.com