that I needed to solve the more general problem of selection. After less than a minute
of trying to see what was wrong I told them
I am sure that Median IS in linear time. I will consult sources and redo this tomorrow.I then did the rest of the lecture (which didn't require knowing the Algorithm for Median) and the next day I did the linear Median Finding Algorithm correctly.
Note that I was teaching well known material. So I KNEW that what I was saying was true even if I couldn't prove it. I also KNOW that I could look it up. I was TEACHING WITH A NET.
When I taught Grad Algs a few years ago I sometimes didn't quite know how the PROOF went BUT I knew that the STATEMENTS I made were correct, and the algorithms and proofs were out there. In one case I emailed the original author with a subtle point I was stuck on. (It really was subtle- the author himself had to think about it). TEACHING WITH A NET
Last semester some of my Ramsey Theory course was taught WITHOUT A NET. Not in termsof the statements of theorems, but in my attempt to find easier proofs of theorems--- sometimes my alleged proof DID NOT WORK. And there was no book I could consult, nor person I could ask, to help me out on these new ``proofs''. One of my attempted simplifications (of the Canonical Ramsey Theory) DID NOT pan out in the end.
This semester I am teaching an honors interdisplinary course on Fair Division (nicknamed 'Cake cutting'). I've pulled material from a variety of different subfields (math, CS, AI. Yes AI!). So I have put some things together that are ``new''(not worth-publishing-new but new in some sense). Some of them have been wrong, or to be more fair, not quite right. But WHO CAN I ASK? Nobody! This is truely teaching WITHOUT A NET. I have made about 2 incorrect statements (both of which were prefaced with `this might not be quite right') but the bigger effect is that every day I wonder if what I am saying is correct.
The effect on the actual course is mininal-- but my mentality going in ``will I make a mistake today that I cannot recover from'' is... interesting.
What to do if you are wrong? Own up to it ASAP. Every minute you fumble around you lose the classes interest.
Is the course working? I think so-- they are learning and having fun. It helps that they are honors students who chose to take this course.