I have been to a number of advanced lecture courses (of between 3 and 10 lectures) over the years, given (in principle) by experts to graduate students and experts in neighbouring fields. Examples of this are summer schools.
My impression is that this usually devolves into lectures given by experts in an area aimed at other experts in the same area. Graduate students are usually left by the wayside in lecture 1.
Is the whole endeavour futile? or do people have principles/suggestions to maximize the usefulness of advanced lecture series
Best Answer
Here are my 2 cents:
1) Assume that the audience knows nothing about the topic you want to present and next to nothing about any other things.
2) Choose one result you'll be aiming at and develop "the general theory" just enough to be able to do the proof. Cut all special terminology to the bare minimum.
3) Do one little thing in each lecture with clear beginning and a clear logical point at the end, so that even if someone comes to just one lecture in the middle of the series, he'll be able to learn something. Never stop in the middle of a tangled proof.
4) Wake up the audience every 5 minutes by stopping and asking "obvious questions". Wait for an answer. If none comes, you've lost everybody.
5) Run question-answer sessions (you can devote first 10-15 minutes of each lecture to that or you can spend a couple of classes exclusively on that, it is your choice)
6) If you are not lazy, make notes for each lecture and distribute them a day before the lecture. If you are lazy, designate somebody to take notes of your lectures and look at what he/she has written in the end of each lecture.
7) Write on the blackboard clearly as you speak and use high-tech (projectors, movies, etc.) only to show pictures. Remember: the speed of absorbing new information never exceeds the speed at which you can write it in full sentences on the board.
8) Above all, remember that your task is to teach other people new things, not to show how much you know or how great your subject is or to impress them with anything else.
That should do it if you are giving a lecture.
1) Read a bit about the topic that is going to be presented before coming to the lectures
2) Sit in the front row and ask the questions as soon as they arise. Don't be afraid to interrupt the lecturer. Believe it or not, but if you don't understand something, 50% of other people in the audience don't understand it either.
3) Make notes. Read the notes for each lecture before you go to the next one. Catch the lecturer before the lecture and ask any questions you have from the previous one.
4) If the lecturer is out of reach and you have a question, ask anybody in the audience.
5) If you have friends in the audience, run "discussion sessions" after each lecture with them. Sometimes 5-10 minutes are enough to make the difference between "being lost" and "understanding everything"
6) Above all, remember that you came to learn, not to admire the greatness of the lecturer and the subject.
That should do it if you are attending a lecture.
This, of course, applies to "lecture series with proofs". There are also "purely expository series" but I would advise to just avoid them on both sides.