I’d never heard of Gian-Carlo Rota before today, but I stumbled upon his “Ten Lessons I Wish I Had Been Taught,” and it is fantastic.
Rota was one of the teachers at Massachusetts Institute of Technology (MIT). He taught a difficult but very popular course in probability, 18.313, which MIT has not offered again. He also taught 18.001 (Applications of Calculus), 18.03 (Differential Equations), and 18.315 (Combinatorial Theory). His philosophy course inphenomenology was offered on Friday nights to keep the enrollment manageable. Among his many eccentricities, he would not teach without a can of Coca-Cola, and handed out prizes ranging from Hershey bars to pocket knives to students who asked questions in class or did well on tests.
Excellent advice on what it takes to give a good lecture:
The following four requirements of a good lecture do not seem to be altogether obvious, judging from the mathematics lectures I have been listening to for the past forty-six years.
a. Every lecture should make only one main point The German philosopher G. W. F. Hegel wrote that any philosopher who uses the word “and” too often cannot be a good philosopher. I think he was right, at least insofar as lecturing goes. Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.
b. Never run overtime Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody’s attention will turn elsewhere even if we are trying to prove the Riemann hypothesis. One minute overtime can destroy the best of lectures.
c. Relate to your audience As you enter the lecture hall, try to spot someone in the audience with whose work you have some familiarity. Quickly rearrange your presentation so as to manage to mention some of that person’s work. In this way, you will guarantee that at least one person will follow with rapt attention, and you will make a friend to boot.
Everyone in the audience has come to listen to your lecture with the secret hope of hearing their work mentioned.
d. Give them something to take home It is not easy to follow Professor Struik’s advice. It is easier to state what features of a lecture the audience will always remember, and the answer is not pretty. I often meet, in airports, in the street and occasionally in embarrassing situations, MIT alumni who have taken one or more courses from me. Most of the time they admit that they have forgotten the subject of the course, and all the mathematics I thought I had taught them. However, they will gladly recall some joke, some anecdote, some quirk, some side remark, or some mistake I made.
On proper blackboard technique (I wish more professors did this when I was in school):
a. Make sure the blackboard is spotless It is particularly important to erase those distracting whirls that are left when we run the eraser over the blackboard in a non uniform fashion.
By starting with a spotless blackboard, you will subtly convey the impression that the lecture they are about to hear is equally spotless.
b. Start writing on the top left hand corner What we write on the blackboard should correspond to what we want an attentive listener to take down in his notebook. It is preferable to write slowly and in a large handwriting, with no abbreviations. Those members of the audience who are taking notes are doing us a favor, and it is up to us to help them with their copying. When slides are used instead of the blackboard, the speaker should spend some time explaining each slide, preferably by adding sentences that are inessential, repetitive or superfluous, so as to allow any member of the audience time to copy our slide. We all fall prey to the illusion that a listener will find the time to read the copy of the slides we hand them after the lecture. This is wishful thinking.
On using the Feynman method (my favourite scientist):
Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say: “How did he do it? He must be a genius!”
On the importance of giving lavish acknowledgements:
I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else. One day, I tried an experiment. After writing a rather long paper, I began to draft a thorough bibliography. On the spur of the moment, I decided to cite a few papers which had nothing whatsoever to do with the content of my paper, to see what might happen.
Somewhat to my surprise, I received letters from two of the authors whose papers I believed were irrelevant to my article. Both letters were written in an emotionally charged tone. Each of the authors warmly congratulated me for being the first to acknowledge their contribution to the field.
Do read the entire thing. It’s excellent.