When giving the first lecture to a group of new students I usually give out copies of "In Praise of Lectures" by T. W. Korner. The pertinent points from the article are that:
- A lecture presents the mathematics as a growing thing and not as a timeless snapshot. We learn more by watching a house being built than by inspecting it afterwards.
- As I said above, the mathematics of lecture is composed in real time. If the mathematics is hard the lecturer and, therefore, her audience are com- pelled to go slowly but they can speed past the easy parts. In a book the mathematics, whether hard or easy, slips by at the the same steady pace.
- Some lecturers are too shy, some too panic stricken and a few (but very few) too vain or too lazy to respond to the mood of the audience. Most lecturers can sense when an audience is puzzled and respond by giving a new explanation or illustration. When a lecture is going well they can seize the moment to push the audience just a little further than they could normally expect to go. A book can not respond to our moods.
- The author of a book can seldom resist the temptation to add just one extra point. (Why should she, when purchasers and publishers prefer to deal in ‘proper’ books rather than slim pamphlets?) The lecturer is forced by the lecture format to concentrate on the essentials.
- In a book the author is on her best behaviour; remarks which go down well in lectures look flat on the printed page. A lecturer can say ‘This is boring but necessary’ or ‘It took me three days to work this out’ in a way an author cannot.
Whilst this is ostensibly about mathematics lectures I think that the points made as just as applicable to other academic subjects.
