18.904: Guidelines for lectures

For the lecturer

• Your lectures should last 30-40 minutes, but they might take less time depending on what you were assigned. It is OK to end early.
• Try as I may to give you topics that fit into the time you are alloted, there will probably be times where you find that you do not have time to fit everything in you were planning on including. Try to cover the main points - but we'll be flexible, too. Choose a reasonable about of material to cover - you don't have to cover everything!
• DON'T LECTURE FROM THE BOOK! In fact, try not to make your lectures line by line duplicates of what appears in the book - digest the material, and convey the essence of it. (of course, some things, like definitions, statements of theorems, etc will naturally bear close resemblance to the source material.)
• Make lecture notes. You can use them or not during your lecture.
• Always make it clear what you are doing. If you are proving a theorem, say so, and tell us when the proof is completed. It should always be clear where you are going.
• Give examples, and convey the intuition behind definitions and theorems.
• Write large enough, and clearly enough so that everyone can read what you have written. Do not make the mistake of talking too much and not writing enough. But also remember that it is not necessary to write every word that you say, nor is it necessary to write complete sentences. Try to strike the "perfect balance."
• Feel free to draw pictures to explain some points (but don't let mathematical precision suffer from this!). Make sure that your pictures are big enough and clear enough so that they are easy to comprehend.
• Pause, look at the audience. The members of the audience actually tell you exactly whether they are following what you are saying by the looks on their faces.
• Be welcoming of questions. Sometimes someone will ask you a question that you will not know the answer to. That's OK - you can just say so. If you are unsure of your response, it is OK to indicate that you are unsure.

Guidelines for non-lecturers

• ASK QUESTIONS! Clarify things that are unclear. If the lecture is going too fast, slow it down by interrupting.
• You don't need to raise you hand to ask a question - just ask it.
• Be constructive with your participation.
• Don't read along in the book as the lecture is going on. Certainly don't do any other work during the lecture.
• Consider taking notes - I'm not requiring you to, but I find that there is no better way to follow a lecture.