Difficulty
An acquired skill: Learning to get information out of research seminars is an acquired skill, usually acquired much later than the skill of reading mathematics.
Approximation of private tuition
The purpose of attending a lecture is to learn from the lecturer’s insights, opinions and ways of solving problems. Private tuition is far better than a lecture. But lecture exists due to lack of sufficient number of tutors. If you cannot follow what is going on, and if it is not too disruptive, ask. If you are lost, ask the lecturer to do an example.
Novelty
(Ravi Vakil) You’ll hear various words, whose definitions you’re not so sure about. At some point you’ll be able to make a sentence using those words; you won’t know what the words mean, but you’ll know the sentence is correct. Later you’ll learn the meanings and fill in the details more efficiently.
Preparation
- Read before attending the lecture. Read after the lecture. Tackle exercises.
- Bringing photocopies of relevant pages of the book to the class helps in quick understanding and orderly recording.
Maintaining attention
Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question focuses the mind.
Try pretending that you will be scored based on your understanding of the lecture.
Sit in the front of the class. During lectures, one must respond with gestures in order to indicate interest.
Following the talk
Try to follow the thread of the talk, and when you get thrown, try to get back on again. This isn’t always possible, and admittedly often the fault lies with the speaker. The initial parts of the talk is very critical.
Check claims; consider limits, exercise intuition, use calculation.
Take text or slides to the lecture, if available.
Post-talk discussions
Befriend a couple of other attendants. Talk to them and to professors attending the talk, question them about the lecture, acquire their insights.
Try to answer the questions: What question(s) is the speaker trying to answer? Why should we care about them? What flavor of results has the speaker proved? Do I have a small example of the phenonenon under discussion? See if you can get one lesson from the talk. Criticize the problem and the solution; see how you can apply ideas thence to your work.
Try to extract three words from the talk and learn their definitions. Assimilate notes immediately after the lecture: avoid backlogs.
On the internet
Video lectures and university course lectures are useful.