Be fast on easy parts and slow on hard ones

When presenting a proof, it is not enough to mention every argument needed; for each argument, you have to give them some time to process it. So after completing a non-trivial argument take a breath before moving to the next one. To decide how long this breath should be try to put yourself in their position, and bear in mind that most of the ideas you consider easy are much harder for them. Special care has to be taken when showing a formula; a long equation, even if it states something trivial, requires some time to process. (By the way, you should always write down the formulas you speak out.)

On the other hand, you do not want them to get bored by elaborating too much on easy parts. When explaining an easy argument, try to use short but precise and crystal-clear sentences. Such sentences are very hard to come up with on the spot though, so you should prepare them in advance.

A. Georgakopoulos: How to give a talk that is not too bad.

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