Sometime tomorrow morning I will be presenting a mathematics talk on something related to commutative algebra. The people present there will probably be two mathematicians (an algebraic geometer and a complex analyst) and some friends of mine.

Now this is the first time in my life giving a mathematics talk; it will not be a "general" talk aimed at the public but will be more technical. It will involve technical terms (if that's what one calls it) like quotient rings and localisation. As this is my first time I am obviously a little worried! I have read Halmos' advice here but I feel it is more for a talk aimed at the general public.

Several things bug me, one of them being how much detail in the proofs does one put in a talk? I am thinking obviously one does not check that maps are well - defined on the board but just says "one can check so and so is well-defined".

Furthermore, what about the speed that one writes? I am comfortable writing on the board and some people tell me I speak and write too fast. Obviously that is a problem and I need to slow down, but also I don't want to be talking too slow to bore the audience and seem to be out of passion. What is a good indicator of how "fast" or "slow" should one give a talk?

Besides, is there a way that one should "act when up on stage"? By that I mean so called "socially acceptable" do's and don'ts. I think any advice given from those who have "been there done that" would be useful for future wannabe mathematicians like me.

Thanks

**Edit:** Since many people have said it is difficult to give advice not knowing the audience, for the moment the audience will be a complex analyst, an algebraic geometer, one person who has just completed honours in orbifold theory, another friend in third year taking courses in measure theory,galois theory and differential geometry, and lastly a PhD student in operator/ $C^{\ast}$ - algebras