HOW TO BE A LECTURER
Well hello and welcome to the first lecture of the course. Er look I
said hello. Look I'd like to start now. Will you shut up. SHUT UP
PLEASE. Oh thank you. I don't mind you talking if you do so quietly.
Now this course is all about complex numbers and I've got a list of
recommended books here. Er well no in fact I seem to have left it
behind. Never mind they're all out of print anyway.
Now let me write up a definition. Where's the chalk gone. Ah here it
is. SNAP. Ah let me take another piece. Now definition 1.1. is ah um
of course I haven't said what this section's called yet. Oh it doesn't
seem to have a name anyway. It's all about convergence of power
series. You did something like it in real analysis, didn't you? Don't
you remember? Well he should have done it in his lectures and I don't
have time to do that now. Now definition 1.1. - scribble scribble
Can you read that at the back? No. Oh well sit further forward then
can you read it at the front. Ah come to think of it I can't read it
either. Perhaps if I turn on this light. Ah, no not that one - Another
one Oh well the cord was a bit frayed. I suppose, well look that
symbol is a capital sigma. Yes what's the problem. Yes well green
seems to be the only colour they have left in the box. Probably
because nobody in his right mind uses it so they leave it for me. Well
look perhaps if I explain it in words it's all in the textbooks
anyway. I can't help it if they're missing from the library. People
eat them or something.
Well now I'll draw a diagram. You don't have to copy this exactly
because it's slightly wrong anyway. This is diagram 2. Good question I
think I forgot to draw diagram 1. Anyway as I say it doesn't help
much.
Phew let me take my jacket off a bit - RIP. Oh well I sewed that
button on myself. You can tell can't you? Mow let me digress a minute
about the history of the subject here it was discovered by Cauchy, or
do I mean Gauss? - One of those people. And he sent a copy of his
paper to someone else who... well anyway it's very important and has a
lot of applications such as, er such as, well anyway you will see
applications in your other courses.
I expect of course they don't use the same notation but then they
don't have the same ideas of rigour as we do and now let's write down
the first result:
lemma 1.2 - lemma 1.2. Oh I haven't actually defined radius of
convergence yet have I? Still let me write it up and we can decide
what it means later. Well I seem to have a few minutes left so I'd
better start the proof.
Let n be this, and r be this and v be that and n be that - No on
second thought I'm already using n.
Now so I'll call it nu.... Pardon? No it's a nu, a greek letter. You
must have seen it before. All right call it v if you like but we're
already using v. Still it won't cause confusion. Now multiply this out
and obviously what we get is, er, clearly um, oh, that can't be right!
What have I done wrong here? Can you see the mistake? Maybe I lost a
minus sign somewhere. Search me.
Oh dear it's time to finish isn't it? Well give me just 5 more minutes
and I'll finish this off and oh maybe I should do this bit again more
carefully. Ah that should have been a nu maybe no it should be a v or
maybe an r. Oh well look, I'll finish this next time. I'm sure I've
got most of the details right? It's really very elementary after all I
haven't done anything advanced yet...
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