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 I didn't ask to do this course you know I wanted to do algebra I told them I didn't know any analysis
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 THUD not very big these platforms are they I keep falling off them
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 I don't have time to go into it 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
now 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 still 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 thoughts 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 you know greek letters alpha etcetera no this one is nu 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 next time ah that should have been a nu maybe no it should be a v oh it's an r is it 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 nontrivial yet...
How to be a good member of a lecture audience
Aaaachoooo! Cough. Splutter. Wheeze. Yes I've got a cold. There's a lot if it about. No I don't use a handkerchief. Sniff. Sniff. Cough. Oh thanks, now I've sneezed on your notes I might as well blow my nose on them. Zurrrrrkkk! Hoooossssh! Now what lecture is this?
Do you think he's got this bit wrong? Well I'm sure you can prove it quickly using matrices. Shall I ask him whether you can? No. Something wrong? No, nothing wrong. I was just wondering if you could prove it more quickly with matrices. Oh I see. Stick my head in a bucket of WHAT? Oh right. Yes.
God this is so boringly obvious. I think I'll do the crossword instead. Mixed-up caterpillar in tribal religion, we hear? Hmm. Can you think of an anagram of caterpillar? Oh I'm SORRY. I didn't realise you were listening to the lecturer. Oh I thought he was proving a different theorem. Excuse me, how do you get x-squared there? You just explained that. Sorry, I didn't realise.
Can I borrow a bit of paper? Have I really borrowed one every day this week? Ah thanks. I don't suppose you have a pen I could use? Yes I'll take care of it. Ooops, it's on the floor. SCRUNCH. Ah well at least we know where it is now.
Eeeek, I've lost my contact lens. It must be down there somewhere. Sorry, yes I'll try and look for it quietly I know you've got a lot to cover today. Could you tell me if there's a contact lens down there? How about the row behind? Yes it is important I can't see without it. Oh it's all right I am wearing it. Just got a bit of dust in my eye. You can stop looking now. Help I'm two blackboards behind now. What can I do?
And how to be a good exam invigilator
O.K. you can start writing as soon as you get to your places. Look would you mind sitting down? What do you mean there isn't a desk for you? You must be in the wrong room. What's your name? Oh. Well there don't seem to be enough desks. Perhaps you could sit on the floor this time. Come on, let's get started.
Ha ha ha ha ha! Oh sorry. I've just seen the joke in question 5. I don't know how they think of them. What a laugh exams are, eh? Anyway don't let me disturb you. Sorry about that.
What do you want? Well why didn't you go beforehand? Honestly, the incontinents you get round here. Well why didn't you bring a pottie with you? Oh all right I'll find someone to escort you. Can't have you stinking the place out, can we? Though maybe you should have a doctor's certificate (rustle rustle). No, it doesn't mention that. O.K. get a move on.
Creak, creak, creak, crash! Bloody hell, they don't make chairs like they used to, do they. I bet Chippendale's chairs never gave way when you leant back on them. Oh well, now I've nowhere to sit down. Tramp, tramp, tramp. (God what a useless answer that chap's writing. Even I know that 2+2 is 4 not 5. Must be nerves, poor chap.) Oh sorry, am I putting you off? I'll go and breathe down somebody else's neck.
Ah, this one looks calm -- he's writing away nineteen to the dozen. A-a-a-a-a-SHOOOO!!! Oh sorry. Yes we can pick up all the sheets of paper. And I'll try and find you a clean question paper. What was that sheet that went through the window? Question 2? Oh well, maybe somebody will pick it up and hand it in to us. You wouldn't have got many marks on it anyway, it's quite tricky.
Right, all writing must cease now. In fact if you knew your stuff it would have ceased 20 minutes ago. Look I told you to stop writing. Well you'll have to hand it in anonymously then, won't you? I don't suppose it'll make much difference to your result.
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