Friday, May 18, 2007

3 x 3 x 3 =9

Was the genius answer yours truly came up with today. I probably, actually most definitely would not have remembered that had I not performed a 'post mortem' of the paper. 'Did you get 1/27 for the radius of convergence?' Bella asked me. Erm... no- I got 1/9, was my reply. Then it all came back to me (3+1/n)(3+2/n)(3+3/n) tends to (3+0)(3+0)(3+0) by the algebra of the limits, and so a_n tends to 3.3.3=9 as n tends to infinity. I should get fulls marks for that! Yes, I'm pretty annoyed at this moment. Obviously I can't resist discussing the paper afterwards, since me, Milo and Bella are all like that. But I can't believe what I did. I should have written, in my world this is true- you can't mark it wrong!

Yes, I'm annoyed. You see that's the only thing I'm thinking about now, and not stupidly checking the last answer.

In my previous post I mentioned that I intended to wake up at 1am today. I'd love to sit here and type that I did wake up at that time, much to your amazement, but alas things didn't go as planned. I had decided to put reminders on my phone that went of every 10 minutes. Well my alarm would have sounded at 1am, and then every 10 minutes til 40 past, my phone would have woken me up! My phone, isn't a new model and it's pretty basic- just the way I like it, so I was confident of being up. 7pm was indeed a weird time to sleep yesterday, especially having not eaten anything, so obviously no one was considerate enough to not disturb me! (No reason why they should be, but still....).

Anyway I was woken up twice possibly before 10:30pm, but then I woke up at some time unknown to me and I think I must have still been dreaming, but was kind of awake! I turned right and I was in a subspace. I thought to myself- I have to get out of here because I have to sleep. So I turned over to my left, and then once again there I was in a subspace, but this time I saw vectors around me! I mean v's and x's were all over the place. In whatever state you want to call that, I thought to myself that how the heck am I going to get to sleep now! I can't get out of this bleeding subspace. I then lay on my back, and all was well for a while, but I can't sleep on my back so obviously I kept on moving from subspace to subspace wondering how I'm going to get any sleep and wake up to revise! I did eventually drift of but it seems that no matter what I do, Linear Algebra will always remain a part of me. I was afraid before, but I've considerably calmed down now. I mean rather Linear Algebra than stats right!

Anyway, at some other time, my mum walked into my room and said 'I thought you were going to wake up at 1am and revise beans! Are you not going to revise?'. I shot up in bed and asked her for the time. It was 5am. I was sent into a panic- '5am, no mum please tell me it's 1am. It can't be 5am- you're joking! Why am I still asleep if it's 5am. This can't be happening!' and on it went. My mum told me to relax and do as much as I can now, and not to worry. I calmed down slightly but still I was worried. Obviously one has to look at what went wrong, so I picked my phone up and interrogated it. It seems that someone had sent me a message whilst I'd been asleep but my message memory was full so an 'error' message had popped up. This I take it is the reason why my reminders failed, since as soon as I pressed the OK button, the reminders all went of shouting, 'revise'!

However, that being said I would probably have freaked out more if it had been the Linear Algebra exam today rather than sequences. You see like I said, it seems that I might have spent far too much time trying to understand sequences and hence, all I had to do was learn the proofs and do the questions. So without any breakfast I tried to memorize the proofs- well the thing is in the notes it says 'write N'(e)....' and I always don't write that. I mean I don't think that it's necessary, but I thought that it's best that I used the same epsilon and notation as the notes. Shockingly I had had roughly 10 hours of sleep- the most I've had in a long time, so I was pretty awake. Maybe that's telling me something!

Funnily I had decided not to learn the proofs for divergent sequences, I mean I knew how they went (eg a_n and b_n tends to infinity, prove a_n+b_n tends to infinity), actually I remember now, you're meant to take N(k/2) for the sequence a_n and the same for b_n, well something like that I guess! Thankfully this question was in section b so I didn't do it. I had two breakfasts this morning- weetabix, tea and toast at 6:15am, and then tea and more weetabix at 8:30am! Oh and a banana. Ok, I'm waffling and if you're reading you're probably wondering whether this bean is feeling ok.

My answer: how can I feel OK after I claim that 3x3x3=9! I have been complaining about this at home since I've got in. Po got sick of hearing, 'I can't believe I wrote three times three times three is 9!', and retorted that why can't I just say that 'three cubed is nine?'. Maybe I should have wrote 3 cubed down, since I then wouldn't have stupidly added them up! I had written it as 3x3x3 hence why I have to say it that way. Sigh again. Yes that's probably I teeny weeny mistake, but yet it's eating me up! Makes me wonder what other silly things I've written down today.

I'm not sure whether it's the 'right' thing to say that the paper was 'ok'. I mean I hate coming out of the exam and saying 'positive' things about the exam. Seems to me like I'm jinxing things and one never does know how one has done. I mean I'm glad in a sense that I realised this 'error' since now I'm not sure whether it went 'ok'. We had two hours, and I first had a quick glance through the paper making a mental note about which questions were in the paper and section B. Surprisingly I was very relaxed throughout the exam, I mean normally I rush through the paper and then chill out at the end and check my work. I think I miss doing that since doing things 'slowly' is the reason why I've been making so many darn errors recently. So one can say I was casually doing the paper, and talking to myself about random odd things at the same time. I did actually have to shake myself out of the dozing and bring myself back to earth.

It's weird but it doesn't feel like 'exam season' it's just too soon. I did that exam the way I'd do my homeworks maybe, or the way I do the questions in the example class. (without help of course!). I do feel for the person marking my exam, since it started of pretty neat, but slowly my writing deteriorated. I can't help it! I started too many sentences with 'hence' and 'so' so I edited them and wrote 'thus' instead! I did the same thing about starting the answer with a variable as well. The marker is probably going to wonder whether I sat a maths exam or an English exam! The thing with sequences and series is, that you have to write every single little, minute, small, teeny...etc! detail down. If 2/n is null, you've got to first write that 1/n is null by the 'standard list' and so by the scalar multiple rule 2/n is null. You probably don't have to do this all the time, but from the courseworks and the solution sheets I felt that 5 marks can't have been given for saying that the sequence just tends to a limit!

I also foolishly wrote too much in the answers again. It said use the limit comparison test and what did I do: The limit comparison test is blah blah blah... and then proceeded to answer the question! Once again the marker is probably going to wonder whether I was answering the exam questions or trying to 'teach' someone! Sigh again- is that the third time already. I'm not sure whether what I'm doing is a 'good thing'. I mean in assignments it's different! I think this might be a reason for why I've become more 'relaxed' and my exam technique has changed! I'm not liking this change to be honest, since it no longer feels like an exam. It does actually feel like I'm 'teaching' someone and I try to write the answers down so the 'reader' knows every single teeny step that I have done. The markers obviously going to know what say the limit comparison test and the modified integral test are, so why is there a need for me to state them?

Ah well, will just have to wait and see how I do! But seriously, I'm quite eager to actually now get a 'copy' of my scripts after it's been marked just to know what the marker makes of it. I mean if it's not liked, then for the sake of passing the exams I shouldn't do it! I answered all the questions, some as I've mentioned incorrectly, but something weird happened in the exam. Maybe it's because I was relaxed but for the last half hour or so I had a splitting head ache- like the one I got that day when the demons visited! I couldn't walk away as well. You don't know how tempted I was to get up and leave. In my head that felt the right thing to do, since the exam didn't feel like an exam. :/ Weird and weirder, my hand went all silly and I was holding my pen in the way your hand makes a fist! These two combinations didn't help.

Yes, I sit here and write about my exam and other random things- is this my way of 'celebrating' the end of the exam? To be honest, my mental fatigue seems to have been transferred to physical fatigue. Physical is worse I've got to admit, and well my darn back is at it again. I mentioned to my mum that I feel 'old', she laughed, but I couldn't walk stood up straight. I suppose my 'sequences and series' file has increased in magnitude quite drastically which is one reason for this, but I do regret not looking after my back. If someone tells you to lift a stone slab- don't do it because you want to prove that you can! Not straight away anyway! Now it's a 'trivial' thing to do, but you see we did some building work once upon a time, and as you might have gathered in my adventures with the jigsaw, I like doing stuff like that. You know Bob the Builder is great.. 'and lofty too, bob and the gang...' ahem. Well lofty was the blue one if I remember correctly, with the sad face. :(

Oops getting sidetracked again- I just like doing stuff like that, 'physical activities' I suppose and making things is always fun. (Me and my brother made this 'kennel' sort of thing for a cat. Well there was this stray cat who used to sit in our garden. I think it had ran away and it looked sick, so we first started putting water out for it. Then it kept on coming and soon we were buying cat food and leaving it for it. I think it got bullied by other cats, since once this ginger cat came and poor Gandalf ran away! That's what I named it- Gandalf since it was grey and white. It used to always run away if we went too close to it, but gradually it used to come and wait for us to feed it. It once came in the house, and my mum wasn't impressed so that was the end of that! (we'd bought new sofas you see :D). One day Gandalf never came back. I want a cat but mums eh! (I'm content with going to my aunties house and playing with her cats- they're cool.)

Now the real reason I'm typing random nonsense, well there isn't one, but you see my headache hasn't disappeared since the exam. And well being mobile is out of the question, so I type. I've realised that I should be banned from emailing people! I won't embarrass myself further by writing why, but I seem to have a knack of emailing people. I mean that's natural but I seem to 'bug' people with emails! Obviously to me, it doesn't seem that way at the time, but upon reflection I should resist! It's not that I email, but my emails at times, sometimes sound like my posts. Imagine sending a lecturer one of my posts. Never mind that- imagine sending anyone a post! They'll probably have more reasons to avoid me! Anyway I will exercise more control on that front, well... I'll try to anyway. (15 minutes before my exam, I was emailing!)

Something else weird happened in the exam, but alas I feel that it's silly writing about it. Two down one to go. Got this Tuesday to look forward to i.e. the day I turn 6.95. Not 7- that's in June sometime,but 6.95. I wonder which maths book I'll be getting. ;) Haha, I confess that I bought another one today, however relax- it was second hand! (Concepts of modern mathematics-Ian Stewart). I have buried my grudge with sequences and we have settled the argument like 'mature mathematicians'. There were tantrums, and the boat did rock but let's be glad it happened eh! :D Now I've got real analysis to look forward to next year-woohoo. (hopefully). I was going to end with 'another' lame joke, but sadly I don't think that you have the patience for that! (if you're reading that is).

Damn- one last thing.... my plan to be the next maths \sout{dictator} leader (why does that always happen!) are already in motion. Last time I mentioned that bear doesn't like maths today this is what I made him type on the keyboard on this very screen. (well I held his hand and he pressed the keys, but still it's progress I tell you!). You'd think these kids would avoid me wouldn't you, but bears great. I was particularly happy seeing him bound down the stairs as I came home.

'red is my favorite colour. i like maths. beans made me write this.' by Bear. (He knew he was writing the first two sentence but no idea of the third!)

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