Thursday, May 17, 2007

I'm a survivor..

... ahem. Well for those of you who went into a mild state of panic (i.e. no one!), I made it through alive. This post is going to be littered with spelling errors, and sentences which do not make sense. I was scared last night that I wouldn't wake up at 3am, so I quite a few alarm clocks set up. One went of at 2:45am. The weird thing is that because I had been worrying about 'not being' able to wake up, my head shot up! Alas, if only it stayed like that! That's where the other billion alarm clocks came into play. 2:55am. 3am. 3:10pm. Dammit I want to sleep-leave me alone I cried! 3:20am and I was finally up and out of bed. I organized myself and headed downstairs, since that's what I do!

My mum knew I was awake- she always does. I mean everyone in my family knows what I do on the morning of exams. I can't remember ever not waking up at some unearthly hour, to do 'last minute' revision. Would I recommend it? Well it you wake up at 4 or maybe 5am then definitely, and if you haven't got an exam the day after then go for it. See where I'm going with this? I didn't have breakfast till pretty late... I mean early for you, but late for me, since I mean I didn't have it straight away! Rattled through the problem sheets, and since I'd just woken up I was doing pretty fine. Well until my stomach starting grumbling that is. Breakfast was a quiet affair, and I debated whether to make a post saying 'BOO'! Once again I decided against, since then the computer would be on, and then I'll just generate more weird lucks. (posting at 5am what the heck!). Some call it dedication- others call it madness.

Me I call it pure madness, or just me. Anyway, I decided to do a quick recap of the the first half of the course and I'm kicking myself for not doing it properly. I had decided not to learn the proofs anymore for the second part of the course and so time was on my side. Now I have a question- some might call me mad for waking up at some random, yet planned hour! But who in the world phones your house at 7am?? I mean I was having a nice small nap as well, when the phone rang... thankfully I didn't pick it up (dad did) otherwise I might have made another enemy.

So how was I feeling in the morning- I was pretty hyper, and felt that I won't let Linear Algebra ruin my life! I mean, the sun was rising, birds were singing, I was doing the questions! And those I couldn't... erm well the solution sheet provided me an escape route. I didn't manage to attempt the questions for the first half, but the methods used for the first half of the course were used again (slightly).

At this moment my head is falling and it's feeling very heavy. I intend to sleep in the next half hour and wake up again at midnight and then do all the problem sheets for sequences and series. The main thing is that I'm not going to be learning and trying to teach myself anything new- I'm just going to do the problems, past papers and learn a few odd proofs. The other day Noddy told me that I've been 'working' throughout the year, and I objected. Noddy then asked, 'so what have you being doing'? 'Sequence and series', I replied. The module which you can't do or struggle with is the one you're meant to spend more time on. I've probably spent toooooooo much time on sequence and series, but it's been ongoing, hence why I'm slightly less panicky about the whole thing. (thankfully, compared to what I used to be like).

I've not eaten since the banana I had at 9:40am. I was walking out of the library at that time and my exam was in five minutes! It's either I was pretty relaxed about things, or once again I've demonstrated how uniquely mad I am. The equally weird thing is that I was the last one up. They had to drag me away from the table- it was quite a scene! I was kicking and screaming and refusing to let them have my paper... hmmm, maybe I should keep comments like that in my head. If you're as gullible as me and believed that then I'm sorry! But that didn't really happen- I just had an invigilator standing over my head, watching as I wrote my details, since I'd come 'late-ish' and not filled them in the beginning. I didn't deliberately take my time, but he was really off-putting! Fine- I did take me time, but he could've at least smiled back. The invigilators were like the prefects from the demon headmaster! Scary.

So I'm blabbering about everything but the exam. It's sat here right next to me as I type this- watching my every movement. I think the resit paper is going to be the exact same one! Previously or do I say 'earlier' I mentioned that maybe 3am is too early. I had my reasons! The first question required us to write the augmented matrix and hence solve the system. I wrote the augmented matrix but then got an inconsistent system!! That wasn't possible since the question asked for the general solution. I had copied the augmented matrix out incorrectly. Muttering a few well chosen words to myself and looking to the skies I continued.

I forgot to take my watch with me to the exam. I don't wear my watch anymore since whenever I used to write I had to take it off, because it was irritating. Consequently I lost it on more than a few occasions, so nowadays I tend to take it when needed. Since I was sat at the back-ish I couldn't really see the clock at the front, and this was when I wished that an automatic voice announced the end of each hour. I was far too relaxed you see, taking my time, writing proper sentences. You wouldn't believe what I did. Initially I wrote, 'v \in.....', but then I stopped and thought to myself, 'hmmm can't start a sentence with v, so what do I write before it?'. I can't believe I did that, and it wasn't only then- I spent far too long trying to 'prettify' my work! Making sure the grammar etc was correct! Unfortunately as the marker of the paper will soon realise, my writing soon started to deteriorate as the pain in my hand increased.

Normally when I row reduce things, I do it as quick as possible and don't write the row operations which are being done. This time, I had to do it in 'slow motion' and write every single little, minute, minuscule...etc detail down! That was another factor which contributed to my writing the incorrect row echelon form matrix. So twice already eh- is anyone else sensing a bad day?

Don't worry I'm not going to dissect the whole paper- although that's tempting and I'm the saddo who would do that. I'm just 'reflecting' on the 'major' incidents in the heat of the fire! Two words: Gram-Schmidt Method. I liked this method, I mean I've got it in my head as lots of projections, so it's easier to remember, but G-S don't like me. You know I'd love to get my paper back and see how it's marked. I mean how much does it actually matter, that I wrote sentences and thought to write every single small (etc) detail down. I couldn't help it. I didn't read the question and so blindly applied G-S to the three vectors and obviously I got the same three vectors since they were orthogonal! That made me smack my hand against my forehead, and so allowed me to read the question properly. I made a big cross through my work, and started again.

We had to find an orthogonal basis for R^4 containing three given vectors. After some help yesterday, I'd understood why etc. So naturally you look towards the vectors from the standard basis. Now on my question sheet I'd written e_2, but on the paper I'd written e_4. :\ So e_4 it was. I once again started fresh, 'we are now going to use the ...' etc. Wrote out the steps, but realised that I really was after v_4 this time round. I calculated v_4 and it was the zero vector. :@ I was mad. Mad as a red hatter, and smoke was coming out of my ears. I knew that I'd chosen the wrong vector to add, but why I didn't know! I did another cross but in my anger I moved on. (lesson learnt from first semester!)

There were a few questions, which I struggled with in section 1, but managed to write bits and bobs down. Once proof was in the example sheets, and once again I'm kicking myself for 'skimming' over it! The thing is the whole questions were six marks and how many marks part a, for eg, was not given. So I didn't really know how much and what to write. Obviously in these circumstances one tends to write more than necessary. Dare I go onto section B? Nah- it was silly. We had to write a long page essay, explaining the LU factorization and describing how to find it! I mean the best way to show these things is an example, and I felt like creating one so I could write, 'now we do this, then that then this ...'. It was painful since I wrote a lot of extra rubbish down which unfortuantely didn't make sense. (didn't check that part since I was 'annoyed'!). So after this whole essay on the LU factorization we had to solve a system of equations using it.

Ok, I thought- I know what to do, so let's get on with it. I slowly wrote everything out, making sure that I wrote the row operations as R_2-(-2)R_1, so I could read the multipliers of. Strike three happened, however here is when I award bonus points to Dr Coleman, for helping me in an exam which had nothing to do with! 3 hours is an awfully long time for an exam, and I did day dream and doze off one could say for a few minutes. I had actually day dreamed of sitting in the same darn place doing the sets exam and thinking how the question had been wrong. I was actually hoping that maybe of the questions which I couldn't do (G-S) was wrong! Anyway, in my day dream, I remembered that in my sets exam on every single little, minute.... question I'd written 'CHECKING' where applicable, since Dr Coleman had drilled it into us! I made it clear that I had checked my answer, so if my answer was still wrong then have some mercy mate!

Now these thoughts brought me back to reality. I had an L matrix and a U one. Obviously with thoughts about what Dr C had told us, I thought hmmm let's check whether A=LU. It didn't. Hell broke loose for 10 minutes. I panicked. I couldn't find my mistake. What had I done wrong. It was only the very last entry which was meant to be 13 but was adding up to 18! I had made 'elementary' errors in my calculations it seems, but thankfully I snuffed them out before things got serious. You see had I not checked my answer at that moment, then the my solution to the system of equations would have been wrong! If I'd checked at the end, I'd have freaked out more and probably wouldn't have been able to spot where I'd gone wrong. Phew. Bonus points power infinity indeed.

We had to choose three questions from section B, and I chose the three from which I could answer the most! Avoided transformation matrices and kernel, but got in a muddle about column space and null spaces. (the proofs of them that is!). I suppose I can't complain since I didn't exactly learn them proofs, but are we allowed drawing black boxes at the end of proofs in exams? :D I did a box with a question mark next to it, since I was really making it up and writing things for the sake of it. Ultimately I went back to attempt the questions I'd left out first time round and GS was an obvious target. I spotted the e_2 thing and this time wrote, 'We will (again!) use the GS method.' I was going to write and I hope it's third time lucky, but I'm not sure who marks the papers, so I didn't want to test anyones humor/patience! I did write an ickle sorry somewhere, but that probably won't be seen.

Anyway, no more linear algebra for a while now. Woohooo. (the way Homer does it!). My thoughts on the module will have to wait for another day, but I'd rate the exam fifty-fifty. I mean the big if surrounds everything, but I'm not sure whether I've done enough to hit my 'marker', which is what I ultimately hope for. It says 'marks will be given for the quality of mathematical writing', so it makes me wonder that maybe it wasn't time wasted trying to start a sentence with a word. But really who really will care- it's just an exam paper, not a report! Sigh. One down and two to go. Can't wait till tomorrow night. Weirdly I'm still not hungry, my heads banging but my stomach is surprisingly well behaved.

Before I head of to bed, I must say that I was most upset to find that the Tweenies (apart from Milo) had gone AWOL after the exam! Milo took his exam elsewhere, but I walked to the back to find.... no one! I did ask Dr C whether he'd sit the exam for me tomorrow (and obviously get 100%), but I think he was worried that he might get 101% so obviously declined!

This post probably doesn't make sense. I mean name one of my posts which has made sense?! I bid thee goodnight and hope that I wake up in 7 hrs time to do some sequence and series!

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