Tuesday, January 22, 2008


That word currently describes how I feel about myself.

Before I dive into the deep end, a warning must be given about the length of this post. One could say I am in an exaggerated mood, but I think a lot of my mood is due to the vault of anger I am keeping a lid on.

I will start with Monday and then about today. On Monday I woke up at 6am(ish) to finish my revision and do the problem sheets. I was in a semi-panicked state, because although I felt that I had finished my revision, I just couldn't make a start on the problem sheets. I was skimming through the questions saying: "Have completed this, know how to do that..." and so on. After a nap at 9:30am I thought I might be feeling slightly calmer. That wasn't to be. I actually threw up yesterday morning, which was very surprising. (I can't recall exam stress ever being that bad before). After coughing my guts out (a horrible experience might I add) I was still on edge.

It was at a later time that I realised it was in my best interest to actually do the questions on the sheets, rather than nodding yes or no to them. I have been having problems with cyclic groups, or subgroups of cyclic groups to be precise. I had gotten myself into a confusion over the notation and even now my mind is still prickling about this. If G=, then H= is a subgroup of G. But then the question I need myself to answer is what is a^s. I had been doing questions in Z_30 etc and not been able to figure the story out. Anyway, I think this question can be addressed another time! I sent a panicked email before my exam and from the calming reply things are coming together. In Z_30 I might be OK, but what about other cyclic groups?

Enough of that already! At 1:30pm I was sat on a bench doing the questions, knowing that it would be take me about 5 minutes to get to the exam hall. If I had gone early and revised there, then I would have just panicked and not revised. Hence why I found a bench, which did result in me getting weird stares from people passing by! (Well it was a nice cold day...)

I won't mention the horrible Sugden Centre but will go onto talking about the exam. There were four questions and we had to choose three. I flicked through the paper and realised (with a small horror) that I couldn't answer the first three fully. Each had a proof, which I knew that I had revised, but my mind was firing blanks. The last question brought me some comfort when I realised I could attempt the proof (vaguely). The proof questions decided which questions I chose to do--this happened to be all four questions! Thinking back, this was a poor decision on my part. From the three questions that I wasn't able to do properly, question one happened to my first. I shouldn't have bothered attempting it, and instead should have focused on getting something from the other questions.

Ah well, there is nothing I can do about this now but hope. (Weirdly Fizz did the exact same thing as me, and we both started with question 4 and worked back to question 1!) From all of my exams so far this has been the nicest\{proof questions}. I was actually quite ashamed of my attempts at the proofs. They were really disjoint and I didn't have the heart to draw a cheeky black square at the end of the dodgy ones. I was just writing information down and "stating" the conclusion without proving it. Do you think they'll notice this? (Actually I nearly got the idea behind one proof, but already had I written too much rubbish down to try and salvage the situation). I like Rings better now, namely because I was able to answer the whole question on them! Another ten minutes would have been great...

The weird thing is that yesterday I was really unsure about this exam, and was feeling disappointed. However after todays earthquake, my attitude towards yesterdays exam has changed. I just hope that I have done enough to not be disappointed.

After reaching home at 5 something, I fell asleep at 6:30pm. My intention now was to wake up at midnight and then revise for Real and Complex analysis after I woke up. So yes, today that is, I have been awake since midnight. It felt strangely serene being awake whilst the world slept. It felt as if everyone was actually awake, but doing their own thing. I revised complex analysis until my head could take no more. I was scared to have weetabix this morning, due to yesterdays "tummy upset", so tea it was. I did have a small nap at 7ish, after which I revised real analysis.

One thing which I am utterly annoyed with is that the proof that I decided not to learn came in the exam. It was an integration proof, and I can probably remember bits of it, but because I hadn't recapped it I didn't do the question. (It was about proving that monotonic functions are Riemann integrable). The rest of the question I could do with my eyes closed (so to speak!) It was just definitions you see, and I felt that at least 10marks were up to grabs for that proof question. Humbug. Because of that I suffered with the other questions.

The exam was in the Armitage centre and I was going with Bella who has previously been there. We ended up turning up to the exam a second before it started--I wasn't too pleased, for the exams started on a horrible note and ended such. Since the exam has been over (5pm) I have been in mild depression. I have been subdued. This comes with my feelings of shame. I did all three real analysis, rather stupidly everyone tells me. The complex analysis questions were "easy peasy", just like last years! I hadn't revised complex to a good enough level to even think about attempting three such questions. (We had to do two questions from both sections and choose the final one).

I don't know why, but once again the exam felt like an example class. I wasn't in exam mode and was relaxed! (Well until I got to the questions that I couldn't do). I feel depressed because I really enjoyed real analysis this year. That and algebraic structures were my favourite modules. I feel like I've let myself down. I can't recall answering a single question fully. All my answers were doodles on some scrap paper. (My writing was really scruffy).

This post was meant to be long, but how long it is I don't know. My anger has once again disappeared, and maybe on Thursday I will share it with you. I could feel the physical tension flowing through me veins, but yep, I was well behaved and controlled myself...

My last exam is on Thursday. Worse than PDEs. Worse than your biggest nightmare, children of all ages, I present you with statistics. What joy.

I feel ashamed because of letting myself down. Someone reassured me that you only need 40% to pass. I then told them my own pass rate and we had a hearty chuckle. But yes, as people keep on saying the second year doesn't contribute that much to the final overall grade. Never would have I entertained the notion of not answering questions in an exam, yet here I am, missing questions left right and centre.

Why do we hold such expectations for ourselves?


Jake said...

I had gotten myself into a confusion over the notation and even now my mind is still prickling about this. If G=, then H= is a subgroup of G. But then the question I need myself to answer is what is a^s.

I wouldn't worry about things like H normally being a subgroup of G because the context will always state what is a subgroup of what etc. and if you are introducing a subgroup yourself, you can always just use a different letter.

a^s (for an integer s) on the other hand refers to the repeated application (extended by associativity) of the group operation to a according to the following rules:

s > 1: s-1 applications (s a's)
s = 1: a
s = 0: identity element
s < 0: (a^|s|)^(-1)

With regards to the Riemann integral, remember that if f is monotonic on [a,b] then it is continuous on [a,b]
Then, assume WLOG
f(a)<= f(b)
then f(a)<= f(x) <= f(b)
so f is bounded and you can use continuity and Riemann's criteria to show that it is Riemann integrable.

The choice of questions is very personal really, I don't think per se that the complex analysis ones were neccesarily easier, it depends on what you know best and feel most comfortable with. e.g. I missed the lectures on the Residue theorem and calculating residues and real integrals etc. so the day before the exam I read up on it and did loads of examples so it was fresh in my mind and those questions came pretty quickly to me so I chose to do three complex analysis ones but if the real analysis was fresher in your mind then the sensible thing was to do three of those questions. The complex analysis ones were risky in a way because more so then the real analysis ones, the latter part of the question often relied heavily on using your answers from the earlier parts (especially the one on integrating functions of the form Q(cos x, sin x) around the unit circle)

Anyway, I am sure you have done better than you think in your exams, I'll even let you know what I get in probability and stats and that will probably make you feel a whole lot better!

Good luck for later!

Beans said...

Hi Jake,

You're right about context. I think I am still not as "abstract" as I would like to be. But hey, got algebraic structures 2 to look forward too!

I had a vague idea of the monotonic question, but because I hadn't looked at it at all, thought best not to risk it! I felt it was worth 10 odd marks, but on the other hand the other question wasn't completed so it wouldn't have mattered.

Had I actually revised more for complex analysis I would probably be saying the same. That's the very reason why I only did two complex ones- I could only answer certain parts of the question!

Lol, I don't think it's about doing good, but about not doing as well as I would have liked. The quote of the day best explains my situation. Not one single paper that I sat, did I fully complete. That's why I am not very happy. Sigh. I don't think the stats paper was that bad! (And I doubt that would make me feel better! :p) I would rather we not be told our results this year... "they got lost due to an administrative fault"?!

No more stats is what is giving me comfort!