Saturday, October 27, 2007

How full is full?

Now when you say to someone that you are full, why do they tend to still offer you some more food or double check? I mean if you had a jug and it was full of water, no one would try putting more water in it because it is obviously full. Maybe it is because people can see the jug, whereas they can only ever dream about the 'fullness' of another's stomach. Don't ask me why I am talking about stomachs (apart from mine rumbling!) but the real 'fullness' I wanted to talk about was my week. This week that is! This week has been ridiculously full. Never in my life have I ever experienced this sensation of 'being full'. It has been 9am-5/6pm for the whole week. Today was the only day that I allowed myself a break from the 9am start, but 10am is not that better.

The question that I am asking myself is how 'well' have I juggled this fullness. The first fullness was my lectures obviously, and studies. I only managed to spend time on real analysis, calculus and algebra this week. Once again pde's, complex analysis and stats have lost out. However, it can clearly be seen that I am actually the real loser! I am still behind in everything, but have come to a decision. For the next week I promise not to look at my analysis stuff ... OK, I don't promise that since I know that I can do no such thing! I will just try to ease of the real analysis sounds much better. (I just need to complete the example sheet and section one of the notes, and then move onto section two which is rather non-trivial.)

What about algebra? Well I can't afford to 'not' spend time on this module, but I think since this story has been quite brilliant to follow, I won't have to spend 'as much' time on it. I sort of skipped half of problem sheet two, which will need finishing and the proofs from sheets one and three too. I have been a big dodo (as per usual): to prove that two sets A and B are equal, we have to show that $A \subseteq B$ and $B\subseteq A$. It is enough to say that I wasn't trying to do such a thing!

Yes, this is my periodic review to see where I am sitting at the moment (apart from the chair). With calculus, if I can do integration and partial differentiation I am half way there. The other half is the more complex Fourier analysis and other coordinate systems. I need to learn the definitions and understand the picture in this module. However, since I have done 1.5 of the problem sheets, I only need to do 1.5 more. (Not as easy as it sounds I am afraid).

With complex analysis I am not sure where I am at. I can do the 'easy stuff', but I am still unable to say the definitions in my own words. This is namely due to the fact that definitions etc in this course are not as rigorous as analysis (well some aren't). Also because some proofs are not given, my understanding is slightly jumpy. However I have a book for that, and should hopefully be able to catch up and reach section 5. I have given myself permission to bang my books against my head, if in future I spend too long pondering over what the lecturer may have wrote on the board. Next time I will stick a question mark next to the section, and ponder over such sections later! You see I have been doing this a lot this year, and it bugs me sometimes. I fell behind in this module due to the OHP (well I need my excuse and that seems perfect). Anyway, all that is required here is for me to understand my notes and be able to do all the problem sheets without problems! (Very unlikely I know...)

All I can say about stats is the amount of hours I have put in is... 5! Ha - you all thought I was going to say zero right? OK, five is nothing to be proud of, since for everyone lecture I should be spending at least one hour of 'private study'. We have definitely had more than five lectures, so someone hasn't been doing what they should!

Finally pde's. I think I might have found another course I dislike as much as stats. Namely because I really don't follow the lectures. I have become used to really writing my own story out whenever I do work, or copy notes. I might have taken this, "Don't start a sentence with 'f: A->B is a function'" thing too seriously, but my notes and solutions have to be such that I can follow them at a later time. No such 'following' exists in my pde notes. We don't even write that many sentences! It's an equation here and another there (both numbered) and then somehow or other we get what we wanted. How very bizarre. I do try to write words everywhere, but this is not a very good story. My friends though feel completely different and like this story. I have honestly tried, but I just can't follow chunks of my own notes. I think they will soon make sense, i.e. the mechanical sense, which is the sad thing. Man I miss DH and DH, or should that have been (DH)^2!

My main reason for disliking certain applied courses is because the lecturers at times, always make a distinction between pure and applied maths. Now someone might say there is a difference and I won't disagree. However, why do people give the impression that applied maths is 'less rigorous' and maybe 'easier' than pure? I mean if I had an award for the most 'authentic' branch of mathematics, I would definitely give it to pure maths. Stats I would never consider! (sorry statisticians), and well applied mathematics doesn't seem to want this award. Reasons such as "this is applied maths" are given for proofs, which shouldn't be the case. A proof is a proof, whether it is stats, pure or applied maths you are talking about. Am I to believe that being an applied mathematician means I can just give sketchy proofs? I seem to be a complaining a lot this year when proofs are not given! That transformation still shocks me, and I bet DC is happy! (Humbug).

I am just picking on the proof thing, but do people do applied maths because they don't like proofs? Mechanics last year was excellent because we were shown what angular momentum is - not told what it is! That is what I want. I want to be shown what the heck pde's do. Funnily enough, the lectures in the first five weeks were meant to be showing us that.

So as you gather, I lot of work has to be put in on my part for that 'showing' to happen, hence the grumbling. I actually welcome my own opportunity to get some pde work done, so hopefully the grumbling will soon decrease. Oh, and it is not my intention to offend any applied mathematician! It is just that it can get a little frustrating when the reason for not doing something, is that this is applied maths.

Is that everything covered? I will summarise my to do list at the end, but now onto 'any other business' i.e. the other degrees of fullness.

I was given some more welcome advice today, "Don't spend too much time on "_ _ _ ". You have your studies too." Clearly I am no longer talking about my studies. I am behind on schedule for this thing, but it may be under control. Although I shouldn't be spending time on this next week, I know a considerable amount of time will be spent doing such a thing. Having said that, my aim should be to try to stop that. Sigh. I guess if ever I needed a time where I was able to exercise self-control it is now. Already I am losing in that department, but the suspense should make this a good game. I need one more name; a template; confirmation and then the flood works... I need the base case to be true, and only then will I be able to try and prove the induction hypothesis. (You know what I mean).

So that is the second degree of fullness, and the most annoying and pleasing one. Annoying because it is a big massive distraction, and pleasing because I am enjoying every minute of it. (But of course I am not enjoying it when I realise how much of a distraction it is, i.e. now!)

And finally, my other two duties. These are not too difficult, but just mean that I have to pencil a few dates in my non-existent diary, and hope to remember them! They fill a small cup of tea, rather than jugs and what not. Can potentially not taste nice, but hopefully I can cope with that. I have just noticed something unfortunate: the word hopefully has been used too many times! I can't think of another word, and can't be bother looking one up, so maybe that tells us something about my current state of mind at the moment. (Although desperate would be a better word).

So how full is full then? I really have no room for anything else, but with the stomach analogy, something always manages to find its way down.

My week has been rather horrible at times. I can put my finger on these times, but I am not sure whether or not they are finite? You see two of these horrible things will be infinitely horrible, and one is finite. The infinitely horrible ones are disjoint.

One is closely connected to a certain bet of some sort. This horribleness is more of a wanting, and the pain associated with it is due to never being able to achieve something. This is a recurring theme, but yesterday I found myself telling someone things I have never told anyone (not in a certain domain). I don't know whether the reason for that is embarrassment, or because I normally tend to accept these things and keep them to myself. Now that is proving difficult, and my acceptance is rebelling. I wanted at least someone to understand my function, and I hope it is understood. The conversation felt natural, and I would probably have never shut up! We talked about lots of things, and one thing that stuck out was how we are sometimes restricted by the actions of others.

This horribleness can potentially disappoint someone, apart from me that is, but there is no chance of anyone not being disappointed. So it is a lose lose situation for me. However, this is when the little 'bet' comes in. If I was to give a probability of such things happening, at the moment it would be zero. Sadly. Six words I hope to be able to here one day are: "For he's a jolly good fellow!" You meet some really cool people in life sometime.

The second infinite horribleness is more of an inevitableness. The difference on this occasion is that I have the power to make it finite. It is a trivial matter indeed, but I have been walking around with a fear hanging on my shoulders. Say that you have an empty jug and a half-full one. If someone was to ask you whether you have filled a jug up, would you be lying if you said no? Technically speaking that is true because you have one that is exactly empty, but ... there lies my problem -we are dealing with technicalities here. An invisibility cloak would be damn useful at time. I think being asked about the water jugs in private might induce a different response, since it is unfair of someone to ask another to respond in public.

And that was me being subtle! The finite horribleness is not really something horrible. It just means that I can't moan about postgraduate students from any example classes here! [nudge nudge wink wink] Not that I have any reason to do so (yet), but you never know about these things!! I am really hating the new building. And I am hating the uniqueness and existence theorems we did in ODEs! I have used them to prove that I am unique, and having pinched myself I deduced that I obviously exist. [This is an entirely different context as you have gathered]. Weirdly, previously it had been global existence and that had been perfect. It is local existence which is a pain in the neck. (But only because of the members not part of Wednesdays community).

The horribleness aside, I think the week was pretty great. Wednesday's lecture was good, Thursdays are always good because of the ultimate lecture i.e. the classic story. And today? Nearly perfect! I even gave a lecturer quite a fright - well it was a harmless 'boo', but in my menacing voice! Muhahah... ahem. Well it was so perfect that I am too tired to write about anything else (much to your relief!) Maybe tomorrow when I try to outline a 'to-do list'. I need me some sleep.

PS: The lecturer only bounced with the function f(x) =sin(pi/x) for a finite amount of time, and so fast that I am sure the bouncing around x=0 wasn't as bad as I am led to believe!