Friday, November 30, 2007

A Song... Against Mathematicians

Four posts in a matter of two days means someone is not doing what they should be! Anyway, this poem/song I found was worthy of posting! (It is somewhat amusing....)

-*-*-

Of all the lunatic professions which are practised on this earth
Mathematics is the craziest, and has been from its birth.
Take a look at its practitioners, examine each in turn,
And watch them going further round the bend as more they learn:
The proud arithmetician, who can contemplate infinities
With crude familiarity, and not see what a sin it is,
(Infinities of such a size, he calls a set equal if
The greatest of their differences is small compared to aleph;)
The negligent dynamicist, Procrustes of equations,
Ignoring any higher power which foils his machinations;
If there is any man with more impiety than him, it
Is the unrepentant analyst, proceeding to the limit.
There is a young geometer, aged 23 mod 40;
His views on art are trivial, his views on life are naughty;
The only scheme of government this student can envisage is
To couple all constituents in independent syzygies.
Ye narrow minded bachelors, whose one joy is to figure!
Were you cut up and randomised, set down in utmost rigour,
Your singularities enclosed in everlasting cedar,
Who would lament your absence? ...

But I leave that to the reader.

D. HANDSCOMB.

Thursday, November 29, 2007

Events before my Wednesday lecture

EDIT: This is a sequence of three posts. This one is about the events that occurred before; the one below this is about events on Wednesday 28th November including the lecture, and the final one is the aftermath of my lecture. I have posted them so that all you have to do is scroll down to read the next one. I think three (very) long uncontrollable posts made more sense that one awfully long one! Don't read them all in one go....

---

"Good afternoon ladies and gentlemen, and .... "

So it began. Yesterday it was The Galois Group's first ever student lectures, which was indeed an exciting and nerve racking time. That has become my favourite word: never racking! Thanks to DC I can also spell it correctly, but that is another story.

As I mentioned previously, yesterday I was up at 4am practicing one could say. I might as well stop this dumb vagueness, for if you read my blog and are at Manchester then you probably know who I am. If you don't come to Manchester and know who I am, then hi! [Just don't go announcing it to the world that I have a blog: my friends don't know!]


Before Wednesday

From day one I knew that I would talk about Galois, and then about The Galois Group, but that was all I knew. One week before Dr. Steele's lecture, a lecturer at the University had emailed me and said that unfortunately he couldn't make it to my lecture; but he had a project about Galois, and if I was interested he was willing to let me borrow it. I excitedly emailed him back, and the very next day found a very interesting project in my hand. The lecturer had discussed with me, how ET Bell and others have fictionalised Galois' life story, and how the project aims to narrate the most accurate version. (This lecturer has yet to teach me, but I first met him in a meeting during week 6). I disguised my ignorance when he gave me the project, for indeed I seemed to have an inaccurate version of Galois' life in my head.

Nevertheless, sticking the project away for later (due to coursework tests) an idea started forming in my head. It was one of them ideas which you allow yourself to carry, because it gives you a small comfort of at least having an idea. The idea was to do with me narrating two versions of Galois' life - one hopefully being an accurate version, and the other not to dissimilar to ET Bell's version. So this idea brewed in my head for a while, and many other mini ideas started expanding from it. During the time of Dr. Steele's lecture, my idea had become concrete and grown some flesh. Now it was just a matter of making it alive.

Indeed, it wasn't until I took my unofficial one week of study leave, that I got to work on my idea. Upon being asked about how my preparations were going, I used to reply with: "I am hoping to make it funny; well the first part anyway. And then the second part will be somewhat more serious." This had people intrigued, but I then panicked for I felt that my idea of funny isn't generally the same as other peoples. I vaguely ran my idea past Dr. Coleman, but first checked whether or not he had watched Shrek! Yes, that was a semi pre-requisite for my talk which was making me slightly worried. I didn't give the whole plot to DC, but he reassured me and told me it would be fine. (Text book phrases I felt at the time...)

I was going to try my idea past PS but he wisely declined, otherwise he would have "been bored throughout"! So it was just me and my idea now. The talk had to last for 20 minutes, and my plan was to make a power point presentation.

Eventually as I got started on the presentation, my idea was moving places and rapidly changing. I kept on chopping and changing things, until I had a spine. (This was for the first half of the talk). I probably over-prepared for this, and consequently spent less time on the serious bit. Twenty minutes didn't seem to be enough as well, because I had too much content. I wanted to talk about everything, and didn't know what to cut out.

Nothing is ever easy in life, and I was faced with many problems relating to the room that the presentation was going to be in. The computer panel was locked and it wouldn't open without a key. This had me very worried and I kept on pestering the computer technicians about this, until finally it was opened. (Thanks guys!) But then the damn sound wouldn't work and so my pestering continued.

Feelings before Wednesday: I was nervous and very very worried. I knew that the second half of my talk was sketchy, but I didn't know how to tweak it successfully. The first half though looked alright, and as did the ending. The inevitable feeling of messing the second account of Galois' life was hanging over my head. When I am stressed, it seems that in the process of releasing this stress, I stress everyone else out! When I do release the stress, I hope that excitement will flow through my blood: giving me courage. My dress rehearsal at home on Tuesday had gone really badly. I had put one of the audience member to sleep! (Noddy zoned out for the second half, which was understandable, and Nuno had put her hand up when I had asked the rhetorical question!) So one could say that I wasn't fully ready for Wednesday.

The "Wednesday" of the lecture

The "Wednesday of the lecture" aka Doomsday

At 8:40am I crawled into the AT building, having only had four hours of sleep and very little breakfast. With me I had some milk for the refreshments, which I went and gave to DC. I was a zombie and DC even enquired about whether I was OK. I didn't say much (surprisingly) and rambled about nerves and lack of sleep. I was advised to take a nap - a nap!! In my zombie state I was also informed that the building was having water problems, but I didn't take much notice of this. I asked DC about the sound problem and was given directions to another person. Apologising before hand for missing the example class, I headed to G209 to practise. Unfortunately there was a lesson there so I went to the next empty class room. I practised for a bit and then followed the directions I had been given about the sound. Annoyingly I was directed elsewhere.

Now this is the weird part. In my weird state of mind, I sat down with my talk in wait of the person I had to see. The next thing you see is that I am down and out for the count! I wouldn't say that I had a nap, but after about 20 minutes my head shot up and I spotted the students in the example class. It was quite bizarre for I looked very startled and didn't know where I was for a minute. Thankfully only one person from the example class had seen me! I have never done that before - well not when I am not at home. (Rbt at the cafe had said he had seen my head flop like a fish, and thought that I had had a rough night!) As I try to recreate the zombie mood, let it be known that I was desperately waiting for my nerves to become excitement. I was waiting for the adrenaline to kick in the way it should.

DC is the staff coordinator of the group by the way (in case you were wondering)! I was mightily relieved when that decision had been made too. Anyway, I really did bug DC a lot on this day. On the way to the lecture I asked him if he could try to speak to the sounds guy, and if he could give me a paragraph about Galois Theory. I was worried that Dr. E would ask me a question to do with that! I was becoming more and more nervous, and another text book phrase was thrown at me - something about being here tomorrow... but I was also told that due to the water not being fixed the building could close DOWN! Rather perversely, relief didn't flood me but I became annoyed at this. I didn't want to go through this again and wanted it over with today!

Everything that could possibly go wrong before hand, was going wrong. The real analysis lecture was cool, but I had my excuse for snoring in it. I did pay attention but there were periods when my heart stopped beating and clenched into a fist: my mind was elsewhere. The same was true for the vector calculus lecture; I just couldn't concentrate.

At 12pm, with an hour to go, I walked back to the AT building talking to Dr. Ha. He was going to attend the lecture at 1:10pm, and we both discussed the art of talking fast! I had to force my lunch down, but tea helped. My mind was everywhere. Everyone was throwing different advice at me; people were telling me to relax! "You have got to be out of your mind," my heart replied. How can I relax, when I am walking to my demise?! The sound was still not working and DC told me that he hadn't spoken to CP. Instead he told to me to speak to Rb, which I did. Rb informed me that sound was not possible and I should have brought my own laptop. Despondently I informed DC of this, and he asked whether it was necessary. I did think it was, and so DC had a brainwave: ask Rb if I could borrow his laptop! The excitement was starting to appear now. After a heated debate: "You ask him." "No you ask him." "But you're staff and he'll listen to you." "It doesn't matter, just ask him and he will let you borrow it." "But...gah."

Yes, I had to ask Rb! But Rb is great and said that I could borrow his laptop. I was overjoyed at this and was to return at 1pm to take it.

Now another piece of advice which I had received was to spend the 20 minutes before the lecture, reading and rehearsing what I was going to say. So after the sound drama, I was back in an empty classroom rehearsing. The second half of the talk was still messed up! I had too much content, and kept on going over time and I became very nervous all of a sudden. (As I am typing this, my heart just clenched; remembering yesterday of course!) Having done my mock rehearsal I decided to accept the fact that it was too late to do anything about the second half. It was going to be messed up, and I had to live with that. The adrenaline was only half there, but 1pm signaled for me to get Rb's laptop.

Rb was in the staff common room, and so once again we have deja vu: "Please can you call Rb for me." "No, just go and remind him about the laptop." "But I can't go to the staff common room." "Just go and remind him - he will have forgotten." "But why can't you go, you are staff and you like walking!" "No, just ask him."

So much for DC being the staff coordinator!

I mustered the guts and managed to call Rb (and come out alive). He was great though, because he came down with me and set everything up in the room. But guess what?!!! PEOPLE WERE ALREADY SAT IN THE ROOM.... waiting. I lost it then and completely went crazy. Asking Rb to quickly press F5 when the power point had loaded, (I didn't want to spoil the first half of the lecture) I ran out of the room. My composure was going. I was panicking. My friends were concerned. I went back to G209 and Rb told me that he would come at 1:50pm to collect the laptop. I woodenly nodded and said I should be finished by then. Lecturers started entering the room and I didn't recognise a few. I couldn't run out again without reason and was relieved when Dr. Coleman entered with the milk! Taking the milk I ran out again, and gave it to Rbt. I can't really explain what I was going through, for it is not something I have ever experienced in my life before. This new feeling was strange and it was that of doom and dread.

Going back inside, all panicky, I noticed that Dr. Walker wasn't there and she was going to do the introductions. Hence I quickly decided to see if I could find her, giving me another excuse to escape the suffocating room. Outside I saw Dr. W walking towards G209. I was crouched against the wall, and my personal tutor had been stood next to me, reassuring me and telling me to go for it. Everyone was telling me that it will be fine and to calm down.

Like a boxer, I prepped myself up and entered the room for the final time to do my first ever lecture for 20 minutes. The audience consisted of lecturers, post grads and undergraduate (shockingly many second year students were present!) I wasn't scared of the audience. I wasn't scared of being in front of everyone. I wasn't even scared when during my introduction I had tried to escape, but couldn't. I was though, terrified that the second half of my lecture was going to be a total mess up. Yes - that was what had me nervous and on edge. Nothing but that and maybe it would have been a good thing if the building had closed and I had another day! Weird isn't it? I didn't mind my lecturers being there that much, but my own stupidity was causing me so much discomfort.

"... and thank you all for coming. Today I will firstly be giving you an account to the life of Galois. Then, rather perversely I will be giving another account to his life. "

So I began. Now I cannot give a recount of my lecture, for I was giving it! However, if anyone wants to write something about it (the way I wrote about Dr. Steele's, then you are most welcome to do so). Members of the audience did laugh which I take to be a good thing!

Because the first half of the lecture was my story, I was able to communicate it better. However, the second half was more factual and so I think I slightly messed the ordering up. As I first spoke, my voice actually shook and I could feel my heart shaking! That is the first time this has happened to me i.e. the shaking. I think in situations like that when you want the adrenaline to kick in, you always worry about there being too much of it. In my case I had an overflow of adrenaline. I think I didn't really put on a professional act, but behaved like "me", which did make me slightly calmer. (Although those who have never met or come across me before, probably thought I had gone mental.)

I am beating around the bush indeed, for my lecture seems like a blur now. A very clear blur, but I don't know what to write about it. During the lecture, the nice and friendly face in the audience had been my PT's. My friends, DC and PS had all sat at the back and to the left so I don't recall making eye contact with them (next time I will ask them to sit near the front!) Whenever I felt that I was looking at one person for too long, I quickly swept the room with a look. There were about 12 lecturers there (which I didn't know at the time!! :/ Unfortunately though, my eyes kept on diverting towards a lecturer at the front who had looked very bored indeed. What made it worse was that when I tried to look elsewhere, the first person I saw was a student on the left who was either yawning or who looked equally bored! This did make me think: "Damn, they are all getting bored." and maybe panic a little, but then my PT saved the day.

The first half went semi-smooth, but in the second half as expected I faced some problems. I realised that I was running out of time and slightly rushed things. And because I was rushing, I forget where I was at and repeated things (I feel). I stupidly didn't have a paper in my hand, and should have done so. At least then I could have been more calm and gone at my own pace, rather than the pace in my head.

When remembering proofs, one tries to learn the tricks so that the rest will follow. When rehearsing my lecture, I had certain key words which would trigger the next part. Some say that having said "an appademic of Cholera", I lost all my senses. Yes, after saying that stupid thing which didn't make sense I stopped before clicking the next slide and looked at the audience. Scratching my chin, I muttered "its not appademic: what's that word? Ah yes - epidemic of cholera!" That had people laughing, which was a relief for that meant the tomatoes stayed in everyones bags. So later when it then came to saying the word abdomen during my lecture, I had looked at my PT and checked with him whether I had said it correctly! (During the morning I had been discussing the pronunciation of the word abdomen with DC, which made me double check with my PT. It would help if I could spell the word!)

So because of this appademic, I forgot the key word that I needed for my conclusion. I skipped it and went to the next bit, only to slap my head in agony after realising this. Everyone was quiet. I stuttered and stumbled..."wait a minute, what is that word.... one minute." Everyone waited, and then bang I remembered it, and concluded my lecture. Not as composed as one would have liked, but I was just grateful for the word coming back to me. The final slide came as a welcome relief. [Apologies to the mathematician Noether, whose name I unfortunately didn't bother to pronounce, in case of mispronunciation. (But my PT told me the correct pronunciation later on so all is well.)]

My intention had been to talk about The Galois Group during my lecture, but after I had finished Galois' second account Dr. W sort of stood up and thanked me. So after this I then talked about The Galois Group. Now that is one thing that I don't need notes to talk about! I unfortunately did forget one more connecting word, but on this occasion it didn't matter. I think due to my excitement of having reached the end, I spoke rather fast during this time. Anyway, I just told everyone that I wanted this interaction between members of the department. I wanted a community to exist, and well, you have heard it all before!

I did try to embarrass DC (subtly, as he had semi-done embarrassed me during Dr. Steele's lecture!) but now DC won't be wasting his money on pesticides anymore. (They don't work I am afraid.) Dr. W told me to write my email address on the board, so that anyone wanting to volunteer for a student lecture could get in touch with me. As I wrote my email address, discussion happened in the audience. Arthur (my friend) narrated a funny discussion between two lecturers who I shall not name! (You can try guessing though).

Lecturer one: Ah, that is nice handwriting on the board.
Lecturer two: Yes, better than some of our colleagues.

Haha, that had me in tears for the obvious implication within that statement, especially since I was told who the lecturers were. (I think the blackboards were rather nice in that room).

And so concluded my first ever lecture, to an audience consisting of class mates, lecturers, friends and people who I didn't know! The twenty minutes flew, but I don't know whether or not I said this, but I have to agree with Dr. Coleman's statement about your first ever lecture being an exciting one indeed. I think the whole process, nerves included makes this so. And it is exciting because you feel eager to do more; well that seems to be the case at the moment!

The aftermath (of Wednesday's lecture)

After the lecture

Straight after my lecture Fizz gave her lecture, and it was very interesting. Like my voice, Fizz's voice had also shook due to nerves, but I am eternally grateful to Fizz for volunteering. It was about Babylonian's number system, and how they worked in base 60. Interestingly, although they never proved Pythagoras's theorem they used it. The Babylonians basically had two symbols, one representing 10 and the other representing 1.

Then she went onto talk about Egyptian maths, and how once again, the Egyptians had developed mathematics due to their needs i.e. is due to their physical surroundings. They even had used Pythagoras's theorem without proving it.

Interestingly, it was the Greeks who first studied maths or deduced maths from axioms. They created some sort of order, and it wasn't the physical surroundings which motivated them to study maths. Fizz was more composed up there than I was, and did a fantastic job. Having been up there, you can't help but appreciate and commend everyone else who does that. Especially if they are there because of you! During my lecture she had been sitting like a bag full of nerves, but thankfully apart from one moment of recollection I hadn't been in the same position as her. (That is why sometimes it is useful to go first!)

Fizz did finish slightly before time, so maybe I shouldn't have panicked about going over time! (I had gone over by 5 or so minutes). Having both completed our lectures, I thought that was the end of it and felt the refreshments calling. (Actually that is a lie: I was too excited too eat anything, and during the day had also forced my sandwich down). Before we all rushed out though, Dr. W said: "Any questions... to both of the speakers!"

Damn! You see there hadn't been a chance to ask me questions, and I thought that I had escaped! I was actually worried that Dr. E would ask me something non-trivial, for the day before my lecture he had asked me how old Galois had been when he had died. It was a trick question you see! Many people think that Galois died when he was 21, because the year he died was 1832 (and he was born in 1811 on the 25th October). However, he died on the 31st May - a few months before his birthday - so he was still 20.

Thankfully Dr. E didn't ask me any such question, but I can't remember whether I was asked two or three questions! A lecturer who I didn't know before then asked me a question, about whether what Galois discovered could have been discovered by others and Jake asked me a question. However, I seem to have someone in between them asking about his life and circumstances?! (I think I'm going mad!) I believe others could have made them discoveries, but it would have been after a very long time. I am of the opinion that sometimes, you need individuals like Galois to spark something new. [I discussed this with PS on Thursday, and how when it comes to art and music (say), no one else can create what was created. However, with maths it is there to be discovered!]

To make a good read a think a some misleading has to be done by authors. I myself had been taken back by Simon Singh's account on Galois' life, but the extent to which Bell and friends have done this is silly!

Dr. E though, did make a remark to Fizz about the doubling of numbers and nurses after which Dr. W brought an end to the proceedings. Fizz and myself were slightly shocked and relieved at the same time, that we had survived this ordeal. People were saying things which didn't register at first. I just found myself nodding and saying thanks at first - I still can't remember who I spoke to directly afterwards.

As I eventually left the room, Simon appeared from no where and gave "The Key" to Dr. Coleman; but since he was doing the open day interviews straight after the lecture, I took the key to give it to Dr. W. I stood for a moment with DC, and Prof. Sp happened to be there too. Prof. Sp hadn't attended the lecture and I pointed out to him that this was inexcusable. He agreed (naturally) and so I made the bold remark that I will not attend his lectures next time! Prof. Ply (who had asked me the question) was there too, and it was after a few seconds that all three lecturers came to the same conclusion: "They won't have to sit an exam for my lecture!" We shall soon see about that.... I thought as they all laughed away.

It seems as DC said, I had passed my stress to everyone else before I had given the lecture, but I for one do not believe that DC was stressed! He can't have been... but I better check just in case. (Let us hope I am wrong!) That is why everyone else was probably mightily relieved that I had come out in one piece. My first instinct straight after was to ask for feedback, but I can't remember exactly what people said at the time. There was no time for a proper conversation with DC about the lecture (open day calls) so I hurried with the key to Dr. W. It was here that I became very happy. People were talking to each other and no one was eating the jaffa cakes! [Note to self: next time we won't make "as much" coffee. It seems, as my learned coffee drinking friends informed me, you can't really drink coffee at any instance but the right one. However, tea can be drank whenever one feels like it, even though one isn't really in the mood for it!]

Initially I happened to be talking to Dr. E about Bell's book Men of Mathematics. He was shocked to hear that I hadn't read it(!) and I had torn it apart during my lecture. (It feels cool it in a weird way saying that. :D) This was actually quite a funny moment, for we then went onto discuss Bell's other maths books. (I think he had to recover from the shock when he learnt that I hadn't read that book.) Dr. E then dissappeared for and I went everywhere for some time. I sat with PS for a while to get feedback, and everyone seemed to be telling me that I hadn't done as badly as I feared. PS said that he did notice when I had made an effort to slow down, but he said it was my first ever lecture. Unable to sit down for too long I was back where the refreshments were. (note I only had some tea and a jaffa cake myself). Due to the jaffa cakes still shockingly being there, I decided to give some to PS, DC and Prof. Sp (even though he hadn't attended!)

The atmosphere was electric at this moment(in my opinion), and then finally I happened to bump into my PT. [He drank tea as well!] I thanked him for being the friendly face in the audience, and he said well done. {This is rather a waffly part of the post, for it is merely about me writing about every little thing that happened; but such was the nature of the day that I can't not do this. }

My PT gave me feedback and told me that considering it was my first time doing such a thing, it was "cool". (That's my word though!) I didn't believe it when people were saying this, because I kept on thinking about the mess ups. My PT however, told me that he had liked the way I had done the first half, and that we all have moments when we forget things. We talked for quite a while, until Dr. E returned from out of the blue. With him he had a book. The book was called Men of Mathematics! I was once again in stitches, but felt it was very kind of him to lend me his own copy of the book. He felt that I had to read it and told me to look after it because he doesn't normally lend books to students. (He gave us a rather amusing story about an instance when he had done such a thing!) What can I say: I am honoured. I made no promises of looking after the book though... (It is on my shelf at the moment, waiting to be read sometime or other).

Another lecturer happened to walk past at that time, with copies of a newspaper which had something about maths magic in them. He was giving them to the lecturers, but he also gave one to Fizz and myself because of our lectures. (He had been in the audience) Once again I thought "cool" to myself. There you have it students: there is no need to fear your lecturers. They are actually very supportive and cool, but it all depends on your attitude. Another member of staff JB, who I also never knew, spoke to me as well. Well there was a group of us and we discussed the likes of Hilbert and Galois and about how he couldn't attend the lecture. Due to this lecture, I now know some more lecturers and a few first year students. But more importantly that community is ripening.

In the end of the day, we need student undergraduate volunteers. So yes, I was rather pleased when two people volunteered, and when a first year said to put him down as a question mark! Sadly there were no third or fourth years at the lectures, but hopefully they will attend the next ones and volunteer. Because I am a second year and second year students probably know me, the volunteers so far have been second year students. (I need three more undergraduate volunteers: so if any are reading this, then please do get in touch.)

Slowly everyone started leaving and it was just us with the refreshments, and no Key. (The Key episode I will refrain from mentioning, but in future I will try to "not touch" the Key.) Cleaning up brought a sense of completeness to things. I think I will summarise the feedback I got and what I learned from the lecture in another post. (Out of sheer kindness of course). The end also signals the beginning. The next batch of posters have to be made, printed, stuck around everywhere, and so it continues. It is very exhausting actually, and I am fearing for my studies.

They say red bull gives you wings. I say do a maths lecture and you will be left wondering about what the heck red bull is. Oh, and this is another one of them instances when I say something about something which I haven't tried or read! DC gave me more feedback when I went to store everything, but as I said I will leave that to another post.

The event I shall naively put down as a success. I was surprised at the attendance (especially 12 lecturers being there!) but I hope that it continues like this. Most importantly I am still alive -- hurrah! Thanks to all those who attended, and those who gave feedback. Is there anything I have forgotten to mention? ;)

Wednesday, November 28, 2007

Maths holiday over.

Ladies and gentlemen; children of all ages, I present you the most foolish and stupid bean of all time,

Thursday, November 22, 2007

Hating Cauchy by association

This has happened once before in college: the culprit then being Euler. I used to hate his method or formula to solve differential equations (namely because I probably didn't understand it). I also had a hard time getting to grips with complex numbers and his name had popped up there as well. The perfect scene for this hating to begin.

However, last year I made my peace with Euler after reading more about his life. I forgave him for his formula, and let bygones be bygones.

Now it's Cauchy's turn. "Cauchy's estimation lemma", "Cauchy's integral formula", his theorem for a star domain, triangular domain and million more! His name even popped up in real analysis on Thursday, (after Rolle's theorem) giving me quite a shock indeed.

Today the lecturer even semi-apologised for this (and appeared exasperated by having to write Cauchy's name everywhere). Actually that might have just been my imagination...

I don't want to hate the guy! I don't even know him. I mean, he sounds like a cool character, but his theorems are giving me a head ache.

I read somewhere that he fled France around the time King Charles did. Why did he leave? How many mathematicians work has he .... STOLEN so that he was forced to flee? (Don't shoot the messenger, but ... fine I am just bitter and want to make a villain out of him*). I mean I wouldn't mind writing

Wednesday, November 21, 2007

What Complex proof?

You may or may not recall the proof which I posted about some time ago. It was for a theorem from Complex Analysis, but naturally it holds in real analysis as well. I had been trying to prove the theorem by contradiction (i.e. me being perverse) but this had led me to a problem, of which I may have a solution (but need to write it up).

However, as I don't like to leave shoe laces untied (NOTE: If you know me then please don't say that I walk around with mine untied!) OK fine, I will correct myself and say that on this occasion I feel it neccessary to tie the laces! (In my defense it can annoying having to bend down and tie your shoe laces every other minute...)

So now I will provide a conventional proof for the theorem. This theorem was presented to us in real analysis and a rather long and dodgy proof was given for it. I say dodgy because we had to choose epsilon as one and then play around. I had asked DC whether or not the nice and short proof that I will write, was also correct. It was and hence in yesterdays lecture he gave that to us too.

Alas, once again due to my perverse nature (I am liking that word more and more!) I will not be posting the proof in the normal way in this post. That is I am going to let you do the LaTeXing!

For those without TeXnic centre, winedt or any other editor, just copy past everything in between the dashed lines into this link and then click submit. (Trust me, you wouldn't NOT want to do this! There might be a mistake lurking...) Having done that a document should appear with the nice proof.

Unfortunately due to my not using LaTeX for quite some time (darn these coursework tests), I seem to have made a mess of a few things. I don't really have that much of an understanding of my preamble anymore, but I can claim to once having a slight idea. Leave nothing unquestioned (apart from the black square at the end)!

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\documentclass[titlepage, a4paper]{article}
\oddsidemargin=0in
\usepackage{fancyhdr}
\usepackage{amssymb}
\usepackage{upquote}
\usepackage{amsmath}
\usepackage[top=3.5cm,bottom=2.7cm,text={6.5in,9in},centering]{geometry} %can change lengths to suit own needs
\usepackage[pdftex]{graphicx}
\pagestyle{fancy}
\rhead{Your name}
\lhead{document details}
\cfoot{\thepage} % page number?
\parindent=0in %when we press enter for a new paragraph we don't have to write \ noindent.
\date{}
\begin{document}


\textbf{Theorem}\\
If $f$ is differentiable at $a\in \mathbb{R}$ then $f $is continuous at $a$.\\

\textbf{Proof}\\
Consider $$f(x) - f(a) = \frac{f(x)-f(a)}{x-a} \times (x-a) \quad a \neq 0.$$

Let $x\to a$ so,

$$ \begin{array}{cc}\displaystyle \lim_{x \to a} \frac{f(x)-f(a)}{x-a} = f'(a) & \text{ which exists by our assumption and}\\*[2ex]
\lim_{x \to a} (x-a) =0.&
\end{array}$$\\

Since both limits exist we can use the product rule for limits to say that,

$$ \begin{array}{ccc}\displaystyle \lim_{x \to a} \left ( \frac{f(x) - f(a)}{x-a} (x-a) \right ) & = & \displaystyle \lim_{x \to a}\frac{f(x)-f(a)}{x-a} \times \lim_{x \to a} (x-a) \\*[2ex]
&=& f'(a) \times 0\\*[2ex]
&=& 0\\
\end{array}.\\ $$

Hence $ \displaystyle \lim_{x \to a} (f(x) - f(a)) =0$ i.e. $ \displaystyle \lim_{x \to a} f(x) = f(a)$.\\

Thus $f$ is continuous at $x=a$ as required. \\
\flushright{$\blacksquare$ }
\end{document}
-------------------------------------------------------------------------------------------------

Wow - that took ages.

Now I must retire to my misery, for silly Mac has made me feel this way. And the premiership is meant to be one of the best leagues in the world... I need to start writing my speech as well, but maybe another day!

PS: I will be posting the proof with LaTeX on my blog if you haven't managed to see it (or couldn't be bothered). And what say you if I was England's manager?

Tension and being late

I feel really tense at the moment, and my heart is clenched like a fist. Why, I don't know? I have to be somewhere at 1pm, and then rush away to get somewhere else for 2pm. I will be late obviously, but I have notified the people concerned.

Today I felt a sense of gratitude towards Bella. Another thing which I just can't explain. But I wanted it to be noted, and I am still feeling this.

I don't like being late for lectures; I just hate it. The weird thing is that for exams I try to be exactly on time, because then I know my seat is my seat. For lectures that is not the case. However, these past few days I have been at least five minutes late on more than one occasion. (Today included). I am talking about the first lecture of the day of course, and there is a solution to this; well two solutions.

(1) I go to sleep on time, so I wake up on time. Hence I get to have my breakfast and get to my lectures on time.
(2) Go to sleep at the time I have been doing so, wake up late-ish; skip breakfast and get to lectures on time.

I have been doing number 2 at the moment, but trying to squeeze in breakfast! (Hence the lateness.)

Sigh. I have an annoyed appearance today. But do talk to me, for I not fully annoyed. It is just that my internal processes are sensing a problem which isn't being communicated to my brain.

I have just gone and double booked for next Wednesday. That is what is causing my heart to tense up. It is nothing extreme, but it has put another load of stress on my head. I couldn't decline: my school got in touch with me and they want me to talk for five minutes about my experiences there, on presentation evening!!! That is indeed nerve wrecking, and I was stupid enough to say yes. (Actually Bob convinced me to say yes.)

However, I think we only ever say no if we are 100% sure of meaning it. If we say yes with some reluctance, then that means that somewhere some part of us wanted to say yes. My problem is that I can't ignore this small part, so end up saying yes. Unlike some people I know who can push the minute yes to the dungeons, I can't. I have no idea about what to say and then I have a brief idea! It is only five minutes though... but still my heart is becoming nervous already. I have a week to prepare for that and other things: if I vanish from the face of Blogistan, you will know what killed me. \hyperbole

Whoopie it's 12:52 best get a move on now.

Tuesday, November 20, 2007

A disjoint post

I don't really know what to blog about today, so maybe I shouldn't write anything? Alternatively I could write something short and (obviously!) amusing, just to pass time and for the sake of it. Well I am already writing, so why stop now?

I am going to become a Charles Dodgson (Google him) soon; well I am in discussion with someone about this, and I will have to pull "the usual face" to achieve this. The chances of success are low, but it is the minor chance that exists which I will be playing on.

Today was meant to be a day of hard work. Today wasn't a hard day of work though.

One thing I learnt though is that I HATE manipulating inequalities! Honestly, I have a stinker of a time with them. The inverse function theorem was presented last week sometime, and the proof was given too. (A deliciously long proof as well... and yes PS is my inspiration in describing proofs, lemmas etc in exotic ways. :D ) However, the last part of the proof had some deltas, a gamma and an inequality. After the lecture I had spoken to DC and in the short time he had then, he had told me something about flipping the inequalities as the signs changed. I knew that but didn't know what that had to do with my notes. Yesterday night, as I worked through the proof I came stuck or couldn't make sense of two things. One was some implications, but I wasn't seeing what we had done. (We had taken two bits of information and they had led to a contradiction).

Anyway, today I finally resolved the issue I had with them particular inequalities. I think DC was exasperated at my failure to understand this; but then again I was equally getting vexed out by my mind block. He said something and I said something else, and then nothing made sense. Finally he took the pencil and wrote a few lines: "Assume...." "Consider...." and "Use the fact that.,,," . Then bham all of a sudden I saw what he had done in the notes! This was a revelation. The delight I experienced was immense, but I think my questions tired DC out today. :p I think the word consider made the biggest difference, but still I can't stop disliking inequalities. Due to my "fear" of them, I hate it when DC drops things "just like that" by making something bigger. I know it is correct, but then I have to stubbornly and annoyingly try to see if I can do things without "just dropping" things. (Which is indeed difficult in proofs when you want to find an x >X).

I really enjoyed today's Real analysis lecture: the theorems and their proofs were ..... (I am still an amateur at using PS method for labeling cool theorems and proof - although I found the "stupid theorem" funny). Anyway, it was a rather pleasant lecture and I followed all but one thing. You know that feeling you get when you are relaxing and everything seems so peaceful? Not a feeling which I would normally associate with a maths lecture, but a sweet melody was playing in the back ground of this lecture. (Does that sound better?)

The vector calculus lecture too, was cool today. I think, due to my nature, I prefer lectures in second or third gear, rather than reverse or first gear. (What's a fourth gear? ;) ) But then again that depends on how comfortable I am on the course material and a million other things. In stats I liked the first ever lecture because it was on a board, and nicely paced (now due to the OHP I will have to reserve judgement until I get my test result). I don't like PDE lectures because there are too many intervals for me to "zone out". They are fun as always, but we never seem to get very far. How can a maths lecture only fill one page of notes at times? The minimum has to be two pages, and the maximum an infinite amount!

I didn't plan this post, hence the randomness. Tomorrow I am going to be very busy. I hate saying that, and then sometimes I don't mind saying it. I think being busy is not a bad thing, but being busy doing the right things is what we should aim for. Today was my day to study Algebra... well I guess my conversation with Jake can fulfill that requirement, but I seem to be spending too much time on real analysis. I am running out of adjectives, but that module is invigorating!

Today as I queued for my tea (which I didn't have to order due to my understanding with Will (fake name)) I was startled to see my vector calculus lecturer behind me. No... I wasn't talking badly about any of his lectures. ;) I was even more startled to see that he too was drinking tea! Upon my query, I was brought back to sad reality as I learnt that he drinks coffee for breakfast and after meals, but tea at this time. Well at least he does drink tea so that is a positive. He doesn't have any sugar, but as I said: he drinks tea though! (We discussed green top and blue top milk, and I was told that sugar and blue top milk isn't that good for you. I don't know how people can drink tea or coffee without sugar. I know two spoons of sugar isn't technically good, but 1.75 spoons is just not the same!

I best shut up now and get back to my \sout{real analysis} work. I wasn't really going to do Real Analysis, because as Po says I am saturated with that at the moment. (Read I need to just check a few things with DC and see whether my perverse train of thought is right for once!)

This blog needs a thank you from me as well. Well it has helped improved my English on this occasion! Today as Fizz, Bella and myself conversed and ate, we talked about doing maths because of not liking English. I don't deny hating English for a finite amount of time (Year 1 - Year 9), and my favourite line used to be, "In maths you can always check whether or not your answer is correct, and it is more systematic". Naive words indeed, but "with English it all seems rather vague and free flowing", not something I liked. I actually hated comprehension and the grammar rules (which probably explains why I have to Google certain things now), however I loved the creative writing aspect of things. That was very free flowing, but I was in charge of where I took that flow.

Year 10, due a brilliant teacher taking charge of the ship, my attitude to English transformed completely and so did my work I think. (Also the teacher I had at the end of year 9 was very encouraging too). Fizz really hates English and as we both wrote paragraphs, Bella the genius threw some nice words at us. I find myself not hating it anymore and actually defending it! we had a good conversation indeed, thankfully not only about the English language.

Benefits of a blog updated: interact with cool* people; learn new things; improve English; get inspiration to do certain things and maybe improve my maths! Any others you might want to add? [Didn't I say I was going?]

Actually it was 63 people!

I had forgot to include the speaker, in my previous total of the number of people at the lecture on Wednesday! Without him there, I think it is safe to say that there would have been zero people in attendance.

The sixty third person is my PT of course! I went to see him today to get my complex analysis result and we talked about the lecture. However, the unfortunate thing is that my PT came a bit late (due to him having a lecture just before) and upon entering the room saw the people stood near the door. He thought it was a full house and didn't stay for long, but what matters is that he stayed for some interval (no matter how small it is!) From my friends I am the only one who really talks to my PT (as I do with most of my other lecturers!) Milo had been with me, and I think he was getting impatient as we had talked about the lecture.

Todays stats lecture was lost on me. I am trying to make a link with college work, but I can't write and listen at the same time. If I try to listen first, then I never get a chance to write since there isn't sufficient time. I am having a complain about this because I want to stay on track. I have been devising a mini-plan for my recovery, for it is indeed painful tossing and turning in bed thinking about next week and anything but my studies! Fizz said that you tend to think about what's more important to you before going to sleep: next week is very important to me. Ah well, I have to find that balance between excitement, nerves and appearing like a dodo. It is the last one which is causing me more sleepless nights if truth be told.

Topic change! I sort of embarrassed myself today. It is just that sometimes one feels that no one can be bothered reading ones long posts, and hence no one reads them. Other time one doesn't know who reads what!

Today I had a slowish day, which picked up pace. I sort of learnt that applied mathematicians like writing du/0, something which "I can't do". (I say that in quotes, for in a lecture DC said "But I can't divide by zero." in a way that that said maybe someone else could!)

Algebraic structures was fun today, apart from the two erm.... *not nice people* (insert appropriate phrase which you find necessary!) who would NOT shut their mouth. I huffed and I puffed and then carried on copying of the board. Dr. Coleman got a cheer in todays lecture as well (as he always cleans the boards when his lectures are over) and PS also remarked about the "physics" left on the board!! (His exacts words were more amusing.) Strangely enough the stuff that we did with DC last year is prickling in my brain, but I am glad that someone else shouted that (a,n)=1 was what was required, for I was going to say (a,b)=1. [Also another thanks if you are reading(!), because I had misinterpreted unit for the identity, and nearly said zero when asked for the unit in Z!] ;)

I enjoyed the lecture because it brought things we have done before together. Like C* and R*, and also Z*, so you could say that a rather lame sense of achievement was present. (On Friday we had a test an hour after PS's lecture, and unsurprisingly only a few people were absent. On the other hand, the PDE lecture had much less people attending.)

Before I head to sleep I have a question. If examples classes are voluntary to attend, then why do you bother coming if all you are going to do is talk? (Especially the classes where the lecturer does things on the board). Maybe this is what is known as a rhetorical question?

Being positive is killing me, so I am going back to being realistic. I don't know what to focus my energy and efforts on? Next week or my studies? I am being pulled towards my studies, but maybe on this one occasion I shouldn't be. Another "ah well" and good night!

Saturday, November 17, 2007

PEACE!

Is that too much to ask for? After having a very hectic and busy week, I thought that the weekend would be a nice time to relax and reorganise myself. No such thing can happen it seems, for whenever I want to do nothing, everyone wants me to do something!

I have to a small degree tidied my room, i.e. put all my last year files and books away, and all loose paper has gone into one big pile! I am now in the process of trying to order my notes for this year, since due to the coursework tests my numbering system has got messed up. This is indeed a tedious task, but it is telling me that I have misplaced some notes! Hopefully I will find them in some plastic wallet or other, but if not then I will not be very pleased.

This morning I woke up when everyone was probably having their lunch! I didn't wake up feeling great and what not, but just very slow. Unfortunately my slowness could only last for a few minutes, and soon everyone was shouting different things for me to do. I am not sure how many of these things actually registered, but nevertheless my weekend has not been calm and how I wanted it to be.

My cousins son (Power Ranger) has bacteria in his blood. Well one of them has, and he has become really sick. He went to the hospital yesterday and so his two younger brothers came to stay with us for some time. The baby one stayed the night here, whereas the other one didn't. Power ranger, as I will now call him, is only in reception at the moment so that makes him fourish I reckon. Here's hoping he gets better soon! (He has some weird rash thing on his neck, but the poor kid looked really depressed.) It can be quite exhausting entertaining little kids at times, especially power ranger 2! The thing with children is, if they find you doing something that makes them laugh, they want you to do it infinitely many times. How long can one balance a bottle on their head for, and watch it fall?! The baby power ranger is a funny guy. He laughs at whatever you are saying, which can be very encouraging. :D Another cool thing about babies is that you can have a whole conversation with them, and you tell them every little detail. I was telling baby power ranger about Wednesday's lecture, and he showed more interest than other people. (OK that maybe makes me sound like a loony, but we got a picture of him laughing in his sleep (thinking about what I had just told him obviously!))

That is enough baby talk for a while. I have been taking my stress out on various things today, but at least now England have a chance to qualify! My weekend plans have gone down the drain, but one thing I will be doing is reading the links that KTC posted. The website is related to something else I am working on, and needs updating. I invited one of my school friends to the lecture on week 10, but she got worried and said that everyone will know she's not a mathematician! I quickly told her that they are open to everyone, and she said she will think about it. Last year I had invited her to PS linear algebra lecture. She even made it to the lecture theatre and sat with us. However, unfortunately when the lecture was about to start she ran like the wind. That was a shame for she didn't get to see PS in action.

I am talking about random things now, because having calmed down slightly I am chickening out of posting the two posts I have in mind. (Maybe after my website gives me a few problem I will be back posting!)

A third year student I spoke to the other day, gave me some advice. Well not really advice, but he discussed his experiences. I had asked him whether or not he would consider studying more maths once he's graduated. He replied, "Heck no - I am sick to death with this studying, and so will you be." At that moment in time I disagreed and mentioned my desire to study. He said that the amount of modules you do and the studying required is too much. Once again I disagreed because I feel some of my modules are fun. The weird thing is that I am sick of it at this moment in time. I don't know what is wrong with me. I can't shrug this feeling of my shoulders! Don't get me wrong, I still love the maths and find it cool, but what is wrong with me then?

I think it might be because of the stats and PDE modules, and maybe these coursework tests. Which in itself brings me further to the root of the problem: I have fallen behind badly. I know I should be catching up, but that is what I can't be bothered doing. Am I just having a lazy moment? This feeling has thrown me off track. I am only really enjoying two modules at the moment, real analysis and algebra. Complex may be potentially cool, but it vexes me out. I am yet to see the beauty of it, and frankly can't care less that you do things in complex analysis which can't be done in real analysis. I know which I would prefer studying any day!

Sigh. This is why being a motivated and inspired learner is not good. The Tweenies are the complete opposite from me and can put their head down and get on with things. That is what I need to do now, but I just can't find that desperate final third to do so. I am sick of exams. If PS was to ask us whether we would prefer assessment 100% by exams, I would love to reply no to both options and say yes to no exams. I know this is just wishful thinking, but ...

OK, I will shut up now. Maybe this week will be much better, maybe not. The rubbish line I said to my friend was, "I can be bothered with all this anymore." What do I need to do to change that attitude I wonder!

Friday, November 16, 2007

Fail to prepare, prepare to fail.

My (year 10) maths teacher's words came back to haunt me this morning. I was in quite a bad state at 7am, having failed miserably at answering any of the questions on certain stats problem sheets whilst revising. I had already had my second breakfast too, which thankfully didn't result in any toast being destroyed. My problem with PDEs had gone from "OK I can find eigenvalues, but no I don't understand the superposition concept and what Fourier series are doing here." to "THIS IS BORING". I was sick of writing, "Consider mu=0 then blah blah trivial solution. Then consider m is more than zero etc etc." Due to this I thought that I would do the final, and most important (one could say) problem sheet straight after algebra.

Where am I going with this? Well I have been awake since 3am and it is now 8:17pm. I do not have the brain power or the courage to calculate how many hours that is, but I am conking out. Do I dare use that as an excuse? I think not, for on this occasion it is my fault that I left my revision in such a disastrous situation. Anyway, just so you know I am not with it today.

In the end I actually had three breakfasts. The third when everyone else was eating, and when asked, I didn't dare mention the time that I had woken up! (No one bats an eye lid anymore, but still 3am would raise a few eyebrows). My third breakfast made me somewhat calmer and I slowly packed my stuff into my bag, ready to head into university for a 10am lecture. I wasn't feel nervous any longer, but knew what I had to do in the time I had remaining. My bag was unfortunately extra heavy today, so I had to leave most of my lunch at home. The idea was to drop my heavy load into the "store room" before my lectures, so then I wouldn't be dragging it around with me for the whole day. That didn't happen because the store room keeper wasn't in at 9:53am!

I was in the AT building at that time and guess who I bumped into today! I will give you a clue... he's another blogger. It was actually quite a different experience, but I pulled the cool calm look I hope. (Actually I jest, I was so frightened and cold that my tears actually froze...) You decide when I am jesting, but I think I spoke extra fast but this was the first time I guess. It is slightly weird meeting people who might your blog for one or two reasons. Indeed they already have an 'impression' of you and so technically speaking meeting in person isn't like meeting for the first time (although it is different). Also, depending on what you blog about they already know a lot about you. I have now spoken to at least 5 people about this blog and they all know who I am (which isn't too hard to figure I suppose!) The 5 people have read my blog at least once, but I honestly don't feel weird talking to them about it: they're proper mathematicians! (It is the other mathematicians that you have to be wary of). ;)

One thing I need to do: fix the time on my damn phone. I don't wear a watch for personal reasons (that's just my cool way of saying I don't wear one), and always use my phone. Yesterday, as I had been drinking tea and having my lunch I was sure that I saw PS making his way to the example class. Surely enough many other second year students were exiting the AT building. I was bewildered and upon checking my phone I carried on eating. I can get to the building in 5 minutes on a good day, so wasn't really concerned about being late. Anyway, finishing my sandwich I got ready to leave (with about 8 minutes to get there according to my phone). On my way there I bumped into Prof. D and as always I couldn't resist having a chat with him (he's cool). We talked about yesterday's lecture, and I was quite pleased to remind Prof. D that he was going to be away on a conference in week 10. After some time I remembered the example class so said bye to Prof D. and hurried on my way. (Did I mention that he's cool - I just remembered something funny he said about an American president with surname Ford last year. Something about him not being able to chew and walk at the same time?)

I still had two minutes to get there and I marched to my destination as quickly as I could. Upon entering the lecture room I was appalled to see that it was about 2:06pm! I was late! The same happened today as I walked to the PDE lecture (seriously contemplating whether or not to miss my first lecture this semester to revise for stats. In the end I thought a stats test was not worth missing a lecture for, but had it been a real analysis test who knows!) I confess to having the stats example sheets on my lap, but I was just trying to jot down formulas that I had learnt. I could not do the questions! The PDE lecture was... ask me another day (I followed what was being said, but the same thing has been said for the past few lectures, just variating by a small degree). So although I was doing stats at the same time, I wasn't a complete lost case.

Now onto the stats test. It didn't go bad and it didn't go great, but I am 100% sure that I answered one question correctly! (It was about a false statement, and I had identified three correct ones.) This test was multiple choice but with no negative marking. That made me feel more at ease and unafraid of "guessing". The question said a pdf f(x) = {2 for such a such values, and Y = e^X. Find its cdf.

The cdf was log X which was one of the possibilities. However it had no conditions etc on it and I chose that option - the wrong one! I had stupidly thought that if it is written with a curly bracket { and lots of conditions here, then it is a pdf, so not a cdf. I know I am pretty thick when it comes to stats; unnaturally thick I would say.

I arrived for the test just on time because I had wanted to ask the PDE lecturer a question before hand. He encouraged me to not be late, but I dismissed his concerns. I had to confess to him that I have already changed my mind about the evilness of stats and pdes. Stats is now infinitely worse, and I will tell you why. With stats you can work hard at it and learn all the definitions etc. and you might even want to visualise concepts and understand the theory. You can also do the same for PDEs; basically you can read the notes and try to tell your own story from them. With stats the story will never be complete (in my case).

You have to be clever to be able to completely understand stats, and I will now try not to say "Eugh - stats!" to any statisticians (no promises though!) I am not saying complex, real analysis, algebra, pdes etc are "easy". They are own difficult in there own right, but after a certain amount of time they will hopefully make sense. If you persevere in telling your own story, you will tell it one day. No such thing exists for stats apart from the special or "chosen ones" (i.e. Fizz and Bella). You have to have a certain type of brain for stats and I don't have it. This brain allows you to manipulate and understand the rubbish that has been given to you.

I understand the definitions and can reproduce them, but do I really understand them? Will I be able to explain them to you? Never. One reason for this could be that my stats education has been scarred from day one, and the second obvious reason being that my brain will never properly understand it due to its make up. Why am I going into this? I read the stats question and my brain said conditional expectation. I knew the result that was required but that was all. Sigh. I am hoping to have got at least 40%, even though in an ideal world I get more. Ha. I am not happy with stats, I find it pointless and meaningless and a waste of my time. Harsh words I know, and apologies to any statisticians (inc. my lecturer), but my inability to understand it has drove me this far. Do you think that one day "I will see" stats? I shudder to think about that day.

When I was revising PDEs and doing the questions, they were more systematic. In the exam I wrote a rather beautiful story out if I may say so myself! Once again, because of my stubbornness to write sentences everywhere I rushed through the last fifteen minutes. We will be getting the papers back which made me feel happy. Indeed it will be funny if spelling mistakes and grammar is corrected too, and even funnier if the maths is seen to be OK. Ideally that is, for I did make at least four silly mistakes and didn't check my work. The person who was sat next to me made my life uncomfortable to some degree, and in the end I wished that I had folded my details. (He was spending far too long looking at them, or maybe I am being suspicious because of the unease in the test?) I hated the seating arrangements for there were no gaps, and I have a natural habit of spreading out when doing maths. It was a very restrictive setting for someone like me.

The test went OK and I even wrote the thing about eigenfunctions which I had mentioned in the morning. Please someone don't tell me that was wrong? I think I may have written too much, for I could have gone from the ODE: X''=u^2X to the general solution, without mentioning the characteristic equation (i.e. m^2=u^2 iff m = \pm u). I just feel a need to write down everything I am doing (unlike Galois - which is why I am the bozo ;) ).

I forgot to mention the algebra lecture in the middle, and strangely I was awake all throughout it. I was slow when it came to copying stuff from the board, but that was for some non-trivial reason (I was wanting to see whether I could squeeze the proof on that side of the sheet!) I think the good thing about the lecture was that it wasn't a heavy one, but a light one so not too hard to digest. I didn't write the warning at the end, but it was something about not confusing the integer n for something. By the way, which do you prefer Groups or Rings? PS made the lecture entertaining as usual, and he said something which I can't write in quite the way it was said. Groups have one binary operation and rings two. It was to do with the number of wives corresponding to a binary operation ... :D

The answer 'neither' is not allowed, so I will have to be a chicken and choose groups. They seem easier! I was going to say neither because sadly I have fallen very behind in this module and need to get on track. I am lost about generators, but something about 1 being the generator for R is springing to mind?? My ignorance is really due to not spending time on the course, which should no longer happen now for there are no more coursework tests remaining!! Just got the dreaded results to look forward to. I actually cheated this week and went to the algebra example class, without having done the problem sheet beforehand! That being said, I found it did help me understand a few things but the "damn, I wish I had had a go myself" feeling was ever present.

I have now missed two examples classes so far. One which I wanted to attend, and todays ... well in my state I felt it best to get home as soon as possible and get some food down my throat. All day my heavy load had made me weary and as I went to get my cup of tea at 4ish, I heard a voice! It was the store keepers and I became confused - the store keeper was leaving it seemed, so I quickly waved my hands madly trying to attract his attention. I was spotted and taking my tea and load, I headed to the "store room". Well it is not actually a store room, but I am just utilising someones book shelf. I got really lucky for the store keeper had been leaving, and I would have been very annoyed had my burden been a pain in the back for nothing.

I am just writing random cack now. My idea was to have a horribly long post like this one, another with a neat proof and a final with an outburst. Yes - three posts! The proof though is rather tricky, but I am definitely going to hope to post it. And the outburst has been waiting for sometime. Both posts have something to do with what I discussed with DC today (to a small degree in ones case). My fingers are twitching to start typing here but I won't. Some person though did try to kill us today. I crossed the road once again without checking, and DC kept on looking at the direction the cars were coming from. Only one car had been there but the jerk driver had not slowed down, but rather sped up as we crossed the road! Gee, I was on the right side to get knocked down again.

I never seem to think that my posts are that long because I read them relatively quickly. The stress that has been on my shoulder for the past two weeks was uncountable! I thought it was due to GG, but it was namely because of the tests, and my not revising for them due to TGG (and other things). I feel unnaturally light now, and feel that I can once again start learning maths. Truth be told I have only been going to the lectures and not doing much else. As a vote in todays algebra lecture indicated, students like the 20% coursework element. However I think it is rather ridiculous that we had six tests! Couldn't we have been given a written coursework for fourier series, stats and PDEs? I know that the tests actually made me roughly revise the material up to lecture 10, but at the cost of making me fall behind for material then onwards. If we had three tests (algebra, real and complex analysis), then that would have been less stressful. It may have helped me in the long run, for my revision during Christmas might be better but the tension I was under was scary.

Tomorrow I will relax and clean my room after years, and post my two posts! (It seems that my posting routine is weird; I post more when I shouldn't...) I have a really bad feeling that I left something behind when I made tea for myself. It is just one of them lingering feelings of dread, and because I left straight after putting the stuff in the store room I didn't check. There is nothing that can be done now, but tomorrow when I unpack my bag the story might be different.

I wish this semester was never to end. :(

(And I wish that I hadn't drank tea on five separate occasions today. It is 10.25pm and I am still awake!)

Don't try this at home folks.

That is waking up at 2:30 and then dropping dead until 3am, and then finally crawling out of bed after muttering a few expletives! And boy is it cold at this time.

I haven't started revising stats yet, but will begin at 4am. Just had some weetabix, and then decided to have toast too. Leaving the bread in the toaster I lost all sense of smell, and five minutes later the whole kitchen was smokin'! So toast it is then.

Two tests today have forced me to wake up earlier than usual. Don't worry I am "experienced" at this and have been doing this for many many years. (Year 8 is how far back I remember doing this). Therefore, as I said above, do not do this unless under supervision.

What will become of me today, I don't know. Will I manage to stay awake in the test, or will I starting walking in the clouds? I think I will manage, but one test is just before Algebra and the other an hour after! Why must these things happen? We will be starting rings today as well.

I hate stats and PDEs: it's officially official now! Now for a want of disliking things, but because I am very 'perverse' and hate having only an artificial understanding. I started liking mechanics more because my lecturer brilliantly enhanced our understanding of things. Fizz and myself were commenting on how cool some lectures had been. And then you have PDEs. I can't believe I am saying this, but at the moment stats is the lesser of the two evils.

Hopefully it won't remain like that forever! I think I have finally understood "separation of variables" and eigenfunctions.

When we solve for eg. functions of the form u(x,t), then most of the times their solutions are of the form u(x,t) = X(x) T(t). That is, u(x,t) is a product of a function of x and t. For the separation of variables thing, we suppose that the solution IS of that form and then do our business depending on the PDE.

Once the substitution into the PDE etc is over, we might have something like X''T = T''X, i.e. X''/X= T''/T; one side with t's and the other with x's. (I have dropped the T(t) notation and just wrote T).

The bit I wasn't getting: whatever value t is inserted into the right hand side does not have anything to do with the left side. The left side remains constant, so we might as well just write the right hand side as T T'' = mu (1). Similarly the same applies to the values of x into the left hand side, so again we get X''/X = mu (2). We now have two ODEs, instead of a horrible looking, ugly (etc) PDE. ODEs are 'relatively simpler' but somehow because of the darn PDEs flying about I don't feel that way. (This all sounds dodgy so don't take my word for it). If we rearrange (2) to give X''= Xmu, then mu is the eigenvalue and X is the eigenfunction!

Imagine having an "aha" moment after reading the above, and then imagine seeing Fourier series pop their ugly head around the door. That is enough to shatter anyones confidence.

I am really having bad vibes about these two exams, namely due to my artificial understanding of the subject. In the other four tests I had an idea, a picture, of what was happening. In these two modules I am having a stinker of a time. Tomorrow is officially going to be my worst day. Damn me - I mean today!!

OK, that is enough from me. Back to the stats and tea it is.

PS: The irony. (link of "sleep deprivation", not that I have had the chance to properly see it).

Wednesday, November 14, 2007

A fantastic lecture!

EDIT: I am of course talking about the lecture by Dr. Colin Steele on Life in a two-dimensional universe, which happened today at 1:10pm in the Alan Turing building room G205.

Well firstly I hope you are glad to hear that I am alive! Secondly, I must sort of apologise to my friends for being a jerk. Milo did manage to come, and so Milo and Bella saved me from being in two places at once; hence allowing me to be slightly more relaxed! I did for a second think that both might not come, but it is a relief that they did attend. I know for a fact that everything would have gone pear shape otherwise.

Thirdly: if you weren't there then shame on you* - you missed out on a fantastic lecture, and the refreshments at the end! *(apart from the people who said they couldn't make it of course).

Do I go to a 'fourthly' or do I first steady my shaking hand? For those who did see me today, running around like a mad man, then I have yet to calm down. My post at 12:20 was the bout of nerves that had attacked me, and they did get much worse for a short period. Straight after my post I had to get this key. They key wasn't there and off I went into another panic. However I was given a name, and rather than using more labels like MS (which are confusing me now!) I will call this person Simon. Simon had the key and was busy with something else. I decided to be a bug and hung around until he was free. We discussed the possession of this key and it was decided that Simon would keep the key for I wasn't 'technically' allowed it.

I needed the key at that moment in time, so Simon decided to help me shift the stuff to this room. As we went to get the stuff from DC, he remarked, "I don't know how you get people to do things "A mathematician is a device for turning coffee into theorems." and about the corollary about tea.

However, who needs coffee or tea for that matter? I don't (well not always).

This is a cyclic business now. The process will continue and already I have to think ahead about week 10. I might give that one a miss though. ;)

To conclude (finally). The greatest happiness has to be that atmosphere which was a result of the turnout. So once again, three cheers to everyone who came, even if it was because of the face I tried pulling in my previous post! The other thing which made everything taste nice, was the fact that the lecture was real and no longer a figment of my imagination. I have yet to calm down, however I really most bring the focus to my studies now. I am not going to complain about that in this pleasant post, but my heart is twitching due to the two tests on Friday.

Here is to many more lectures by TGG \{the ones in week 10!}.

PS: If I have NOT mentioned anything, then please let me know. I will try to edit this post after some sleep anyway.