Primary Decomposition Theorem

Just a random Maths theory I found.

I have just been looking at the syllabus for the final honour exams of the Oxford University Mathematics Degree - whew boyo:

"Dual spaces of finite-dimensional spaces; annihilators; the natural isomorphism between a space and its second dual; dual transformations and their matrix representation with respect to dual bases."

Just a brief, relatively simple sounding, excerpt from the Algebra syllabus.

Sounds fun, doesn't it?

I would really like to do Mathematics at Oxford, but I'm not sure if I'm good enough. I'm good at Maths, sure, but I only seem better than everyone else because I've read ahead. Hmm...

I have a theory (well, poached from one in a Discworld book, but I've dwelt on it):
Everybody has one Talent. One thing that they are really, naturally good at - that completes them as a person. Very few people find their talent - those that do, become famous in that field.

Being such a geek, I can currently think of only Mathematic Talenteers - Gauss, Euclid, Euler, Riemann.

The trouble with Talents is, few people ever try them - I think once you've tried your Talent, you know it's your talent. And some Talents may not have even been invented - like flying vehicles at hyperspeeds, or somesuch nonsense. I'd quite like to find my Talent. Heck, maybe it is Maths after all.

I was statistics browsing yesterday, being bored, and I was looking at the Times University Guide:

Oxford has been rated the top University in the UK.
York is the 7th overall, the best for teaching quality.
Cambridge is 1st for Mathematics (Oxford trails behind at 9th)
Sheffield is the number 1 university for studing Russian and East European languages.

Oh, and I have had a hair cut. It is very short (comparatively).

Last night, I watched the Passion of (the?) Christ. It was a very good film, though very bloody - not much more than showing how much Christ suffered. It was apalling - whether you believe he is the Messiah or not (I do not), no man - especially not one who's crime was no greater than telling people to love each other and not pay taxes - deserves that much suffering.

I wonder if Mel Gibson is a Christian.

Anyway, I'm off to figure out how to complete that thrice-damned Laplace transformation.

Put the following number into the form a+bi

Hello again.

It has been (2 weeks?) a while since I last blogged, so you would expect me to have a lot to say. Well, mayhaps I do - but a lot of it is far too personal for you (if it's not, you already know it), so nyerh.

I shall say it again.

Nyerh.

I have just finished my 3rd week at Kings School, and I am so far thoroughly enjoying it.
The teachers are (mostly) good, and the lessons (Maths, Economics, Religious Studies and History) are all interesting - hence why I chose them.

This has to be a short blog - for now - as my sister is haranguing me to get off.

This evening, I have been occupied with browsing the Oxford University website and its affiliates - all very interesting.

I would really really like to go to Oxford, but I probably won't be able to get it.

Still, I am reading the lecture notes given on the Maths Department website, so at least I'm getting a head start.

A more detailed blog when I have the time and the inclination.

Look behind you!

*runs away*

Missing teachers, Skittles in the canteen, and a lot of naked women...

OK, maybe not the women part. But try telling Andrew that!

There is a point to this post, aside from the shameless nudity - I have started the new school year at Kings School! (I am unsure on whether there should be an apostrophe there...I have seen both usages in equal amounts around the school, and the latin - schola regia - I just cannot figure out at all. schola regum, perhaps....

Wednesday:

My Dad dropped me off at school in the morning, as a special first day sort of thing - Kings was his old school, so he is practically hopping around with excitement now that I'm going there (at last). I found out my form room is actually on a different continent to the rest of the school, apparently as part of some fiendish plot to strengthen our calve muscles or something equally bizarre. I need to invest in one of those nippy little scooters. Most of the day was just sitting around in the form room doing not much, some of which I spent talking to Hannah, a girl who actually went to my old school, but I have no recollection of her. Doesn't really surprise me, though.

We also went to the Cathedral for a service, to dedicate the year, etc - it being a Christian school, and all. I'm not a Christian, but that doesn't exactly make me stand out...heck, half the boys there think they're God anyway, as Alex pointed out today. Except Nick - he actually is God. A long walk to the Cathedral, some bad singing (the first thing Hannah said to me when we stood up was 'You're a really bad singer') and then a long walk back to the school.

Uh...some other stuff....memory block...uh...cover it up with a funny joke!

What's funnier than a fish?

A dead fish!

Then we had a talk in the Hall about Wednesday afternoon activities - we're actually expected to use our time constructively! Crazy foreign ideas.

Um...went to Julia's....drank tea...home...food....sleep....blah blah, etc.

Thursday:

The first day of lessons at Kings! Excited? I wasn't. Well, maybe a bit.

I was picked up by Nick and his family in the morning, talked to Bob about murder in the Inland Revenue before beginning the trek to my form room. I lost two sherpas and a yak, but made it there just in time.
My memory is hazy, but I had Maths, Economics and Religious Studies.
Maths was quite dull, but Economics was quite good - I sat next to Julia, and in front of Jack and Stuart. We made paper fish, the point of which was - for my absent minded, but better, half - to understand how developing economies need to work together in order to develop, and the principles of mass production, imports and exports, economic survival...all neatly summed up in a paper fish and poncho.

Uh...memory gap...another joke!

What do you call a man with no arms or legs?

Whatever you want to!

I'm sorry, was that bad taste? I can never tell.

Uh...school...stuff...anyway!

Went back to Julia's...slept...

Friday:

Arrived at school bright and early, though with a slightly damp shirt.
More lessons, no frees. First History lesson in the afternoon - very dull, though I have learnt a surprising amount.
My bag is so heavy it has formed its own gravitational field. Ooh...nerdy joke there. Want another?

What do mathematicians do before they go to bed?

Put on their pi-jamas!

Anyway. School has been good, with my friends, made some new friends, could write more but I am bored, so I will sign off.

Bye!

An daring daylight robbery of Fort Knox on Elephant back?

That's the dumbest thing I've ever heard.

So...here we are again. How cosy. Just me, an empty mug, and this empty white screen glaring back at me, slaughtering my innocent rods and cones in their millions. Just listen to the screams. Hear them?

To try and stem the massacre, I will - because I'm such a noble guy - fill this screen with black writing, to shield the deadly white glare! Huzzah!

Well, I can see spots, better get started...

The extremely long Summer holidays are nearly over - just 4 more days off (including this one) before starting at my new school in Sixth Form - oh how different things will be. In a good way, hopefully.

I have begun my sporadic learning of Latin once again...I must try to stick with it this time. I would also like to try and learn Arabic. Thinking about it, I may try to find a good book (like my Latin self-teaching books, which are excellent). Books are so much easier to get along with than people. Julia's mother has kindly lent me one of her beginner's Kanji Dictionary (Japanese). Very interesting so far.

It is Sarah's 17th (!) birthday party on Monday night. We will be camping out at Sacrewell Farm, a place with many fond memories for myself (and hopefully for at least one other person...)

I have also offered to try and tackle an essay on Islam - the homework of a Sixth Former I (barely) know. Merely to try my hand before starting the course, I don't expect it to be anything like what the teachers are looking for.

Uh....other things...um....my main occupation as of late as been...well, Julia. And I'm sure she would not wish me to disclose such details to the ravenous internet audience. Sorry, fans.

However, while in her illustrious company, I did this personality test, and apparently I am an Idealist:

• Make sense of the world using inner values
• Focus on personal growth and the growth of others
• Think of themselves as bright, forgiving and curious
• May sometimes appear stubborn

Idealists put time and energy into developing personal values that they use as a guide through life. They may seek fulfilment by helping others improve themselves and often want to make the world a better place. Idealists only share their inner values with people they respect.

Idealists enjoy discussions about a wide range of topics, particularly those that deal with the future. They are typically easy-going and flexible, but if their values are challenged they may refuse to compromise.

In situations where they can’t use their talents or are unappreciated, Idealists may have trouble expressing themselves and withdraw. Under extreme stress, Idealists may become very critical of others, or lose confidence in their own ability to cope.

Recognition for their work is important to Idealists; however, they are also good at spotting false praise.