All 12 entries tagged Mathematics

Relating to all things Mathematical in nature.

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December 07, 2005

Grammar and Parsing

Today I got interested in the parsing of computer languages. I stumbled upon the definitons of LL(k) and such like things, and was very interested. Then and idea for a parser hit me, so I designed a LL(1) grammar, which was quite easy, and not unlike writing mathematics. Then, I wrote a recursive descent parser to do the parsing of my grammar. Its really sweet, and I have plans to integrate it into a slightly bigger project.
I'm quite proud of the parser since its bitchin' fast and very lightweight, as it will need to be for where I plan to deploy it, oh did I mention I did all this in my least favourite language, java?

November 28, 2005

Thinking of Maths

I just wanted to share that I'd been thinking about mathematics,

oh dear, I'm in love!

You know people always say you know you're in love when you just know that you are, well I know!

I Love Mathematics.

But, wait, oh dear what will the children look like, argghhhh. Maths I love you but you do consume my life, oh I really need a lovely female to distract me, preferably a mathematician so we could talk about maths argghhhh!


November 22, 2005

Mathematics

Recently I have been thinking about just how cool mathematics is, now, I know that most people at this point will think I'm a little crazy, but once you understand what mathematics is, you just can't help but be in awe of its overwhelming greatness.

You see, the problem is, that unlike every other subject out there, Mathematics doesn't live in the real world. Mathematics lives in a purely abstract, imaginary universe. When most people think of maths, usually after I've told them I'm on a maths degree, they think back to their GCSE days and think that maths is all about sizes of angle in triangles and solving quadratic equations, NOOOOO. This isn't what maths is about, Maths is about looking at the logical statements we have already made, and using them to deduce new ones. Group Theory, where my main interest in maths lie, is massively abstract, you work with objects that only exist because you write them down, but Group Theory also gives you the tools to say when one object equals another, and so you can then say which sectons of mathematics are equivalent.

Group Theory is just so good, it stems from four axioms, and with that a huge area of maths, if not maths itself, arises.

Anywho, just a quick rant, about maths, the only super-subject.


Strange Lectures

I've had some very odd lectures, recently, there was one on Friday when the lecturer recieved five pints, and drank all but one,

And yesterday, we had this,

Yes, that is a giant hand being used to point out equations.


November 04, 2005

LaTeX

I just remembered a little piece of code I wrote, so now I can add maths to my blog!

How cool, all thanks to LateX (pronounced Lay-tech), so now I can do cool things like:


November 03, 2005

Long Day

What a long day its been!
up at 5am, yes at five, doing mathematical excursions work, that was due in later in the day, my own fault for not doing it any sooner, but I've just not had the time. Okay, then a purely liquid breakfast, helped one of my housemates put some pictures up, I'm the local DIY'er seemingly. Onto campus for 11, lectures until 3 then 2 hour mathematical excursions seminar, which aren't much fun to be in, because the maths is really really hard, but like a few hours later, when my brain has worked it all out 'behind the scenes', its all really cool.

Okay then I had something to eat, then read the Union Council agenda, and then came up with some points to raise about the general crappyness of a policy.

As for Union Council itself, we had more stupid amendments, the general flow of Council seems to be that at the moment, what happens is someone says that they'd like an amendment, but when asked what that amendment is, they don't know! They say "umm, err, can it say something like this…". I mean everyone's been to like two meetings now, get with the program already.

I then briefly entertained the idea, in my head, of aiming to become chair of council, oh such a bad idea, but I'd probably be quite good :-)
I always seem to moan, it comes naturally, so I'll end on a high note.

I'm going home on Saturday, so I get to see my family, including sister's children, ahh how great is that! Oh and maths presentations to my tutor group tomorrow, awesome!


October 31, 2005

Addicted to Proof

Today I realised that I was addicted to Mathematical Proof, this is just the latest in a long line of addictions, including, but not limited to:

  • Jam on toast
  • Going to the Gym
  • Cheese and Pickle Sandwiches
  • Coffee
  • Unnecessary Capitalization?

Anyways, proof is the new, and greatest, thing. Today when I couldn't come up with an analysis proof it was driving me crazy (withdrawal) then when I came up with one it was so much of a rush, a little song left my lips, just to inform the world that Steve had a proof.
So yes, there I was sat in the mathematics dept. giving the proof the physical form it needed, as it was until that point just a mental notion, humming away to myself, so happy, so content, so high.

I can only hope that other people enjoy their subjects as I enjoy mine, I'd be really sad if I were stuck on a course that I couldn't stand. I can't wait until the second term when we get to the interesting (hard) maths!


October 27, 2005

Proof By Triviality

A Mathematicians best (only?) friend.
A subset of proof by intimidation.

To prove a statement one must use a myriad of convincing mathematical arguments to reduce said statement to one of logical equivalence, but so stunningly obvious that one may write the rather poetic line:

Trivial.

Notes:

  1. Not to be used in conjunction with Analysis. Analysts will require some sort of epsilon argument, these are never trivial.
  2. Proof by triviality doesn't make for elegant proofs, but they are bloody quick to write.
  3. Often confused for an actual proof.

October 21, 2005

My week that was

Well, what a week!
Firstly, the maths:
Only two interesting points here, a question from mathematical excursions that puzzled nearly the entire class, does a 2-dimensional polynomial that's positive everywhere achieve it's infimum?
The counter example was a very strange function indeed, and leads me to rethink my ideas of continuity and differentiability in R2. This could be a good topic for asecond year essay? generalising Anaylsis I+II into RN (this should have been done in vector anaylsis, but wasn't)
Other point of interest was a Algebra proof that baffled me for an entire day, until in a tutorial earlier today just as we were about to be show the proof, the untire thing fell into place in my head, it was oh so simple, how could i not have seen it. At one point I had had something so similar written down, but failed to progress with it, oh well.

Now the injury, Tuesday I decided to attemp a jump that I'd made before, but failed this time, landing prematurely, being forced to vault the object being jumped onto, and landing the other side of said object onto my hand. 80+kg of my weight was put through my hand, ouch. It hurt a lot at the time, and enabled me to have just 2 hours of sleep, crap.
Next morning, I went to hospital, other side of cov, urgh, and got no less than six x-rays of the effected region, as well as i nice white bandage for "support". They almost gave me cocodamol too, but I refused on the grounds that codeine makes me feel rubbish.

Went to the UGM, mostly interesting, I even spoke, shame it wasn't quorate, next time eh?

I'm sure more than this happened in the last week, oh! I attended some lectures, but have decided to attend some third year ones as second year maths lectures are rubbish, its all too easy (optional vader impression).

Better go, or I'll be late for a film.


October 12, 2005

Maths Crazy!

Over the past few weeks I've gone maths crazy! I really really really really really really really really really really really really really really really really really really really really really really really really love mathematics. Its the most fun ever, its so big, so understandable, so god damn lovely. It has the power to confuse, to inspire, to repulse and tom ake you seem quite smart, even if you're not.

My passion for rigourous mathematics has really come to a head over the past few weeks, to the point that when a lecturer says: "I will not prove this, I will just assume the result" it really cuts me deep inside. How can we hope to understand, let alone trust the maths, if we don't have a proof. Argh!

I got into a few philsophical discussions about maths over the past week, and one point that was debated was if mathematics was part of the very fabric of the universe, interesting.


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