All entries for October 2005
October 31, 2005
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
- 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
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:
- Not to be used in conjunction with Analysis. Analysts will require some sort of epsilon argument, these are never trivial.
- Proof by triviality doesn't make for elegant proofs, but they are bloody quick to write.
- Often confused for an actual proof.
October 24, 2005
October 23, 2005
October 21, 2005
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
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.
October 05, 2005
that will never, ever, happen, ever.