Friday, August 31, 2007

Student Problems

Read that as student loan problems! As I'd been getting excited about university starting, I had forgotten about university fees.

21/08/2007: Post -Combined Maintenance Loan & Tuition Fee Loan Payment Confirmation Letter.

That's what it says on my on-line application window, but I still haven't received any letter. What with the Royal Mail strikes happening, I think I'll give it another few days though.

Why have I suddenly remembered this? Well we got an email from the university about registering for our second year. However, until I have my loan confirmation letter I can't register!! As my heart rate increased, I did for a second consider whether or not I'd be at university next year. I can't afford £3070! (Wow- that is a lot of money).

This will get resolved in a few days, of that I'm confident, but now I have to dwell on what my year would be like if I didn't go to university next year. I'D HATE IT. REALLY REALLY HATE IT. Woops, the shift key was playing up then. Honestly, I have made cool friends and love my course (touch wood), and even though I could potentially do a lot of things in that year, I wouldn't. I would spend it in mourning! Yes - I'm that sad, but I wouldn't mind being a student my whole life. ;) At least then I'll have an excuse for being lazy and not doing things when I'm supposed to.

That drama aside, after a few months I have finally bought another maths book! Not the Fraleigh one (I think I'll buy that when the year starts otherwise it'll look weird :p ); but another one about algebra. Why did I buy it? Well it was for half price... Oops, you just gave me that look! I'm a student is my excuse, and a very gullible one as well. The second reason for buying it, was that it had mention of Galois in some reviews. The silly thing is that the name of the book I cannot remember! I'd rather not ask you for an estimate, on how much I have spent on maths books so far, but leave it to your imagination. (Well a post on my book list might help you somewhat, but that is still in waiting.)

Did I mention Dory from finding Nemo before? Seriously, I'm becoming like that! Only a few hours ago I was telling someone that I'd bought The League of Extraordinary Gentlemen today, when someone else came. To this person I then said, I bought... 'erm... what is it called... that movie we watched...' I'd forgotten what I'd said not two seconds ago! Thankfully I was kindly reminded of it, but that was the second time it happened today. (First time when I was playing Resistance fall of man). I was probably having a good day today. ;) It is quite annoying forgetting things. I get distracted too easily and hence, forget as well.

I doubt that is going to change, but for the past week or so, Bob the Builder has been back in town. :( Or should I say, Beans the Builder? There is something that I might hate more than stats at this moment in time - PAINTING! It is a boring job and paint smells badly. As you've probably gathered I have not been having the best of weeks, and I think today (Friday) isn't going to get much better. After breakfast i.e. lunch on a good day(!), I'm off to paint and do other jobs. I was going to have another bash at using the jigsaw but didn't because the task was of great importance. The painting etc should be over soon, so I will be free once again.

I lot of groans in this post, and no maths! Strangely I feel exhausted; lethargic, and without energy to do anything. I think we should create some general rules about how to drive your trolley in a super market. What say you, that the rules that apply to roads are applied to super markets? I was driving down the aisle, on the correct side might I add, when some silly driver just pulled out of no where causing me to stop! Thankfully no one was injured, but the bread did complain about a few twinges. It happened on more than one occasion, which makes me wonder why people don't be considerate to other aisle users. One person had parked his trolley at a weird angle and obviously an accident had happened. (Not with me though). You should only be allowed a trolley if you have a license. :D (wishful thinking, but it would be fun!)

Sorry no maths - the darn multiplication and addition tables for bases were taking ages! (My fault for choosing a big base, but erm... there is always another day). Milo is coming to Manchester on the Sunday before term starts. I had volunteered to help him unpack his stuff, but might not be able to make it on the Sunday! I don't know what to do, since my help is required and I do want to go. :/ The countdown begins: 17 days remaining!

Oh, before I forget, a warning to all users of Blogistan. Some malicious people are currently out there on a job: 'Bloggers battered by a viral storm.' Just be careful on what links you click on! It normally appears at the bottom of the window, so always double check. Viruses, worms and the rest are nasty. (I speak from experience!) I tried posting a link-less post, but had to post the one above to inform.

*My challenge for them days: post the blimmin' draft posts!! Pfft.

Wednesday, August 29, 2007

Cheating in maths...

... i.e. 'adding zero'. Pft. Call it whatever you want, but don't tell me that it's a trick!!

I have been told that it can make things nicer, but do you reckon that things can be done without adding in zero? I mean, how many proofs have relied on this so-called trick? What if it wasn't used?

EDIT: I don't think my computer wants me to post this - the Internet died whilst I searched for an image. Back to the drawing board it is, i.e. paint and then waiting for the net to start to working again!

Wooh- it's working again, and my google search seems to only come up with this:
I'm sure you'd agree that my 'work of art' in Paint is much erm... better\sout{?}.


Don't hold back on the compliments now. ;) *runs for cover*


OK, I confess it is a nice trick, but one which I can never spot or think about doing, hence my ... sweet bitterness!

Tuesday, August 28, 2007

A base quote

Many children grow superstitious, and think that you cannot carry except in tens; or that it is wrong to carry in anything but tens. The use of algebra is to free them from bondage to all this superstitious nonsense, and help them to see that the numbers would come just as right if we carried in eights or twelves or twenties. It is a little difficult to do this at first, because we are not accustomed to it; but algebra helps to get over our stiffness and set habits and to do numeration on any basis that suits the matter we are dealing with.

Mary Everest Boole
Philosophy And Fun Of Algebra,
London: C. W. Daniel, LTD, 1909


Addition in different bases was evil, but I think that I have got the hang of it now. (I.e. another base post is in store later tonight; or should it be early tomorrow morning!) I hope that today is going to be a good day. :)

Base 13 - Part II: The secret

Normally we do our calculations in base 10, so the number 489 can be written as:

489= 4 \times 10^2 +8 \times 10 +9

In general, for integers a, b, c from zero to nine we have that,

abc = (a \times 10^2) + (b \times 10) +c.

This can be extended for larger integers, but we can completely generalise it by using a single formula. I hadn't originally meant to blog about this, but the comic has given me an opportunity to do so. If we let m denote the integer we have, then m can be written in base 10 by the following formula, where a_n, a_{n-1},... a_1,a_0 are integers from zero to nine and n is any positive integer,

m = (a_n \times 10^n) + (a_{n-1} \times 10^{n-1}) + ... + (a_1 \times 10) + a_0

In other words m = a_n a_{n-1} a_{n-2}... a_1a_0 (compare with example above).

This is also know as the decimal system which we use on most occasions; and for the non-mathematician, probably all the time!! (By non-mathematician I don't mean Physicists or Chemists, but the people who don't like maths... )

However, interestingly enough we can work in other bases like 18, 3, 7 etc. The choice of base is up to you, but according to the book I'm reading (from which I'm getting most of this!!), "the choice of base 12 has been advocated, since twelve is exactly divisible by two, three, four and six, and, as a result, work involving division and fractions would often be simplified."1 Since I mentioned base 13 \sout{above} below, I will use that as an example of a different base.

A reminder for those who didn't catch the previous post. A mysterious somebody in a red t-shirt has claimed that they're '21 in base 13 only'. You join us at .... the moment of truth. :D (Anyone remember that show!!)

We have the number 21, so we're going to work backwards (I think). I.e if we were in base 10 then 21 would mean, 2 \times 10 + 1. Since this is base 13, an integer k can be written using the following formula,

k= (b_n \times 13^n) + (b_{n-1}\times 13^{n-1})+ ... +(b_1 \times 13) +b_0 ,

where k=b_nb_{n-1}...b_1b_0 and b_n, b_{n-1},...b_1, b_0 are integers from zero to 12 (and as above, n is any positive integer).

In our case k=21, which tells us that b_1=2, \;b_0=1. Hence if we plug that into the formula we should get the correct age:

k= 21= (2 \times 13) +1.

So if I haven't stupidly misunderstood this whole base business, then unfortunately the age of the person in the red t-shirt is no longer a secret. If I have done things correctly, the age should be 27. (If I haven't understood this properly and this post is a load of rubbish, then it'll teach me to not read books at weird times like 4am! That's an excuse BTW.) Did you get that answer? :o



1. What is mathematics? Richard Courant and Herbet Robbins

Monday, August 27, 2007

Base 13

From PhD comics I present you with:

My question to you is: What is the exact age of the person in the red t-shirt?

Maybe I should pass on how I work out my age (mod 25)! Well I suppose that actually describes my mental age, but nevertheless it works. I'll add to this post later tonight with the answer, which I hope is correct, and how I obtained it.


(Without giving it away for those who would like to attempt it, is the answer a multiple of 3? Just so I know I did it right!)

Saturday, August 25, 2007

1... Eureka

EDIT: I'm being strange here (as per usual) and have numbered the posts. Number 1 (this post) is the post I wrote first, but not on my computer so didn't post it; number two (after this) was what I wrote on word pad as I waited for the Internet to magically work; number three was just something I found nice and necessary to post. Why necessary? Well I don't know how many of you have the sound 'on' on your computers - but them darn videos are beginning to annoy me! Especially when the volume is quite loud. Meh. Worry not the idea of these three posts is so that the videos disappear into oblivion. And they have - muhahaha!

---

My cousins wife had a boy recently. Yes, it is important to specify that it was my cousins wife, and not 'my cousin had a boy'. So yesterday there was a party of some sort at their house, and family members gathered. As always when that happens, things can potentially become messy. When Mr. Hu once quizzed me about why I was walking when I was late for Biology, I had replied, 'I'm late anyway, so might as well go fashionably late.' I had knicked that from Leonardo Di Caprio. This was towards the end of the year, and I actually remember running across campus to get to my lesson on time in the first few weeks. (As spectators laughed, but it had been Chemistry!)

My Biology teacher* hadn't been amused, and truth be told I had a funny relationship with her. We used to talk about politics, books, biology and what not, and she knew that I was deliberately pushing her patience. She responded quite well and made me stand outside for a few minutes, and the next time it had been more! Don't worry I soon stopped this fashionably late thing, but yesterday I had tried it again. Successfully might I add.

You'd think that I would no longer be invited to such occasions, but it seems that they had actually wanted me to take photos. I felt used. :( [not really - they had some nice food!] Other people did have cameras, but they seemed to want to be in the pictures at the same time! Hence, I proved useful since I enjoy snapping away at random things.

It had been a nice cool day yesterday, and as night fell the weather remained pleasant. I found myself sat outside, eating my food and drinking my drink. It was really nice, sitting outside, watching the clouds playfully move about and the sun play hide and seek. The door had been open and I was in conversation with people, but nothing beats sitting outside and eating peacefully. However, my peace was being threatened. One of my younger cousins stood in the doorway- blocking the light! She commented that it must be cold outside, but I was wearing my trusted fleece so it was quite cosy. 'You might get locked outside by accident you know.' I was told, to which I replied that I would go inside the other way. She was sharp and said that the other door was locked, however I was equally up to it and said I'd go home if that was the case.

After this exchange she sat at the table to eat, and I went back to my food. But seconds only seemed to have passed and she was fully outside now, pulling up a chair next to me! You see there is some history here - my cousin is less than 11 years old and is going to be in year 6 next year. (I think she's 10 though). From all of the young cousins in my family she is one of the brightest. She has an inquisitive nature, and I confess to having been annoyed by it at times. Well I was slightly younger at the time (in my defence).

What is so important about this ten year old kid, you ask? (Apart from the fact that she asks ten billion questions on a good day!!) Well she LIKES MATHS!! Don't look surprised now - she actually said it when I asked about her favourite subject. I was in a peaceful mood one could say, and on this occasion I had a proper conversation with this 10 year old girl. WOW. I think on my previous encounters with her, I'd assumed she was a 'kid' and treated her so. Well you expect that they get on with what they're doing, but she hadn't. The thing is that she looks younger than ten which is why people often mistake her for being younger, and treat her so. The sad thing is that I remember wanting to talk to my older cousins, and being shunned aside by a few of them. I used stand and watch them playing football on the computer - waiting for a chance. I had wanted to talk to them about football and everything but they used to tell me to get out of their faces! (Apart from three non-footballers).

I've probably done the same to this cousin unfortunately, but it is never too late for redemption. My conversation with her seems weird now, because I still think she's younger. We talked about the planets, the human body, English poems and most importantly Maths. I actually, initially hadn't told her about my own fascination with maths and only asked a few questions. When she had said that she likes maths the most, I had replied with, 'but it is hard, is it not?', to which she had replied, 'Well that's the best bit about it. That's what makes it fun.' Do not worry - the shock will soon wear off. I couldn't believe my ears! She is the first person in my family to ever say that to me, and so from this day on she is my most bestest cousin. :D Well, now the rest of them know how to get into my good books. (I think she's with Bear and Mini Bear).

She's been learning cross stitching in the holidays if you want to know, and loves Sudoko puzzles. She had said that she wasn't in the top set for maths, but was for English, but didn't like English as much as Maths. I then told her that you don't have to be in the top set to like maths and be good at it. She really is quite sharp, or maybe it was a lucky guess, but she even guessed my real age correctly (apart from being a couple months off)! I then told her about going to college and University, and slowly let my interest in maths be shown. Then it became obvious, so when I asked her to guess what degree I was doing, she guessed maths. Now was my chance to go in for the kill!

I asked her about her future ambitions and she doesn't seem to have any yet, but might want to do teaching. I sensed an opening and said why not be a maths teacher? :D See what I did there? Hehe, her parents will soon be complaining to me that I've brainwashed her, but that is a risk that I am willing to take. I'm still quite happy about this and can't wait to see her again. I respect her in a funny way. :)

BTW, I have a question or call it an observation. I know sometimes making funny faces to kids can be amusing, but don't people sometimes over do it? I mean, what happens if you... talk to babies or kids? I think conversations start arising when babies learn to talk and that is quite fun; and when they're three or four they never be quiet! (Bear and Mini Bear) But I don't like it when parents tell their kids to 'stop crying and hit him back'. Well one of my three year cousin claimed that he was 'Tony, Tony Motan...' Yeah, he couldn't say it properly, but his dad finished it for him. I mean what is so cool about being the tough kid on the playground?

All in all though - it was a good day yesterday, apart from the gigantic spider who was sat guarding the door when I got home. A yoghurt pot and a piece of paper sorted him out though! Strange, but I just remembered telling my maths cousin about how a friend of mine chucks books on spiders! You shouldn't be killing spiders, I say. (We'd been eating outside and my cousin doesn't like 'insects' so had reacted when one walked past.)

I hope she does end up doing maths - it would be nice to have a second mathematician in the family. Well second when I become one that is! I have given up trying to positively encourage my brother or Po to enjoy maths and study it further. I know its early days, but I feel happy to have had the conversation I did have.


*[My biology teacher was cool -power infinity may I add! Everyone seemed to be scared of her, but I think she didn't like that. Well obviously who would? She wasn't 'scary' though - cool and misunderstood. She made me go to AST once because I had not 'attained my mpg', but still she was a great and mischievous(!) teacher. :D I've just been sat here remembering biology lessons and badly missing them. The experiments, the content, my class mates, and of course the teacher. I hadn't done A2 Biology, but my friends had so I always used to pop into her class. In footballing terms: a legend. ]

2... A discussion

After a long time I spoke to a university friend today. Obviously a conversation with a maths buddy has to have some maths mentioned; even if it is done so forcefully by me! Hence why I took this opportunity, to discuss my mad musings about what I am proposing for next year. First I mentioned the lectures. The response: 'Ha ha ha! No one will turn up.' That and a lot of other similar thoughts. I didn't really mind, since my quiet confidence about attendance might be giving me false security, but nevertheless I'm positive about it - I don't really care if in the beginning only four people attend. That conversation ended there, although I hope it wasn't because of what I said!

However, thankfully (planned) contact was made again later tonight, and this time I gave the full version of everything. I am sure that my friends will be with me in this, albeit reluctantly, but that is encouraging. On my own, my confidence would really melt and disappear (to some degree). And organising things is more fun when there is more of you. (I hope so anyway)!

I hadn't previously mentioned LaTeX to my friends, since whilst we were bogged down with coursework, I didn't want to over complicate matters for them. This time I did mention LaTeX, however I don't think I did LaTeX proud since I wasn't very clear about it. This came about when I put the forum idea across, and once again was met with laughter. I think my friend isn't negative about this as such, but I don't think they appreciate or understand my 'infatuation' with maths. It was mentioned that no one else would give a damn but I am hopeful and positive about there being other students 'like me'. (Well not completely like me, because that would be just scary)! Somehow I have become slightly more determined now. University is starting soon and I can't blimmin' wait.

The other day I had even dreamed about being back with the Tweenies and Trevor! It was weird since from the outside, the maths building had been the mss building, and the inside had been the new one. On this occasion we hadn't gone to any lectures but there had been a mathematical vibe about the place. I was particularly pleased to see Trevor, my school maths friend. I strangely remember Bella asking me deep deep questions about life and everything else\{maths}! (Trevor, Milo and myself talked a little bit about sequences and series as well). I suppose you could call these maths dreams that I'm having as recurring nightmares, but I always wake up happy!

When the year starts I will be having a blogging break. For me that means not posting everyday, like I have been doing recently. I have been testing my self control and luckily I have some! I don't think I'll be blogging about every little, tiny, ickle, minute.... thing that happens in lectures etc! I have a feeling my second year is going to be rougher than my first, and we have a stats module in the first semester as well. :( Hence, I'd like to get a good routine started at the beginning rather than struggling. Yes, I'm already making plans for the start, and Po who starts earlier than me, always makes it a point to rub it in! Humbug. Oh, and I must unfortunately confess to having done very little( \varepsilon) maths this summer! I've read one or two books, but that just makes me feel worse.

I have had a lot of people telling me 'I told you so' and 'stop being lazy'. Do you think that laziness is an illness? (please say yes!) Or is that just me looking for an excuse? I have suffered these holidays because whenever I was hungry, I used to drink tea. Word of advice: don't ever do that. I want Bernard's watch. :/

3...Food for thought

"We are so accustomed to disguise ourselves to others that in the end we become disguised to ourselves."
Francois de La Rochefoucauld

How true is that?

Thursday, August 23, 2007

My LaTeX test post

Keep moving, there's nothing to see here. Well apart from the two aliens that dropped by for a visit, everything is normal. Keep walking... If you're still here, then let me warn you: I used to love playing hide and seek, and surprisingly had the patience to hide forever and the determination to never stop seeking! Be afraid *muhahaha*. (Well afraid of being found and then having to seek me!) Before I forget - good luck to all those who will be receiving their GCSE results today! (or at 6am to be precise for some) I still remember the day I got my results - everyone else had got their's and I had kept on jumping to the back of the line, not wanting mine. Only after my dad had rang asking if I'd passed, did I get them!


From Ars Mathematica, I found a "site to generate images from TeX code for your site. You can link to the site rather than hosting the image yourself, and the site even supports directly encoding TeX into the URL of the image." The site is Texify which uses mimeTeX according to that post.

This post is not to test \LaTeX for my blog (since thanks to Steve, I have that sorted), but it is for the forum I'm making. Well I've been neglecting the forum of late, but it only needs a few tweaks now; \LaTeXbeing one. So that post has presented me with the opportunity to get down to the tweaking. You can find more on-line \LaTeXcompliers on Steve's Blog here: Online LaTeX.

On the forum the following doesn't appear, for reasons I do not yet know:

e^{i \pi}=-1

Most surprising, since:
[img]http://www.texify.com/img/\LARGE\!e^{i%20\pi}=-1.gif[/img] and
[img]http://www.texify.com/img/\LARGE\!e^{i%20\pi%20}=%20-1.gif[/img]

doesn't work on the forum.



(I will most likely be editing this post on numerous occasions.)

Wednesday, August 22, 2007

Fermat's Last Theorem, Germain and Galois

A small introduction. The curse of slow reading has fallen upon me and I must struggle with it. However, through this struggle I finished reading Fermat's Last Theorem, by Simon Singh a while ago. This post hasn't been written straight after I finished reading the book, since I wanted to see how well I remember it. Call it a test of my character! (Or to see whether or not slow reading is pointless.)


For 'completeness' Fermat's Last Theorem states that,

x^n +y^n =z^n

has no non-zero integer solutions for x, y and z when n > 2.

This is a generalisation of Pythagoras's Theorem I believe, and I hadn't really been aware of it that much until reading the book mentioned above. I have come across and used Fermat's Little Theorem, one which I grew to like, but whenever the Last Theorem was mentioned it didn't register in my empty head.

Upon reading that book, I surprisingly feel mathematically informed. I think that is a must read book for any mathematics student. A definite must read. It informed me of the history of Mathematics, which is fascinating in its own right. About Alexandria, Pythagoras and lots of fascinating mathematicians. Simon Singh has brilliantly outlined, not only the history of Fermat's Last Theorem, but the lives of the mathematicians who lived and struggled with that theorem.

The natural choice is to begin with Fermat and his 'ickle' theorem. Fermat famously stated in his copy of Artithmetica, 'I have discovered a truly remarkable proof which this margin is too small to contain.'

A word of warning if I may - don't ever write 'the margin is too small' for an answer on an exam question! You could try it on your homeworks and hope your supervisor has a sense of humour, but don't risk it in exams. [If I recall correctly, Hardy was afraid of travelling by sea and so used to send the message that he had solved the Riemann Hypothesis(?) before setting sail as an insurance policy. His logic being that God wouldn't want for him to drown with that knowledge...)

I know many people believe that Fermat didn't actually have the proof, and must surely have made a mistake, but I believe otherwise. It is strange how we form these conclusions, but I'm certain - having read about him - that he did have the proof. Fermat might have annoyed his fellow mathematicians, but he seems like a Mourinho type of guy! (In a weird way of course). Now this book, as well as enlightening us about Fermat's Theorem told the story of how mathematicians contributed to it. A lot of mathematicians did contribute towards it and a lot of maths was discovered in the process. Apart from Euler, the two names that had a big impact on me whilst reading have to be Évariste Galois (of course), and Sophie Germain. I say Euler because 'Infinite Descent' (the proposed name for the magazine) came about because of his proof for when n=3. Euler was indeed a remarkable mathematician, but I think I 'grew to hate his name' in college, when we solved differential equations by his method.

\begin{aside}
I think part of the maths syllabus should incorporate the history of maths. It doesn't have to be examinable, but if maths students do read about it, they will be amazed and might also become more interested in mathematics. I mean, having read about Euler properly in a different context, I think he was a cool guy! The history of maths puts maths in an entirely different light and mathematicians as well. For others who don't see it as an alive subject, the history of it gives maths a life. A heart beat. When the programme Dangerous Knowledge had been on TV the other day, surprisingly watched by Noddy, I was told that what had been interesting was the life of the mathematicians (and how they were freaks, if I may add!) Hehe, I think this 'Noddy' needs to be neutralised!

However the point is that Noddy found the history of maths and the history of mathematicians interesting. I know that it hasn't 'inspired' Noddy to look at maths in a different light (just given evidence of how I may turn out to be, which is why I discouraged my parents from watching it. ;) ). But that was probably the first time that I've discussed maths with Noddy, rather than spoken to myself about it.
\end{aside}

Back to the 'big three'.** Germain stood out for different reasons. During her time women studying maths was frowned upon and universities were only for men. However, thankfully Germain found a way around it; albeit under the guise of being a male! I think the most striking thing was Germain's determination to study mathematics, regardless of her circumstances. Germain corresponded with the mathematical world, after her parents finally relented and let her study maths, by pretending to be a French male student. Her parents had initially restricted her from studying maths and taken away her candles and ink, but still she had persevered. I'll dodgily skip the bit in the middle, and jump to the bit when she decided to communicate her ideas on Fermat's theorem with Gauss. Or should I say 'he decided to'... ? The communication (and friendship) between the two resulted in Gauss's life being saved by Germain and her true identity being revealed.

Another thing that struck me about Germain, was that when Gauss moved onto astronomy and stopped replying to her letters, she felt 'different' and left pure mathematics. Her inspiration and (role model) Gauss, probably didn't realise what he gave to Germain in terms of motivation. I know there are some people who don't need this inspiration, but as someone who needs to be inspired and motivated most times, I can understand what losing that inspiration feels like. You really can't be bothered with anything for a while, and unless you find a different source or rediscover some back up inspiration, you struggle. However, although Germain had lost her motivation for pure mathematics, she still chugged on!

Now finally there is Galois. His story has got to be the one that has most affected me and had a positive impact on me. Embarrassingly for me, during the year when I had been talking to a lecturer, Galois Theory had been mentioned. I had no idea who Galois was at that time and had never heard of him, so had stupidly come away thinking that the lecturer had meant Galileo! The weird thing is that when I said his name to someone else, they assumed the same thing as me! (Don't worry - I soon corrected my ridiculous assumption).

Galois's story is a sad one. Situations and circumstances were against him throughout his life, which was riddled with misfortune. One example of why political involvement is bad is Galois. OK, times have changed, (correct me if I'm wrong) but political turmoil was happening in France at that time. Galois may have been 'hot headed', but I can sympathise with him. Feeling helpless at times compels you to act in an irrational manner. I'm not saying that it is good to do so, but Galois was a kid and he went through so much! One reason why I probably was taken in by his story, was the fact that when he had been 19, already so much misfortunes had been witnessed. He was 20 I think, when he died - one year older than me!

His genius can't be denied and he'd only studied maths for a short time. Maybe if he had filled in the gaps to his thoughts and calculations, he might have got into the university he wanted? Because he did a lot of working out in his head, he left others who did follow his thoughts, confused. Much of the mathematics that he discovered is not understood by me. I haven't even done Groups rigorously yet, but it all sounds very interesting. (I do understand the basic concept of a group though, but only had two proper lectures in December on this).

I have probably gone on, and could still go on, but as you've guessed this story doesn't have a happy ending. Galois was murdered, and I suppose we can all speculate as to why this happened. I think that the 'powers that be' sent a woman to do the job. Galois fell for this woman and her 'to be' husband found out. (I think he was one of the top guns in the government and wasn't pleased as you can imagine, upon discovering this). Now he was probably a convincing actor in my opinion, and had planned for this to happen. He challenged Galois to a duel and there was only meant to be one winner. :( It wasn't Galois if you're interested.

Indeed there has been less of the actual theorem and Andrew Wiles massive, gigantic, enormous, power infinity(!) determination to solve it mentioned here! However, the book will enlighten you about all that. The book beautifully constructed the journey to the proof, and it is impossible not to be taken in by events. Galois was actually my final inspiration and probably the most important one, to type my proposals up. I had been lazy, as per usual, but when voting commenced on the name, I was back in the drivers seat. The Galois Group might have two meanings, but to me there is a third. That of a young mathematician who had to endure hardships, and not study maths further. (Although it does show massive strength of character to go about heading a rebellion!) The third meaning is that what we take from his story. He sounded like a cool kid as well!

To conclude (yes there is one), I would definitely recommend the book. It might have some concepts unfamiliar to A Level students etc, but read it is as a story book. Read about the links between different mathematicians and mathematics like a story, for that is what it is. This maths story is not an infinite one, but it will continue for a long time yet. You don't have to read the beginning to follow it, but it definitely changes your perspective of things having read from the beginning. And as I've written elsewhere; it is indeed mathematicians of the past that still motivate maths today. (Oh, and if you haven't noticed, there has been an obvious bias towards Galois in this post!)


*Will add links etc \sout{tomorrow} after some sleep! Since it's been a while I've posted a long post, I can't estimate how long this is, which will also be dealt with after some sleep (and painting).
** United are no longer part of the top 3. Humbug.

Tuesday, August 21, 2007

Transformers (and Bumble Bee)

Only a paragraph at this time, since I couldn't wait till my heads glued on properly, and the movie was just great! That sentence didn't make much sense to me, but this movie took me by surprise. I actually enjoyed it, and it didn't even feel that long. Actually I felt that it was awesome - it had me grinning at the end, and was fantastic. BTW, a word of warning - I'm Bumble Bee! Sorry, I've bagsied bumble bee, and since none of my friends etc know of this blog, there is no point in changing my name to prove this to them! Megatron, Iron Hide and Jazz have already been taken, but I'm sure I can always do something about that if anyone is interested. Seriously, I loved this movie. Unlike Spider Man 3, during which I had fidgeted and checked what time it was, I actually forgot about the time whilst watching this movie.

Ooops I lied- it's 1.5 paragraphs- I'll be editing this post tomorrow sometime, after painting of course, but if you've watched it who would you like to be? No one has volunteered for Optimus Prime yet ...(actually no ones been volunteering- we all fought 'diplomatically' i.e. 'bagsying' over bumble bee, and then I chose the rest!) 'Autobots, roll out'.

Saturday, August 18, 2007

You do the maths.

Yesterday I discovered the following:

And if it is not clear what has been done, then have another look:

I think the advertising company should take heed of the above! If they'd like new customers, then having 'you do the maths' on the front doesn't seem to be like a good campaign! Don't worry though - I rescued it from the people who did this (cough), and now it is safely hanging on my wall. :D The prospect of 'doing maths' seems to be having a negative impact on people. I wonder how many other were treated in this awful manner...


PS: Just want to say a few things on the maths carnival and the unrest about the splitting of it. I have never actually read through a carnival post, although I may have browsed through the host blog on occasions. (Well I might have skimmed through the post...) So whatever happens really doesn't concern me that much, because the content tends to go 'whoosh' over my head anyway.

However, since everyones talking about having a 'graduate student' and 'research student' orientated edition, why not have one for undergraduates? Obviously I won't be contributing anything mathematical, since my post seem to be anything but maths! However at the moment, I count four undergraduate blogs (not including Warwicks network) in Blogistan. There is Abelian Soup, Setting the World on Fire one Flag at a Time, Zero Divides and Conditional Propositions. More probably exist but they're the ones I have bookmarked. Do you know of any other undergraduate maths blogs?

As with the mathematical culture at universities, the post grad students and lecturers seem to form one group, and the undergrads a different group. Maybe the carnival should remain as one carnival but have sections instead? One for maths education, another for research students or lecturers, a section for undergrads and a general section. I don't know to be honest. One thing that I do know, is that I should stop being lazy and finish the gazillion drafts I've started! (well not gazillion but about five, six).

Yes, logs again I'm afraid.

What I had wanted confirming in my other post was whether,

\displaystyle \frac{1}{2}\ln (1+x)^2 = \ln(1+x)

Straight after I'd posted the earlier post, it had been food time. I did ponder on logs for a while, but then became occupied with other things. As I sat playing Resistance Fall of Man*, I wondered again and convinced myself that I had done the right thing. I'm not very good at convincing myself it seems, but I hope the following is correct in convincing me.

We begin by introducing the variable z \in \mathbb{R}, and letting the problematic expression equal it:

(1)\begin{array}{cccc} \frac{1}{2}\ln (1+x)^2 &=& z\\ \ln(1+x) &=& z& \text{    Using `log rules'} \\ e^z &=& 1+x &\text{    A `log' thing}\\ \end{array}

That has been done using the rule which I was having a problem with. Now we do it without using that particular rule:

(2)\begin{array}{cccc} \frac{1}{2}\ln (1+x)^2 &=& z\\ \ln(1+x)^2 &=& 2z&  \\ e^{2z} &=& (1+x)^2 &\text{    A `log' thing}\\ (e^z)^2 &=& (1+x)^2\\ \end{array}

If I'm right in what I've done then if we 'square root' the final line in (2), then both (1) and (2) are equal. (I think this is dodgy maths, or I'm doing something rubbish, but I don't think its important to mention whether it is the positive or negative root). Actually, I may naively say that it doesn't matter, since both (1) and (2), if written in terms of x are, x= e^z -1 (regardless of the sign of the root and if I have not done anything stupid!)

There you have it folks - trivial things cause me the biggest problems. The problem tends to be the fact that I can't let go of questions like this. They're like a thorn in my side and no pain killers work! But it is always logs, regardless of it being integration or finding the limit of convergence. Somebody needs to go back to school.


*Any other Resistance Fall of Man players out there? I hadn't played for a couple of weeks, and upon recently playing, I discovered the clan I'd joined has disappeared! I had actually liked that clan, and am investigating what happened. :( (The clan leader seems to have vanished.) Hmmm, maybe it is about time I created my own clan! Well I have a name now at least - 'The Galois Group'. :D If you want to join let me know. ;) [There is this one player whose user name is Euler! I'll send him an invite.] Apart from when my brother is watching me play and muttering spells under his breath, I'm slowly getting back into the swing of things.

Friday, August 17, 2007

Another 'LN' post. (i.e. log_e!)

I unfortunately seem to not get on too well, with the pleasant folks who live in the town called Logarithms. I guess what I'm seeking, from those who do get on with those pesky folks(!), is confirmation.

The question was:

\displaystyle \int \frac{2+x}{(1+x)^2} dx

So, I rewrote it as:

\displaystyle \int \frac{1+1+x}{(1+x)^2} dx= \int \frac{1+x}{(1+x)^2}dx + \int \frac{1}{(1+x)^2}dx

Integrating this gave me,

\displaystyle \int \frac{2+x}{(1+x)^2} dx= \frac{1}{2}\ln (1+x)^2 -\frac{1}{1+x} +c

So what's the problem you ask? Well it is not exactly a problem, but a niggling doubt. Is it correct to simplify that answer in the following way?

\displaystyle \frac{1}{2}\ln (1+x)^2 = \ln(1+x)

I'm thinking that the answer is yes, since \ln x^2= 2\ln x, but why do I always have a problem with this!! I mean, when I differentiate 2x, I do so without thinking twice. But these logs annoy me. :( They seem to have been haunting me since college as well, I mean why does the stinking power have to come down for? The graphs of ln(x^2) and 2ln(x) seems to be different as well!

(So does the 1/2 cancel?) :o

Mathematical Summer School reopens!

A big thank you to all who signed and supported the petition to Save Mathematical Summer School.

I quote the following from the post at that blog:


A letter was sent with the petition to the Prime Minister of Republic of Turkey, on 3 August 2007. Since then, this petition has achieved its immediate aim and its further signing is temporally paused.

The illegally closed School has been reopened -- at least for now-- on 10 August 2007.

Warmest thanks to everyone who fought for the School!

However, Professor Ali Nesin still faces prosecution. Indeed, on 7th August Professor Nesin was summoned to the prosecutor's office for interrogation. The key charge was "education without permission". The prosecutor told Professor Nesin's lawyer that he will open a trial against him in few days under Article TCK 263 of Turkish Criminal Code:
Persons who open or run illegal educational institutions can be jailed from 3 months to 1 year.The actions of the prosecutor appear to be in contradiction with the 27th article of the Turkish Constitution which guarantees the freedom to teach and learn arts and sciences:
Article 27 Freedom of Science and Arts
(1) Everyone has the right to study and teach freely, explain, and disseminate science and arts and to carry out research in these fields.
Professor Nesin has written to me that he is prepared to stand the trial on constitutional grounds in order to create a legal precedent. The issue now is freedom of Mathematics itself.

Regarding the situation around the school Professor Nesin posted a comment here updating the current situation. See the end of this post for more information about the incident, links etc.

Thank you. :)

Thursday, August 16, 2007

Mathematical Mentality

As I sat, nursing my cup of tea, bitterly watching MOTD (Match of the Day), mathematical thoughts intruded the slow frustration building up inside me. (Part 2 of the post before. :p)

What mathematical thoughts could they be? Well that of a mathematicians mentality. This is not about the game football, but a couple of years ago I was asked to help train a bunch of kids. (Call it 'community work'!) The group was rather big and I couldn't filter out those students who didn't know how to play football. We were indirectly told to prepare the kids for a tournament, and that was it. Like I said above, I don't consider myself to be a great footballer- I just love playing the game, and you don't have to be great to play it. In the end, the other person who was meant to take the other team didn't turn up. This was most annoying since I ended up having to work with both teams.

You see there also exists a thing called football mentality. Football awareness which you use on the field. Some kids had it, but a majority had no idea. The first thing I had done was to organise a quick friendly to assess the ability of the kids. I don't think some of them had wanted to be there, but had not been given much of a choice.* (You can spot them a mile away!) Through this friendly I learned a lot. I saw that only about five or six really had that footballers mentality. Some of them didn't know how to pass, and whenever the ball came to them they had kicked it anywhere. This was most frustrating for we had a tournament to prepare for.

What could be done, if not to go back to square one. So I went to the basics. Even for those who could play, I showed them how to pass. I put them into pairs and made them first control the ball and then pass -using the inside and the outside of the foot. The main point of this activity had been to first control the ball. If they passed without controlling, they were in trouble (i.e. a few laps). I was told that many of the kids had 'two left feet', but that was unimportant. What I wasn't told was that a majority of them had sneered when I'd mentioned how great football was. My job automatically became harder. Not only did I have to prepare them for the tournament, but to do that I had to initially rid this negative attitude they had of football. I had to make them enjoy the game.

I tried to do both of these tasks, but it seemed that only the footballers amongst the students really cared for my job. They tried their best to make a go of things but then began doing everything themselves, and not playing in a team. I didn't like that. Every session started with controlled passing, shooting and moving with the ball. They hated me for it - it made their hands sting - but this pain was necessary. The pain of having a ball kicked in your face was also necessary. Not as much, but it all contributed towards their footballer mentality. (You see there comes a point when a ball in your face no longer hurts!)

Anyway, everyday we spent the first half hour or so doing these routine things. However, I always tended to add another extra routine into this work out. As they learnt to control the ball, I told them to no longer control it before passing, but to try and pass with one touch. Quick passing. This was a big ask and many of them stumbled. They could pass, but the problem was passing to a team mate. The pass had to be weighted you see, just right for your team mate. They used to 'blast' it towards their team mates, and most often than not the team mates got a ball in the face. This was when asked not to control it. (However some progressed nicely).

After this half an hour of basic routine building block exercise, a friendly game occurred. I had mentally created the two balanced teams that might work, and made any changes that might be needed. One kid always stood and played near the outline of the pitch. The kid was afraid of the ball and if, during a game, the ball came in the students path, all training was forgotten and the ball was kicked without any direction. That player became a sub. Some resilient players impressed me so I then created positions to suit their playing 'mentality'.

Now you might be thinking, this is all football so what the heck was the point of this post - but I must pause you there. I have on occasions compared a 'footballers mentality' to a mathematicians mentality, as other people compare it with a musicians. Now, if I was to read through my post again using the 'code' mathematics= football, then most of it would still make sense.

In schools we try to help children to build their own mentality of maths. We teach them the basics - to add, subtract, multiply etc. We repeatedly teach them these basics, but when they begin to understand the basics we push on. They may hate every minute of it, and not like what they're doing, but part of our job is not just to make them do the 'routine' tasks, but to make them enjoy doing so. I mean we have to impart on them this mathematical mentality which will allow them to enjoy and learn maths. It is a hard job indeed, but I will say again- the hardest part is in making the students attitudes towards maths positive, as it was with football. After you've overcome the attitude hurdle, things become nicer.

I tell my friends about the joys of football, but they'll never understand until they play it. They may watch it, as kids watch their teachers doing maths, but until you yourself haven't gone through it, you'll be ignorant of it. Watching the game is as important as playing it. Watching mathematicians doing maths is as important as well. But playing it and doing maths is an altogether different story.

You see I've experienced both scenarios. I've tried to make 11, 12 year olds enthusiastic about maths and I seem to have helped a few people. This doesn't inspire me, rather it makes me wonder what can be done for those who 'hate' maths and find it boring. We need to make sure that most students have a sound mathematical mentality. So that on the field, they can sense the pace of the game. They can sense what a question asks them and then do their business. I don't think much explanation is required about this mentality, since it is very much like the football one. If you don't play football for a while you become rusty. In games your first touch becomes poor. Your perception of things is found wanting.

In these holidays my mathematical mentality has become rusty. Questions which I could do without a problem before, are now causing me problems. But once I get into the swing of things and the year starts, the rust will hopefully decrease. What I've ignored in this post are those students who have this mathematical mentality. Those who appreciate maths and are positive about it. The main thing with these students is that they need to be taken down the right path. If that is done, then 'we are done'. There are cases when students have this mathematical mentality but the rust which gathers, never goes away. They may choose a different path in life, and so be it.

As I return to this post, I look at the football academies that exist for teenagers to nurture their footballing mentality. Kids as young as eleven can be seen enrolled in these academies, each promised a contract with a different club if they evolve into a great player. These young players have that motivation. 'I will be playing at Old Trafford one day,' they say. This may be unrealistic, but they don't have to be playing for United to be playing at Old Trafford. These kids have ambitions and they are vigorously trained to help them achieve their ambitions.

Do such 'academies' or schools exist for teenagers to nurture their mathematical mentality? No - well none that I know of. A lot can be argued about mathematical ability, but in my opinion if you're not 'naturally' talented then you can fall into two (or three) categories. You have the lazy teenage mathematicians, the hard working ones, and well the third category I was going to write was the ones who love maths but they belong to the hard working category (at times). I've always thought that the problems started at secondary school - they don't. They start at primary school. Nuno's friend is seven or eight years old and hates 'numeracy'. Another of Nuno's friends (six, seven) wants to be an 'actor'. 'Do you like maths?' I ask, only to be met with a shake of the head and a slowly said paragraph about why maths isn't liked, but history and English are. Thankfully these kids were to young to 'mock me' for even suggesting that they should enjoy maths!

Now I realise that my 'analysis' is empty, since there do exist students who love and enjoy maths at that age. If they're unlucky, they end up having problems in secondary school (Noddy), and never like maths in the same way again.

Does the difficulty lie in nurturing mathematical mentality, or trying to create a way in which this is possible? Will all the students who do end up studying maths always say, 'I got lucky and had great maths teachers.' upon being asked why? That is true, but is it me exaggerating things again, or have I yet to meet a teenager who loves maths. Since I left college I've not met anyone who wants to study maths at University - no one. I know I don't exactly travel the world, but from where I live and my school, no one. I know that one person from my college applied for maths (hope they got in), but is it the lack of 'mathematical academies' that is off putting to students? Should universities - the big clubs, do something about it rather than the Government and other organisations? Actually what can be done?

I have gone off another tangent (since I didn't complete this last night), but what Polya says in his book should be instilled in children at a young age. That book is a great for learning about mathematical mentality. I think I fall into the category of the students who love maths, but this has always been connected to the teachers I had. I have been lucky, and as I always add to the unfortunate questioner, 'I had the right mathematical accidents in life.'

Is this post ever going to end? (rhetorical question!) So to conclude(!), I think the most important thing of a mathematician is his attitude, which is closely related to their mathematical mentality. A healthy attitude towards maths, leaves the door open for everything else. I like the idea of comparing this mentality to a footballers, since when a player has the ball they are also faced with questions. Whose free? Can I find him? What are the unknowns? What do we know? For the person with a superior mathematical mentality these questions will be second nature to them, as will be the avenues they explore and the tackles they make. For the young aspiring mathematician, there will be the hesitancy before launching into a tackle. A naiveness in the next step of their calculations, which hopefully evolves. Mathematics and football is all heart. (If you watched the second video linked above, you'll know what I mean. :D)

\sout{ Mathematical Mentality} Football Rant

EDIT 4.21: I haven't managed to finish my actual post on 'Mathematical Mentality' and I was hoping that it would come straight after this one. I got carried away here, but hopefully tomorrow, I mean later today, I'll complete it. (I need to sleep now!)

As I sat, nursing my cup of tea, bitterly watching MOTD (Match of the Day), mathematical thoughts intruded the slow frustration building up inside me. Before I do discuss more about this intrusion, I have yet to have a 'It's the start of the new football (soccer) season' post, since ... well Manchester United haven't been doing too well! That's an understatement - we've drawn the first two games of the season. The misery.

I'm not being 'harsh' but a new season is a new season, and so you have to forget about the previous season (the highs and lows). We are no longer champions. We're a team who spent an awful lot of money buying players, who I mght not have bought myself(!), and we've drawn our first two games. We didn't need a Tevez and Nani I can't comment on. Hargreaves sounds OK but that much money for a cover player? Sigh.

It is surprising, but none of my friends (apart from Trevor) have been football fans (they prefer cricket or rugby - pfft). Trevor has gone a different way now, but man do I need to vent some of this football 'thoughts' out! My thoughts go to Mrs P (from school), Mr Hu, Mr B, Mr H (all three from college) and Prof S (uni), who I always tend to discuss football with (at inconvenient times of course!) The point is that my 'peers' always tend to disregard my opinions and thoughts on football, and my teachers, well they put up with me! I can't exactly bug them now (although it is tempting!), so the alternative is this blog.

Sorry for those who are not fans of the game, but since the edit, you can safely ignore this post and skip to the next one, if all you are interested in is maths.

Ronaldo - the idiot has gotten himself a red card. He was pretty impressive, but you know what angered me the most today- more than the draw? Pizzaros BLATANT DIVE. I hate divers- they give football such a bad name.



www.nikefootball.com



Gah. I know watching football is great, but actually being out there and playing is better. If you've ever been to lazer quest, you might just know of the feeling I describe. You fall down, but then quickly get back up again - back to the game. Divers make my blood boil! What do they get out of it? It makes me think whether them players are actually playing football because of football. Today what seems more important is the politics of the game. I know a lot of money is involved, but it has given football a bad name. Players that were my 'football role models' were Cantona and Keane. Roy Keane. When we weren't singing, 'Ooh ah Cantona', I was Keano. A box to box player. None of that diving riff raff.

Why wouldn't I have bought Tevez? The main reason is that I'd rather spend that much money on a goal-scoring machine. Yes- that's a tall order, but we need a goal scorer. We need a striker scoring most of our goals in our season. Whoops, I'm reminded that its early days, but we've only scored two goals so far which is far more worrying (and Rooney's injured as well). If only I could stick the number three shirt on eh.... (Aye- that is wishful thinking indeed, I'm as 'accomplished' in football as I am in maths. I.e. all heart(!)- I need to improve my long range passing and possibly be careful when sliding in!) I did have a kick about outside today, but playing a match is completely different.

You forget everything when playing football, which is a bonus indeed. As I've been typing this, my frustration has thankfully slightly decreased - at least now I have football to vent my frustrations on.

A final analysis of what I want to happen this season! Obviously I'd like United to win the Premier League more than any other cup, but if we don't win that, then the Champions league would be nice. I've got a feeling that Fergie has been buying players with Europe in mind. Just a thought, but when playing in the European cup, on most occasions you have to change your game plan. We don't tend to do that. Its OK when you're dominating teams and dictating play, but against the likes of AC Milan, you CAN'T contain them, so don't bother! If we don't get either of them two cups then the FA Cup is a must. And if that fails the league cup it has to be.

That fantasy season aside, I think as alway, Liverpool might finally have got themselves into gear. I always fancy Liverpool's chances during the season, but they always disappoint. I'm not a gambling bean, but if everyone can be kept happy in the 'pool camp, then they'll do good. I wonder- who is the better team, United or Pool? That's a close call indeed and since I haven't seen the new signings in action, I can't really comment. Chelsea will always be a pain and Arsenal have the potential to be painful. Arsenal are going through a transition period, but Wenger is the man for them (no Henry is going to be weird though). Will these four teams be in the top four again? Well if United aren't, then Newcastle surely will be. Pfft.

It is too early to comment on relegation battles but I really hope Sunderland do well. You see even though I support United, I seem to have developed some sort of allegiance towards Sunderland because of Keane being their manager.

This season, more than any other, I want to watch football. I want to see beautifully constructed goals without too much concern of the result. La La tends to watch 'players' rather than the football and as we watched the highlights of the Chelsea game, La La told me the score. It was hoped hat I'd change the channel upon hearing that Chelsea won. I didn't. I said to La La that even if it had been a League 3 game, I would still have watched it (explains why I have a lot enemies when I have the remote!). I watch football to see players develop and interact as part of a team. I watch it for the game - Joga Bonito, eh? :D



www.nikefootball.com



(Just found them videos now and they seemed appropriate.)

Monday, August 13, 2007

Another Maths Summer School Update and a Video

First the update. Ali Nessin has himself commented on another blog and this is what he said:

Thanks a lot for your support.

We never interrupted the teaching. When we were told to empty the buildings we stayed in tents and had classes in the open air. But a few days later the gendarmery came to tell us to leave the tents as well because some were erected in the forest; the next day we are told to leave the camp grounds completely for security and sanitary reasons! We refused of course. Now that the site is unsealed most of us are back to stone houses. Some of us, including I, are still staying in tents.

Our two classrooms and two hamams were illegally sealed for ten days or so, and eventually unsealed.

All that time we never interrupted classes, except for one day, when we had to level the ground in order to erect the tents and to construct a shade for an open air classroom.

I am told to ask for permission to teach, that I am refusing. I think that to oblige a university professor to ask for permission to teach his/her own specialty is against the academic freedom, apart from being insulting. In fact 27th article of the Turkish Constitution guarantees the freedom to teach and learn arts and sciences.

The prosecutor is still investigating charges against me. There are three of them I believe: 1) Founding illegal institution, 2) Illegal teaching, 3) Illegal construction. My answers to these questions were terse 1) There is no institution, 2) I don’t think I need a permit to teach, 3) Yes, the construction is illegal due to bureaucratic difficulties that we are trying to overcome for a year. Not a big deal!

Thanks again for your support.

Ali

I'm glad that they didn't stop teaching, and once again hope that the matter gets resolved soon. If you'd like to sign a petition to Save Mathematical Summer School, please show your support at the blog linked at the top right. :)


Now AOB, i.e. random happenings in my life. If you're still confuddled by my previous post, then my apologies. Yesterday it was someone birthday. I tend to use birthdays as a brilliant excuse to erm... pass on Maths (one could say). So I gave someone a card in which I presented a proof of why they were a freak, (in the nicest way possible of course, or maybe in the way this person means it when they say it to me). The idea of the proof was that we assumed that the person isn't a freak, and we know that I exist and OBVIOUSLY *coughs* I'm not a freak. Hence since this person isn't like me (height difference), they can't 'not' be a freak. So we have a contradiction, and our assumption was incorrect, therefore said person is a freak. Confused? Well, I didn't think proof by intimidation would work on this occasion, so I was going for 'proof by confusion'!

Sadly, I did more. I wrote a sentence on the back of the envelope, in the same manner as I did in my previous post. My challenge: tell me what that says and I'll give you a present. :D All of a sudden the corner of everyones eyes creased, and I felt gazes of hate and hurt fall upon me. How could I do this, was the unasked question. I brushed all this aside, and informed them that anyone could help to work it out. Amongst these upset faces, some determined ones awoke and attacked the sentence. It was late when I gave the card, and so only a few people remained. Now you see, one person was sly- very sly. I've started reading the Code Book you see, and that's where I had got the idea from. One person, Sly, had spotted me reading this book, and as I sat at the computer Sly had a look through the book.

I became overwhelmed and stupidly had assumed that Sly was interested in the subject matter! (I'd left the sentence and forgotten about it you see.) So I discussed with Sly how 'cool' the book was, and if Sly would like to borrow it. Sly was 'reading' it but not from page one. Thankfully, when I'd realised that Sly wasn't actually reading it, I'd asked for it so that I could continue to read it! It was only when I entered the control tower, with everyone frantically trying to work out the sentence, that I realised how sly Sly had been. They all gleefully laughed at me, and someone suggested that it might be mirror writing! (In the morning I'd been discussing that you see). The computer was on in the control room and cipher alphabets were open. They wanted confirmation that the right thing was being done, and I very vaguely answered them.

They were on the right path, and I did my past to throw them off. When they'd worked the words 'Ha Ha' by guessing, I felt that they'd worked the key out. Much to my relief they hadn't, and so they struggled, whilst I safely hid the Code Book somewhere and watched them. The unity of the struggle was great to see. Tweety was the most determined though, and so I did drop a few hints here and there. I was quietly confident that tweety would work the sentence out and it wasn't a horribly long one, but a short and 'sweet' one. :D

Finally, Sly came running with the sentence. I was must infuriated, for Sly had slyly used the Internet to work out what it was (which I didn't know was possible)! A grinch like smile glued itself to Sly's face and I was told, 'I hate you- you made me think!' This made me feel better and Sly crawled away - proud. (I must confess to giving a code in the comments section to Sly to work out!) Tweety was not aware of Sly's slyness, and eventually Tweety worked out the code for herself. I asked if Tweety knew the key, and then realised that Tweety had used intuition and guess work. (Well she guessed that I had written the birthday persons name and already had 'Ha ha', after which things fell into place).

Tweety had really enjoyed this, but I didn't make the same mistake twice and so asked Tweety whether she'd like to read the book. A sharp no shut me up, but it didn't stop me from discussing what I'd already read in the book! Yes, I am truly a BUG - muhahaha. Ahem, well it had actually been quite fun, watching everyone concentrate their efforts to working the sentence out! Luckily for them, my key hadn't been random, and wasn't too hard. I wonder when I'm no longer going to be invited to birthdays. :D

Oh yeah, now to the video. It's brilliant, awesome and ... well you'll soon see. (I meant all these in the mathematical sense of course).



I couldn't remember whether or not I'd previously posted it, and having found the link again, I decided to post it again!

Sunday, August 12, 2007

Gjoefst lffqfst, mptfst xffqfst

Dijmesfo pf bmm bhft (zft zpv bsf bmm ljet up nf!), xfmdpnd up nz cmph. ifz, xbju b njovuf - uijt jt opu nz gjstu qptu, tp xibu uif ifdl bn i tbzjoh. Cux, dbo ju qmfbtf cf opufe uibu j bn tmpxmz cfhjoojoh up ejtmjlf cjsuiebzt. Nz diffl tujmm tujoht gspn bo jejpu opt efjoh dbsfgvm xjui b qbsuz qpqqfs. b dbtf pf pwfs fbujoh njhiu ibwf ibqqfofe, cvu uibu jt opu rvjuf bt jnqpsubou bt uif qbjogvm diffl.

Uijt jt opu b mpoh qptu, tjodf j lopx zpv'mm qspcbcmz mptf qbujfodf bgufs uif gjstu mjof (boe jut ubljoh gpsfwfs)! kvtu xboufe up tbz uibu j bn tvsf xf dbo qspwf cz joevdujpo (ps xibufwfs zpv mjlf), uibu xifo cbe uijoht ibqqfo, jogjojufmz nboz cbe uijoht gpmmpx. zft, zpv sbjtf zpvs fzfcspxt boe efnboe b qsppg, cvu j bn xpsljoh po ju.

cux, up dmbsjgz, j ibwf kvtu tubsufe sfbejoh uif dpefcppl boe j bn mjljoh ju! uijt jt nz buufnqu bu dszquphsbqiz boe tufhophsbqiz. jg zpv ep gjhvsf pvu xibu j ibwf epof, boe ibwf bduvbmmz cpuifsfe dzqifsjoh uijt svccjti qptu, uifo qmfbtf dpvme qrtu zpvs gbwpsjuf upqjd jo nbuit. xfmm jg j tbje qptu uif ovncfs uisff, uifo boz sboepn qfstpo xip ibt opu cpuifsfe sfbejoh uijt, xjmm gpmmpx uif usfoe. cvu j usvtu uibu xf bmm ibwf ejggfsfou mjkft boe ejtmjlft. diffst, boe ep opu xpssx, uijt jt pof pg b ljoe!

Friday, August 10, 2007

Update on Blackboard Under Arrest.

I've calmed down quite dramatically and so now onto important things. I'm just going to give an update on what's been happening (by copying and pasting from other blogs!)

From http://savesummerschool.blogspot.com/ we learn,

"The petition below was sent to the Prime Minister's office by e-mail on 3 August 2007, and then by fax and airmail. However, on 7th August Professor Ali Nesin was summoned to the prosecutor's office for interrogation. The key charge was "education without permission". The prosecutor told Professor Nesin's lawyer that he will open a trial against him in few days."


Yes, there does seem to be something that's not being made clear. I'm just presenting what other bloggers are saying here, and not commenting on Turkish politics. From this other blog's comments, the plot thickens,

"However, it is true that they were building w/o a permit. On the other hand, in rural areas, hardly anyone bothers about a permit.
I guess the most disappointing part was that they were accused of establishing a teaching institution w/o a permit!!!
Wow. I wonder which local official has even thought about that. This is NOT a teaching institution for money, this is a co-op camp of volunteers. No money is asked nor expected.

The sad thing is that all this has happened because Prof. Ali Nesin is the son of Aziz Nesin, a very influential writer of his times, who gave such hard time to the governments, that they labeled him as "communist" and jailed him at every opportunity.

So, the witch hunt goes on."


That is someones take on whats happening, but all this is doing is showing how ridiculous, 'education without permission' sounds. The petition is looking great and now has over 200 signatures on it. You can still sign it, and if I may quote Professor Borovik's post you can be anyone,

"Who can sign the petition? Anyone who loves and/or appreciates mathematics. That's true, it has signatures of Fields Medalists - but also of undergraduate students, artists, philosophers, engineers, medical scientists. Please, do not feel intimiated; if you support the petition - sign it."

The email address can be found at the blog for the petition, or the picture on the right. Professor Borovik has himself given an update on proceedings, which you can find at this post: Black board still under arrest. Other links about the response from various places can be found at the end of the post. That post really sums up how silly the whole situation looks and gives more detail on everything. It would have been better if at least the reason for the persecution was made clear to everyone.

Does this remind anyone of V for Vendetta?

"Intentional Errors"

A found a \sout{nice} funny (I think) post on Intentional Errors by Flip Tomato, an American Physics student in England.

It made me laugh for a numerous reasons. Lecturers will probably be pulling their hairs out upon reading my post, but I'm a beany chicken who is not 'confident' enough to speak up in lectures. I don't know why - is it the fear of appearing dumb, if in fact I've actually said something foolishly ridiculous? Or is it because I can feel the eyes of everyone upon me if I do say something.

I remember a sets, numbers and function lecture on permutations last year. Now I could compute permutations but that was about it. So during this lecture, Fizz and myself were 'whispering loudly' where two was sent to and so on. We were able to whisper loudly since we were sat near the front, and that due to me as well! However, then the lecturer had turned around and asked, 'WHY?'. Yes, it felt like he had shouted this to us. I'd frozen and looked towards Fizz to answer. Fizz had looked behind me, in case the lecturer had asked someone behind us. I'd then pointed at us and gestured whether he meant us, and he made it clear that he had meant us. He waited patiently as I waited for my tongue to untie itself. In the end I'd spluttered that pi sent one to three and then delta sent it to two. (No, I don't remember that - just making it up!) After this I didn't say another 'loud whisper' during the lecture, but meekly whispered to myself.

Why, I don't know! On an another occasion, with the same lecturer, we were doing Euler's totient function. (is that what it's called?) The previous lecture we'd worked out that \phi(100)=40. I had remembered this since I hadn't followed something in the proof during the previous lecture, and had spoken to the lecturer about it. So when asked what \phi(100) was, I had said 40 but this time loud enough to be heard, but not loud enough to be spotted! This lecture was one that I'd particularly enjoyed since I also remember the calculus lecture on that day as well. We were using Euler's Theorem (and Fermat's Little Theorem) to work out things like 4^100 mod 7 etc. The lecturer had made a question up (I think) and asked something along the lines that we might need to use our calculators. I didn't have a calculator on me, and to Milo I had gestured that this was because I had one in my head! The lecturer had spotted this, and so it was me who had to say what 32^2 etc were (and that using my head). How did I manage it eh, since we all know that my brain has no such calculator!! Milo to the rescue it was, who did have a calculator, which found itself on my lap. :D

That's enough of my trip down that memory lane, but even during that lecture when I had said something I'd whispered it 'loudly'. The lecturer could barely hear me and kept on saying, 'I hear a quiet 3 over here' and when he did know it was me saying the answers, I had to say them three times to be heard. Once again, it was really nerve wrecking. * (BTW - the calculator was spotted and found guilty on three charges. Its always sad when a good calculator turns bad... and me, well I was found not guilty of course! I hadn't put the calculator on my lap. :D)

The stupid thing is that I never learn to keep my mouth shut! However, saying what number goes in a certain place is not too difficult a thing. It is when asked why that I freeze. I also find that if I don't understand something that has been written, I'm unable to say so during the lecture. This is also true if I do spot something that looks 'dodgy' on the board. The 'dodgy' things (i.e wrong signs etc) I mention to Fizz and if someone else hasn't already pointed it out, Fizz does. I mean someone eventually does point it out, so it doesn't have to be me right? Most times it is me who is wrong, and after my personal battle with what I've written, I put a star next to it and try to speak to the lecturer at the end about it. (I tend to struggle over a trivial point at times - one being that c(u.v) doesn't equal cu.cv, so it makes sense to keep quiet.)

In my second semester, I found myself in the same position in Linear Algebra lectures. In the last lecture I had \sout{said} whispered the words, 'eigenvalues' and at the end of the lecture, a girl who was sat in front of me had turned around and said, 'I can't believe that it was you who said that! I'd never thought that day would come...'. :D Hehe, I've spoken to her on a few occasions and well she knows my bouncy self you see. It's just that there are about 300 people present! I'd laughed with her and joked that was I expected to shout?

The thing is that this problem only exists in lectures, and not in my supervisions. In the beginning I wasn't as vocal in my supervisions and was the way I'm like in lectures (loudly whispering what I think is the answer). However, after I became familiar with my class mates I became OK. If I didn't understand something I did mention it and did ask questions. (What I didn't do was that if it was explained and I still didn't understand it, I sometimes used to play along and hope that it did eventually click!) The way I learn maths is rather weird. I hope to talk about that in another post, but naturally you can't expect anything I do to be normal! I think I get intimidated in lectures by the people I don't know. I need to sort this mental problem out, since although I can survive, the problem will grow. The thing with my 'confidence' is that its simply weird as well. :D (Just like everything else related to me). If I knew everyone then I don't think I'd have this problem, but the chances of that happening are zero.

I'm not as bad as I make out to be, but there is something else that sounds embarrassing. (I'll try to splutter it out though). Since I've discovered the beauty of maths (when I found the right motivation), I have somewhat become obsessed by it. For some reason I've tried to hide this 'obsession' from the 'real world' and my outlet for it has been this blog. I'm no genius and I think that I enjoy the fact that I have to work hard in maths to get somewhere. It's the same as the Bob the Builder work that I enjoy doing. I like it because you start with a wall, and then you have no wall (sometimes). Because of this I do spend too much time (according to many people) doing maths, sometimes getting no where. I guess we're all on different terms with maths, and during the year my ambitions were sky high.

I don't really know what I'm getting at, but I think because I've been trying my hardest to 'not' let on that I love studying maths, and that I enjoy studying it, I become tongue tied. I know its stupid, but I've never really spoken to anyone who sees what I see in maths. We all complain about exams, homeworks and I sometimes join in myself but that is all everyone seems to be doing. I know we can't always talk about maths, but where is that positivity? Apart from the work shop module and talking to the Tweenies or lecturers (and someone called Bilbo) about maths, I haven't really ... talked much. That is why I probably don't want to 'let on' that I'm obsessed with maths. I know I'm from another planet, which is probably one reason for this, but I reckon I should stop making excuses now!

It's not everyday though, that I find the need to speak, and I don't think I'll ever say more than one number or word if I have to. I think another reason for this is that I normally talk fast, and when I'm nervous, there's no stopping me! (That's probably why I have to repeat everything on more than one occasion). With all this is mind, if the lecturer from that other post was to deliberately make a mistake (which I surprisingly spotted!), and there was a small group of us, I would probably just ask, 'Is that meant to be whatever you've written'. (That's what we used to say in our supervision class if the need arose. :D)

Sorry about this lecturers, (who might ever lecture me), but I only do 'loud whispering'. If you ask any questions and notice someones head disappear, it wasn't me! (and if I do have any problems, I'll most likely, much to your annoyance, try to speak to you at the end!) I know it's stupid of me to stay quiet if I do notice something amiss, but that's why I always tell Fizz who does speak up. :) Problem solved eh? Lecturers do hate it as well, since once after I'd gone home and read my notes, I'd spotted something that didn't make sense. So at the end of the next lecture I had asked the lecturer about it, and he was annoyed since during the actual lecture one student had spotted the mistake(?) but not pointed it out because of being scared. That sounds awfully familiar. :o I wonder how things are going to be like in the second year.... (I think that the size of the class is going to be smaller then so it might not be as bad).

So what would you do - sit quietly and approach the lecturer at the end, or say something if you spotted a mistake? Or if you had a Fizz next to you, would you tell Fizz to speak up?

*During that Calculus lecture I think we'd been talking about Green's theorem. I was once again spotted nodding my head when the lecture said something about wanting recipes. :o

Thursday, August 09, 2007

Dangerous Knowledge

22:05 Dangerous Knowledge
Maths and Madness: Part of the Science You Can't See season. David Malone looks at the work and lives of Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing. [S]



No, I didn't watch it all if you're curious. However, after the Real Hustle (pfft) finished, I was able to persuade the remote holder to flick over to BBC4. I had actually been whinging throughout Real Hustle for the channel to be switched over, and on two occasions (to shut me up) this proved a success. However, supposedly, the narrator of that programme sounded monotonous! I managed to see someone writing something, and then make circles with their blood before it was turned over to the real hustle again.

The teletubbies also made the link to 'Maths and Madness' and so my path in life is defined. (Well to them anyway!) They found the two second viewing of it quite depressing and so I had another mini sulk as I glared at the real hustle. Thankfully, when it finished I was able to watch the last couple of minutes of 'Dangerous Knowledge'. It was quite interesting and TW actually seemed to be watching it. (Well apart from when I was told to shut the heck up, when I got excited to see TW watching it, and explained something further. I was told, 'I can hear you know!' I had asked for that, but it was most shocking and unlike TW behaviour).

The bit we watched was about Alan Turing, and one person was saying how Turing liked to think of himself as a machine. His unfortunate suicide and circumstances were mentioned as TW watched. (Po was there as well but just making sarcy comments which were ignored.) Then Gödel was mentioned (and I realised that I'd been embarrassingly mispronouncing his name as God-el!) Once again it was the cue for me to start talking to TW about Gödel, and once again I was told to shut up. I don't really know what made TW watch it, and I didn't dare ask at the time. However, Eienstein face was welcomed by a cheer from the audience who recognised him! The other mathematicians who were mentioned (Cantor and Boltzmann), I'm not too familiar with. Well I'd never heard of Boltzmann before(!) but I know a little about Cantor.

Anyway, from the bit we watched, the uncertainty of mathematical logic was spoken about. I mentioned this in one of my earlier mumbo jumbo posts, Maths: something .... , however as always, I had a lot of preamble there. I think I want to re-say that I really like this uncertainty business. I think it fits with everything nicely. I don't really know what I'm saying, but to me this uncertainty is like one of them mathematical secrets! You might want to stop reading now, but it's one of them things that when someones talking about maths, you can think to yourself, 'Ah, but I know this one thing that you don't'. Not in a unfriendly way of course, but in that quietly something way. It's that thing that sticks out in a painting and leaves a lasting impression. I'm not saying that other things in mathematics are not fascinating, but this uncertainty has really made me 'awe struck'.

I seem to really ramble a lot about this subject, which I have close to zero understanding off, so please excuse it. What I gathered from that programme was that Turning liked to think himself as a machine, whereas Gödel valued human intuition. I can understand why Turing was probably drawn to machines, since they 'don't lie' and can be called, 'honest'. However, I hate the notion of humans being machines. It seems like a lifeless notion, to call a mathematician a machine! I think one reason why I'm excited to talk to mathematicians and talk to them about their research, (even though I don't understand it), is because a mathematician is very much alive. I get excited by the prospect of discussing maths no matter what the topic is. Mathematicians make mathematics what it is, and it is namely because of mathematicians that other 'young fools like me' want to learn more about maths. If maths just existed and was done by robots and machines, I don't think I would find myself enchanted by it, as I do now.

Mathematics is an alive subject, and you can actually breath it in most times. Mathematicians, who do maths obviously, can't be machines if they're doing an alive and energetic subject!! I mean they make the subject alive and interesting. Machines seems to go against everything. I know that sometimes we're robotic in out actions, but although I've forgotten what Gödel said about this, he was right. (Well its in my head, but escaping being formed into a sentence!) I don't know why, but I liked the sound of Kurt Gödel. He sounds like an interesting fellow, but Po wasn't amused to hear that he made his wife try all his food before eating it himself! :D (when he thought someone was trying to poison him).

Hmmm, I'm not liking the name of our new maths building being called 'The Alan Turing building' anymore. I mentioned this to TW and was shocked to hear TW suggest that can't it be called 'the Fermat Building'. So they do actually listen to somethings I say - hurrah. I'm not saying that Alan Turing wasn't a brilliant mathematician, but I don't like the notion of machines. Which mathematician would you want to name that building after? Naturally I'd choose Galois, but I think they were looking to name it after a Manchester Mathematician. 'The Turing Building', sounds much better than 'The Alan Turing Building' as does 'The Newman Building'.

BTW this was not the post I mentioned in my post a few hours ago! This was as a result of me getting excited about hearing what others thought of the uncertainty of logic. One guy was of the impression that it should be brushed under the carpet. I disagree - it should be there in the middle, making a statement. Saying that we know this, but still we have so much brilliant mathematics that we can create and use. If I was to draw a picture to describe things it would definitely have that in the centre - a dark jewel of some sort. The Music of Primes has just started now, and I must return to my sulking for the remote is once more, no longer in my hands! Wow- I'm feeling rejuvenated! (or has my madness already started).

A (rather long) passing comment. I was asked: 'If you were an employer, what are the three most important things that you would look for in applicants, that were being interviewed.'

The thing that I remember putting down was enthusiasm. That is what differentiates us from machines and robots. We can be enthusiastic about what we do, and we should aspire to be enthusiastic in whatever we do. Since by doing so, we make the task at hand much enjoyable and lighter on the stress points! So yes, although I'm never going to be employing anyone, I know that what I admire in a person is there enthusiasm which can hopefully carry them through and which can be passed onto others.

I think this enthusiasm and energy is a particular trait of maths teachers as well. Mathematicians are enthusiastic about their maths, and this they show to the students, who in turn hopefully feel that same energy. I think this is where I've been lucky. Although there are different levels of this energy and they are shown differently by different people, they make a difference. Sometimes you feel this energy in the way a certain thing is explained, and other times you feel it from the voice and movement of your teacher. You feel a reason to get excited and happy and then you want to know more. You want to be there with that euphoria.

From my own experience, without a doubt, I've got to say that those lecturers and teachers who have taught me without this energy, have sadly made me not like subjects (and consequently I do badly). Thankfully I was saved in sequence and series and also in mechanics! (I can't believe that turn around). And so it is now that I hope that my stats lecturer next semester, can bring about a turn around in my attitude towards stats. :) Should I leave this in the hands of my lecturer? I think that I must, for I will never on my own feel that energy about stats! It's erm.... lifelesss *runs away from statisticians*. My attitude is positive at the moment, which is a bonus, but I should try and bring that energy myself, if the lecturers and teachers don't. I should but don't, but I will.... someday! I think that when I see my lecturers passionate about teaching and about maths, it passes onto me. I don't really want lectures to end at times. (Yep, having watched that programme I'm missing lectures. :( )

Wow that was a very long passing comment. I'll zip it now!