Tuesday, July 29, 2008

A Blade of Grass

A Blade of Grass by Brian Patten

You ask for a poem.
I offer you a blade of grass.
You say it is not good enough.
You ask for a poem.

I say this blade of grass will do.
It has dressed itself in frost,
It is more immediate
Than any image of my making.

You say it is not a poem,
It is a blade of grass and grass
Is not quite good enough.
I offer you a blade of grass.

You are indignant.
You say it is too easy to offer grass.
It is absurd.
Anyone can offer a blade of grass.

You ask for a poem.
And so I write you a tragedy about
How a blade of grass
Becomes more and more difficult to offer,

And about how as you grow older
A blade of grass
Becomes more difficult to accept.


I found that poem through Dr. Coleman and at first I didn't understand it. Well poems are unique in the sense that we all take different meanings from them, but initially I had dismissed this without reading it. And then I read it. I read it twice or three times and I understood what was there for me to understand. My problem with poems is that I could you tell you what I think of them, but I can't write it. Well not properly so I won't bother.

Anyway, I think that poem is simply brilliant, for it echoes some of my thoughts last night which went unpublished. Sigh. Yes, this poem is about growing up to me and the changes that are expected of people once they age. Note the word expected--that dastardly word, which haunts me at times. I don't think you can blame some people for asking for a poem, for the sad reality is that they have been told that there is no alternative: there is no place for people to offer a blade of grass.

Friday, July 25, 2008

Wrting to Learn Mathematics

I found a book which seems interesting and is called: Writing to Learn Mathematics... You can actually read the first few pages of it, which I strongly recommend. The synopsis of it says, "This text demonstrates that the use of journals, learning logs, letters, autobiographies, investigations, and formal papers can improve the reasoning abilities of maths students“. I found the book link thanks to Jon Ingram, but I haven't read the thing myself.

Anyway, the point here is about writing and in particular writing Mathematics. Once again the old age debate is awoken about why people study maths. Now most prospective first years, fresh from their A Levels, might echo that they chose to study Maths because in English all you do is write, whereas Maths is special and only involves numbers.

Boy will them students be in for a shock! (And I say all this from experience.) The first week will be like a blur - finding ones feet and making new friends whilst trying to keep up with the studies from the beginning, You will make the friends and will establish your routine, but then it's week four and the warning bells start ringing. The advice of your lecturers and personal tutor walks with you, shattering your peace - "study as you go along; maths is not a spectator sport, it is like learning a new language" they say.

Week six it's reading week and you sigh with relief. There are coursework tests as soon as you head back, but hey this break is well deserved and revision will have its own time. Now if you are at Manchester you will be cursing the very language of English at this stage. Why? Well we have this workshop module which requires you to investigate a topic, answer some questions in a group and then hand in a written report on everything! Isn't that just brilliant?

Towards the end of reading week you have yet to write your report, which means you have to use sentences, paragraphs and proper words! You have also yet to revise and catch up on things, so you hit your lowest point and think about giving up. The pressure is too much for you to handle and the report is just a thorn in your brain. You start asking questions for ways out, but then you are reminded of who you are... a mathematician. You remember why you studied maths... the challenge. You go back to the friendly territories which pacify you and give you courage. No report (with proper sentences) can bring me down.

Obviously the experiences outlined above might not be faced by any student, or only a few (or one!) Nevertheless, the amount of times I heard "I studied Maths to avoid all this report writing mumbo jumbo" was unbelievable. And yes, in the first six weeks I was part of the group who complained about this until we went blue in the face! I complained some after the first six weeks, but then it was half heartedly as I had been given a second chance. Redemption.

Nowadays I complain until I'm blue in the face, at the fact that secondary school teachers tend to implant the differences between English and Maths into student's minds. It is not uncommon to hear a Maths teacher boast "there's only one right answer and you don't have to write much" to her students. And equally, an English teacher never fails to express the fact that there can be no wrong answers in his classroom, because English is full of possibilities.

You step back from this picture and question both teachers. Maths is full of possibilities, and the correct answer isn't as important as one sometimes makes it to be. (No hard feelings towards "right answers" here, but boy do they kill any fight students might have). Maths is a creative subject, as is English.

Students are not aware of the creativity of Maths because they are not writing Maths using English. Numbers and symbols have no life and meaning on their own (apart from a few delicacies!). It is the words -- the adjectives, joining words, and the sentences which give the numbers and symbols their life. The mathematical story can only be told with both numbers and words.

How can we expect students to believe that maths is a creative subject, when what they see tells them something different? I don't think Maths should be an alternative to English. I mean, if you can't spell then you shouldn't just focus on the Maths and use the fact that Maths has no word as justification to not being able to spell. You shouldn't use the fact that you study Maths to justify anything you can't do. The human is a wonderful creation and we are designed to learn at all times. Learn about the world, each other and how to spell! Seriously, do you think I could spell once upon a time? It's quite embarrassing when I realised that I had spelt a post title wrong, which spell check doesn't pick up! (I still can't spell certain words, and my grammar and punctuation aren't particularly good).

I agree with the synopsis of the book that Maths students should write. Not necessarily write Maths all the time, but anything ranging from articles, stories and so on. My interest in English was developed by my English teacher as she realised that I enjoyed the creative writing part of the exam! She made me enter some short story writing competitions at school and college, after which I gave up. However at University, call it a freak accident if you might, this blog came along which really developed my English.

Somewhere along the lines I think my blog helped me in my Mathematics too, especially the posts when I whinged about not being able to understand something or being unable to do a question. So I am all for Mathematics students creating blogs, or just writing Maths or anything else using words. I guess writing things down helps our brains to process them. Did your blog help you in anyway?

PS: Didn't mean to scare any prospective first years by the first six weeks narrated above! I suffered because people kept telling me to change course, which didn't help, however I am sure you will make the switch to university Maths painlessly. :)

PPS: If I disappear from the face of this planet it is because of the creature occupying my room, which might eat me. The disadvantages of sleeping on the floor I suppose, and for watching Dr. Who! I'm being serious by the way! I don't know where it went and it was not a spider, so my imagination has become even more active. If only my sonic screwdriver was working... erm, just keep looking over you shoulders!

Thursday, July 24, 2008

Circle Theorems

It is that time of the year again, when I can become very frustrated. Today was my one day off and I had planned to do nothing (which means watch Dr. Who and be a couch potato)! However my Dad happened to ask me to study maths with my ickle (and annoying!) little brother. (I guess the annoying factor runs through the family). Grumbling I muttered that I will do so later, as apart from my dad, no one was too keen on this. Circle theorems was the chosen topic and I had the whole day to do this.

More on what I forgot to do later, but in the book there were three theorems of which I will only mention two.

1) The angle at the centre
The angle subtended at the centre of a circle is double the size of the angle subtended at the edge from the same two points.
So in the above case, a = 2b. You can prove this by simply splitting the above funny shape into two isosceles triangles, and playing around.

2) Angle in a semi-circle
Apologies for not labelling my diagrams, but the angle formed when we join lines from the ends of the diameter to the circumference is 90 degrees.


Sadly in all my childhood the concept of proof was alien-ish and not regarded as important. The challenge used to be in finishing the exercises first. However, today I questioned the second theorem and why we get a right angle. My brother thought I was playing a joke on him, but I was deadly serious when I asked him why the angle in the semi-circle was always 90 degrees.

Having just worked through theorem one, the obvious idea that we came to was that the angle subtended at the centre of the circle happens to be 180 degrees. Hence by theorem one, the angle at the circumference is half of 180, which is 90 degrees. I wonder though, why was this little fact or connection between the theorems not in the (GCSE) book?

You can also prove the second theorem by creating two isosceles triangles again. I may have imagined it, or perhaps I wanted to see my brothers delight at having proved the fact, but there was something or other expressed on his face. I think he tries too hard to not like maths, when he actually likes it. (He's not had the best of teachers).

I was imagining the consequences if he actually went on to study maths, and I decided he is best doing something else. (Namely for my peace of mind!) That being said, he is mathematically more able than I am and I think my dad's idea is a good'un. However he doesn't understand that teaching is not always a liner process, and it is best to first let my brother have the wow-factor for maths. That was my plan when I got him to do the puzzle "Who owns the fish?" which he successfully managed to do. I was delighted at this for I had been unable to solve the puzzle when I was at school. (More reasons for him to study maths I suppose, but you didn't hear anything from me!)

If anyone does know any good site with nice and complex (logic) puzzles, then this bean wants them! He really liked the Fish one and keeps on asking me for more. Well what you rather work on, a logic puzzle or circle theorems?!

Tuesday, July 22, 2008

Nesin Mathematics Village in Turkey

Well I am guessing that Nesin Matematik Koyu translates to Nesin Mathematics Village. This is the very same Summer School whose activities made us happy, when reported by Professor Borovik last year. However soon an outrage followed as the school was made to close, due to some "dodgy" reason or other. As Stuart Little once said (or was it his dad?) there's always a silver lining in the cloud, and we were all happy to hear that through the perseverance of the Professor Ali Nesin (I believe) and others who I don't know (but who still deserve credit), the school reopened again.

This post though, is concerning the activities of the school this year. The Summer School has had a make over and is now called... *drum roll*... Nesin Mathematics Village, whose homepage can be found here. (There is a button which says "English" under the banner). As you can see it is no longer a Summer School any more, but much more.

Once again I find this a fantastic creation and wouldn't mind something similar taking place closer to home (eg Manchester). I say this because I am officially a lazy so and so and can't seem to motivate myself to learn from books. (My mum made it official by calling me a lazy ***, which I will leave you to guess!) I feel hypocritical sometimes when I talk about how maths is cool and then I can't open a text book to learn something new. I seem to always need lectures/lecturers to motivate me to study a module further. (This is why I am now rethinking a third year project now... So how many times have I changed my mind already?)

Back to the Summer School. At Manchester MODNET took place this year but that was for pesky I mean, awesome and lucky post graduate students! (Nah--I'm not bitter about this arrangement... honest!) Sigh. That was one of them sighs of "longing". Nesin Mathematical Village is the whole package. It has everything a mathematician could possibly ask for, although I am not sure if I read anything about tea!

The positives we can take from the Village's activity (NO-this is not The Village) is that one should never give up. Regardless of whether the issue at hand is a Maths summer school or an English book club, you should not be afraid to rock the boat. I asked the question to an old friend the other day, about whether or not stubbornness is a good quality to have. Stubbornness has many forms: assertiveness and persistence to name a few. Ali Nessin was persistent and achieved what he has, so here's hoping for another successful year of Summer School.

I can't really comment on the activities of the place, but I imagine that they must be similar to what Professor Borovik described last year. (I'll leave the mathematical activities to ones imagination!)

PS: Anyone interested in started something like this in Manchester should drop me an email!

Sunday, July 20, 2008

How to say that I study Mathematics

I have on numerous occasions, commented on peoples reactions upon hearing that I study Maths. These range from shock, admiration, disgust, paranoia and on I can go. The most common reaction though tends to be: "You must be really clever then. I can't do Maths if my life depended on it. Brain box..." And on they go, embarrassing us in the process. (If you were suffering from low self esteem or were feeling down, you could always say that you study maths to cheer yourself up! I mean, some people will say not nice things and others will back off in fear, but there's always a nice word or two that's thrown in!)

There was a time when I got annoyed at comments claiming that I was a brain box, namely because I wasn't feeling particularly clever at Maths! However, there can be no rest for the wicked, and then the comments about me being stupid to study maths started, and that I should transfer course. These I confess were worse and more demoralising, but I have been braving them as they come along.

Over the two years that I have studied maths, I have started by shifting nervously on the spot and whispering "I study Maths" when asked, and then bracing myself for the loud and horrified reaction from the person who asked. Sometimes the horror turns into ridiculous positive comments, but "you're mad" is always echoed.

However, as I started to mature mathematically (!) I began to scare people when they asked me what I studied. I mean everyone's allowed having their fun right?! This was especially fun on trains, where I used to sometimes take my work out and do some sums. I have an erm... bad habit of talking to myself when I study maths, so this further freaked commuters! And then when I left a book open with beautiful sums, they couldn't take it any more. However my evil side wanted more, which involved talking about maths to a friend who was travelling with me! (Ha, I confess to deliberately having maths conversations on buses to see peoples reactions.)

Sometimes though, as I read my text book on Complex Analysis, I got lucky and bumped into someone who was also enthusiastic about Maths. (Might I add though, this is very rare!)

This game was modified for when relatives or friend asked me what I studied. I said maths and when they mocked me, I sometimes started talking to them about prime numbers or other times about groups. Why? Well no one wants to be sat next to a relative who obviously didn't want to be there? As soon as I got to the part about group operations, people would excuse themselves! (Trust me, if you ever want to be left alone for whatever reason, try this! If you never want the person to bug you again, follow them for a bit and talk about cool maths...)

Yes, I am further displaying my freaky nature, but I have yet to follow someone! (Seriously though, do people have any idea about how many hearts a mathematician has, as they persist in breaking it every time they ask us the question "Ew, why maths?")

Now as I am mathematically two years old (still immature) but with lines of time cleverly disguised on my face, I have come up with a solution to this problem. Next time when someone asks you what you study, look them in the eye (with a serious expression on your face) and clearly say, "I study Mathematics at university". Full stop. Then watch and wait for their response.

Don't laugh and mutter "I study Maths", or even whisper it. Say it seriously and they will take it seriously. (Well there might be a few outliers, but we'll put that down to you using the wrong tone of voice!)

When did I come up with this plan? The other day actually, as I was stupid enough to laugh "haha I haha study haha maths...haha". That's not very funny is it? And the person thought I was joking too, which might be the reason that he didn't take me seriously. Actually no. I am not going to defend him because he's the type of person who feels that only he can do the job at hand, and no one else can. Well obviously if no one has taught me how to use a certain computer package then I won't be able to use it, but you have to give me the chance to learn. Grr. Yes, due to this person looking down at me and assuming I am an incompetent fool (which I can be), I got thinking.

You don't have to be smug when you say this, and there's no harm in smiling. Just remember: It's not Maths, but Mathematics. And no laughing or whispering. Now we shall see how the tables turn. *cue evil laugh* Erm I mean, we have look out for ourselves, wouldn't you agree?

Friday, July 18, 2008

Okay Doctor, what now?

Someone just told me: "Okay Doctor, what now?"

That's the most fantastic thing to say to a Dr. Who fan (and someone whose read The Metamorphosis!) What's wrong with the world today? Is tomorrow going to be a horrible day, hence the sweetness today? Oh, I have been invited to a birthday bash tomorrow, and it's for a four year old--mini bear, a fellow Dr. Who fan. He normally runs to my room as soon as he enters the house, and takes my "Dr. Who toys" downstairs and plays with them, hence why he's getting some tomorrow.

Talking about Doctors, for all those who haven't heard, Craig Laughton (author of Gooseania) has passed his viva with minor corrections. So after his graduation in winter, he will "officially" be called Dr. Craig Laughton. (But we don't really care for officialness here).

Craig's acheivement took me down to memory lane (again!) for it was indeed his and Professor Borovik's blog, which motivated me to create my own ickle thing. Understandably mine is somewhat disorganised (I'm only a child, I mean undergrad), but rest assured not all of us are like this.

I found Craig's blog when I was desperately searching for my workshop supervisors email address, because I couldn't understand something. On the postgrads page though, I found some home pages which sparked my interest. I hope that Craig does continue writing something, for it definitely has been a good read! Indeed, before I made my blog, I invented the "Craig spotting game". One point for seeing him in the Newman building (doesn't that make you feel old!) and points increased the further away you moved from Newman. OK, I'm lying about this game, but I did used to see him sometimes (workshop mainly) and go "found you" to myself, whilst he didn't know who I was. That's obviously changed now, thanks to the new building, but he's harmless so I can breathe in peace!

The trio of Manchester Maths blogs will be broken now. (Now you can get the tissues out, or find someone to fill that hole!) And no I'm not only saying nice things about Craig because he came to The Galois Group lectures... (Am I that transparent. ;) ). He will be missed in Manchester, but all the best to him for the future. It was his blog which got me wanting to do a PhD myself, but I am being realistic about that now. :)

Can I go back to pretending that I'm "The Doctor" now? :D

A first time for everything

I don't normally do "pop quizzes" like what kind of fruit are you, but a friend sent me a curious link which I couldn't resist attempting. Namely because it was called: What one word embodies you? I like playing with words, and my curiosity got the better of me, but still I normally wouldn't post such things on my blog. However I will post the result on this occasion because it is somewhat freaky!

I am the embodiment of Freedom. You are person that loves to live and breathe the open air. You loathe structure and convention, and rather love freeform. There is no such thing as limits or boundaries in your vocabulary, because you view them as man-made creations that are utterly useless. No one can contain you except yourself, and your attitude is that that is how it should be. You are a person that can go up, down, horizontal, diagonal�ultimately any which way you please.

*Shudders* Freaky because just the other day someone mentioned that I have rough edges, and told said that my teachers should have smoothed them out when I was at school. (This person was scared because my "rough edges" were scratching his smooth surface! Ha, but he's an OK guy some days.)

So which word embodies you? (Call me a nosey git...)

One Two Three... Infinity

The following limerick can be found at the beginning of George Gamow's book, One Two Three... Infinity.


There was a young fellow from Trinity
Who took \sqrt{\infty}.
But the number of digits
Gave him the fidgets;
He dropped Maths and took up Divinity.

Rolls of the tongue nicely. Trinity by the way, is a college at The University of Cambridge, famous for its famous mathematicians!

I found the limerick in Paul Nahin's book, An Imaginary Tale, and I can erm.. happily perhaps state that I am on course to finish the book in 218 days, if I keep up my current record of reading a page a day. (Can't you sense my excitement?) Actually I found his preface pretty interesting and amusing at the same time. He's the kinda person I wouldn't mind meeting and talking to, but they say that you shouldn't judge a book by its preface so I will bite my tongue for 218 days before commenting further!

Before I clock of for the day (that's a lie by the way) how do you pronounce preface? Is it "preeeeee- face" or "pref - as"? I'm just curious because I once said "preeeee-face" and was laughed at by some friends, but then I asked a teacher and he said preeeface. However he did debate on whether or not it was pref-as, if it's the thing at the front of books(!) so I'm just checking.

Or is this another word divide between the North and the South? I still can't get over glaaaaaaaaaaaaa....s! :p (I'm joking by the way so you can put away your axes now. And NO I'm not from Manchester...seriously! I guess this is the point I start running...).

Thursday, July 17, 2008

Maths Countdown

Countdown is a programme viewed on Channel Four, and presented by the ITV sport presenter (Des Lynam?!) the last time I checked. Obviously after writing this paragraph I'm going to google "countdown" so I can link it, and will know about the current situation.

.... *googling*

Well here's the link for Countdown, and a new guy is presenting it. They didn't have this name anywhere on the Index page and I can't remember it from before, so I'll leave him nameless for now.

As you have gathered, today has been "one of them days". I am in one of my funny moods and if I was embarrassed easily, I would have locked myself in the attic forever. Well I did get embarrassed because something didn't roll of the tongue nicely, but thankfully no one understand what I was implying so my teeth remained intact.

Is it true that if you drink a lot of Coke/Pepsi, then you can go slightly more crazy? Well this lunch time there was a small do and I do recall drinking a lot of fizzy drink! Surely my behaviour in the last half hour is unrelated to that? (I mean it has been about five hours you see).

Anyway, I digress! Where were we at? Ah, yes, Countdown. The game show I watched after school, but only the part when they did the "maths" (the number bit). My dad and me would have a semi-competition, and neither of us ever won! We would spend too long frantically looking for a pen and paper, and then annoy my mum by holding her responsible if we couldn't find any. That was when I was in primary school, but the numbers ritual of countdown has continued in our house and I still fail at it. (No surprises there, but I'm improving!)

What's this number ritual I talk about? Well you have a set of numbers turned upside down, and you have to choose six. So for example we choose: 3, 7, 9, 8, 8, 25. Now I press a button and the number 369 appears, and you have thirty seconds to make that number with the six ones you chose before. The rule though is, that you have to use it each number once only. (I go into this in "detail" because someone didn't know about it!)

Now I'm useless at the game because I am very poor at mental maths. In secondary schools they have a starter activity where students play countdown at various levels. I feel this activity is very good for mental arithmetic, but I can't help myself and can be found frantically searching for pen and paper! (Alas, there is no mum to hold responsible on this occasion!)

So the point of this post: you should play countdown to help your mental maths. School children enjoy it too because it has some healthy competition to it.

I only ever played it as a student in a further maths lesson in college, and lost on all occasions but the last. That was my moment of glory. I defied the laws of nature and beat my two classmates and the teacher too. Oh that sweet moment will forever remain embedded in my mind. Oh I should shut up now! I'm probably freaking out a lot of readers who didn't start reading my blog from day one... Yes readers, there used to be a lot of these types of posts back in the old days. Please don't sigh too loudly in relief that them days have passed. I can hear your thoughts whenever you read my blog, hence why I have gone into hiding for a couple of days. Actually no. I was abducted by aliens who want me to work and earn money. Well they really want to boss me around and make me feel inferior. They especially enjoy pointing out that "I can't do something" without showing me first! Pftt.

And by the way, I can go on like this forever. This is what you will see when I am on a Galois Group Wednesday. This is me when I am excited and enthusiastic about something and FINE I confess: I've been working on TGG and that could perhaps explain this inane babble and energy.

*makes tardis sounds so everyone gets fooled and believes that I'm going*

PS: Can you believe this (don't comment by the way!): one meaningful paragraph and many others that aren't!

Tuesday, July 15, 2008

Some Latin Abbreviations

Latin abbreviations do tend to pop up quite often, and I recall googling "et al" once upon a time! So below is a list of some abbreviations and the meanings, which I found on the internet.

a) cf -- compare
b) etc. -- and so on
c) viz. -- namely
d) c. -- around, about
e) N.B. -- note well, pay attention
f) et al. -- and the others
g) ibid. -- in the same place
h) i.e. -- that is
i) e.g. -- for example

I actually didn't know a few of them it seems, I mean "c", where would you ever see that?

An old maxim about presentations

The following is something my Dad told me at a very young age. Well I was in secondary school and about to give my first "public speech", and was discussing the topic with my Dad. He then decided to "improvise" on my topic, so I quickly jotted down whatever he started saying, and tried to incorporate that into my speech.

The saying:

Tell them what you’re going to tell them
Tell them
Tell them what you’ve told them.

Even when I did my Galois Group lecture (and offhandedly mentioned it to Pops) he repeated the above three lines, however there was no need this time. Indeed (if I recall correctly!) I started with telling the audience that I was going to tell them two accounts of Galois's life, and it was up to them whichever they chose to believe! I then told them the story (in a slightly messy way) and summarised at the end.

I like them three lines because straight away they give you natural structure. I don't always use them though, for some situations don't require them, however they give you a beginning, a middle and an end.

These thoughts come to me as I think about next year, and think that some students are not volunteering because they have possibly never done something like this in their life. Hopefully though, once the email is sent out, students will volunteer. (Drop me an email if you are interested. Pretty please!)

\begin{aside}
A quick paragraph or two on where I have disappeared too. Well no where really but I am being a really really stupid person and not going to sleep on time. Work and no sleep means my brain is disengaged as soon as I come home. Sigh.

I have got started on TGG's website, but if any person is interested or has a website in their back pocket, then this bean is interested. I have my basic template, but I just need to sort out this css business and, well I have gone to Dreamweaver for help! I've also been playing around with Beamer and more on that when I move from A to B. What else, apart from the usual mumbo jumbo? My holidays will not go as anticipated and are definitely going to be the worst of the bunch. I sometimes wish I had a proper team for TGG and then I wouldn't always be using "the Royal" we. I haven't got started on my jobs for TGG which is causing me to stir in epsilon panic...

Oh, before I forget, The Forbidden Kingdom is a must watch movie. It's not just about Kung Fu (OK I lie) but still, it made me laugh and kept me entertained throughout. There is this one particular scene which still makes me laugh, which is when Jackie Chan tries to "make rain". Jet Li and Jackie Chan in one movie is a must watch. \end{aside}

Sunday, July 13, 2008

The Complex Number Song

(Tune: The Battle Hymn of the Republic)


Mine eyes have seen the glory of the Argand diagram
They have seen the i's and thetas of De Moivre's mighty plan
Now I can find the complex roots with consummate elan
With the root of minus one

(Chorus)

Complex numbers are so easy
Complex numbers are so easy
Complex numbers are so easy
With the root of minus one

In Cartesian co-ordinates the complex plane is fine
But the grandeur of the polar form this beauty doth outshine
You be raising i+40 to the power of 99
With the root of minus one

Chorus

You'll realise your understanding was just second rate
When you see the power and magic of the complex conjugate
Drawing vectors corresponding to the roots of minus eight
With the root of minus one.

Chorus

Now don't go singing that everywhere (otherwise you will have me disagreeing with the chorus!).

EDIT: I found this pearl in Paul Nahin's book: An Imaginary Tale.

Wednesday, July 09, 2008

"Dissappear, evaporate..."

"And teleport?"
"Gah, just *.....* We're trying to watch something here!" (I'll leave the blank to your imagination!)

Fine I confess. I've been watching too much Dr. Who lately, but you've got to let me have my one second of "sense of achievement". "I'll just teleport outside..." No? I see you are "not amused" then*. :D But I like it and I'm using it (but perhaps I should wait for my ankle to heal before I try any more party tricks!)

Whoops sorry again. I got the box sets for my birthday (because they became number one on my list you see!) and they are just brilliant. One reason why I like Dr. Who so much is that I don't have to worry about it not making sense. Isn't that just great? You would think that since I don't make sense half of the time and Dr. Who (sometimes) doesn't make sense, both of us would understand one another!? It's not always like that, but we have an understanding. (I'm slower on the uptake).

It's just my dad and me though, who you will find watching this show, for everyone else finds it (and us!) sad. There is something about the show that amazes me, but ask me what if you ever see me.

I think that's my one second over, so I'll erm... just teleport away! (Don't you just love it?!)

Monday, July 07, 2008

Knowing a little about everything

This post is basically for the following quote:

"Since we cannot know all that there is to be known about anything, we ought to know a little about everything."
- Blaise Pascal

Which I think is a very nice way of putting things.

I was supposed to go back to that school this week but I still can't walk "fluently" so that hasn't been possible. I have been hobbling but I can't run or jump, which is what I'm waiting for. That being said I will be going "back to school" on Wednesday regardless of the ankle because the maths teacher wants me to help with the open day. (Something to do with paper folding!)

I don't want to go back for two reasons. Firstly I erm... haven't completed the resource sheets yet (!) and secondly, I was enjoying doing nothing i.e. going to sleep when the sun is rising, and waking up at midday! Hey, that's my typical holiday routine so don't you shake your heads just yet. Some say it's at that time of the day that I get my bright ideas. Well I will have to contest that myself, but when everyone's asleep I can "work in peace" so to speak, without any distractions. At this moment in time though, I haven't been liking the routine because it can be counter productive; for if I'm unsuccessful in working at midnight, my whole day has been wasted.

Also waking up early is great for then you feel like you have your whole day in front of you. See, I contradict myself! (So I suppose you can continue muttering under your breath and shaking your head!) People find it hard to believe that I do this, but I'm not oversleeping... just sleeping at the wrong time. Perhaps going back to school will sort me out for a few days. I haven't done any work this week due to my sulky teenage behaviour, because of not being able to walk. I did manage to watch a whole series of Dr. Who and a great many movies though, with a lot of tennis thrown in. (Not that exciting I must admit, but to make myself feel better, I had to have a week of being a slob!)

So my agenda for The Galois Group stares me in the face, but it causes me a mild panic now. Here's is a little of what I have to do:

I have to find a lecturer for the first ever lecture. This is very important but I have the names, they just need asking. After this I have to contact all students begging I mean asking them to volunteer to give a lecture, and reminding others of their past promises. If that fails my backup plan is to ask last years students to do another lecture.

I also have to start my work on Infinite Descent, which once again requires millions of emails to be sent out. I'm waiting for the opportune moment to send these emails, which isn't just yet. (I don't think students want to reminded about university soon after their results have been disclosed).

There's loads more too, about advertising etc. but I won't bore you with that. I also have to do some reading about my potential project. After I've done an epsilon amount of reading I will see Dr. C to decide whether or not I want to do a project. Hmm. My next year module options are going to very very tricky. Namely because I'm going to choose them under the assumption that I will be doing four years, even though I haven't transferred onto that course yet, but in case I do. Whether or not I do a project will also play a large factor in this, but do you think it is foolish for me not to do the project because I have a higher chance of doing badly in it, in comparison to a written exam? Sigh. Some people are telling me that I am fool for doing a project when it's not compulsory, whereas others are telling me to go for it. I guess one reason as to why I want to do a project is that if I don't do four years, I'll have at least done some sort of project.

The other cack thing is that my first two years count for Jack if I do do four years, which isn't very good since I've done OK! I can't imagine next year to be easy, so do I let my motivation be "the final end product" that is my degree classification, or should it be maths. I still want to meet my expectations, but this year I messed up by taking the risky option. (I did logic and discrete even though I was advised not to. I argued that I want to do the maths etc whereas my friends told me that the result matters. They won at the end of the day.) Or did I fail because of my other ambitions? Lots of questions but I do worry about how I am going to finish university with the degree I want at this moment in time.

OK, this post has gone on for longer than anticipated. Now you know what my friend meant, during college, when she loudly exclaimed, "Do you know something Beans, you think too much!" I don't think too much (erm!), but I unnecessarily worry about too much sometimes, which can't be helped. (Or can it?)

Well all these tiny beads actually contribute to my heart beat rising stupidly, when I think about next year. (NEXT YEAR! I'm mad - the holidays have just started. Well four weeks have already zoomed by). I need to get into a positive routine during these holidays.... starting from next week of course. :D

I'm in a cyclic mood at the moment so we will finish with a quote too:

"You don't get anything clean without getting something else dirty."
- Cecil Baxter

Maths License Plates

I found this very "nice" post about what license plate a mathematician might want to have. As someone suggested, I wouldn't erm mind having abelian as mine! (Come on now, admit that it's cool!) If someone's scratching their head about that then please follow that link...

Anyway, does anyone else have any bright suggestions? (I can't really think of anything at the moment, apart from trying to use binary). Don't worry about sounding lame or sad (!) we're all mathematicians here.

For the UK plates you can have a play around with trying various combinations here (and no I wasn't really that bored!) I couldn't get abelian but I tried to get the next best thing... (you might want to click on it if you can't read it).

The year 2036 eh? Well that gives me plenty of time to pass my driving test then!

Calling all undergraduate Maths students

If you have a blog please could you post a comment, so that I can add you to my new blog roll on the column to your right hand side. Surely there can't only be about four student mathematics blogs out there? (It's nothing really that fancy but it tells me when blogs are being updated which is a bonus!)

Or if you know of any other undergraduate maths blogs, please do let me know so I can have a nosey through them!

Saturday, July 05, 2008

What do Mathematics students do?

The following questions are taken from "Some myths and analyses on learning and teaching mathematics" by George Brown (Teaching methods and Educational Technology, Nottingham University). I have written the questions and then tried to give my answer to some in another colour. I welcome others to answer the questions too.

1) Do students learn mathematics during lectures?

We do learn mathematics from lectures, but only the "chapter zero" on some instances. Obviously we can't answer this question on a general level because it depends on the type of courses we take. For courses which are more about computation and about applying certain methods, we learn from lectures. (How much we learn is debatable, but most importantly we learn some things). For more conceptual courses, like algebra say, the lectures are there to put the stepping stones out. We get a general gist of what the course is about, but we do learn something. So if one listens then one can learn, however some students don't listen and don't learn in this way.

2) What proportion of the lecture class is devoted solely to copying notes from a blackboard or overhead projector?

Once again this varies depending on the course and lecturer. Some are able to balance the two nicely, which is a "Eureka" moment!

3) What are lectures in mathematics for?

Lectures are there to tell a story. The more fascinating the plot (determined by the author/lecturer) the more attentive we are. I can't think of a better way to describe lectures in mathematics. The lecturers are obviously the story tellers and I have met some fantastic ones during my lifetime! (hehe)

I did write a post about this and I will link it when I can find it. The stories have a plot

4) How do students work in problem solving classes?

Erm... I will take this to mean the example classes we can attend, which are classes of at least 30 people (on a good day), where you work through the problems and members of staff are around if you become stuck. Some students work in groups during this time whereas others work alone. Me... I don't tend to do any work during example classes, but instead I have a nice conversation with the lecturer present about a variety of things.

Well I take my problems to the example classes and try to get them solved, rather than working there. If I don't have any problems to take I can sometimes work on a problem I've partially attempted, and get on with it. However it is very rare for me to actually sit through the fifty minute slot and work through the question sheet. I can't really explain this, but sometimes (if I'm being brutally honest) I get annoyed when the people present loiter over my shoulder watching me attempt the question. That is my cue to strike a conversation you see. I understand where they are coming from, but if I'm stuck I will put my hand up and ask for assistance. I don't need to be asked if everything is OK every two seconds. (Once is enough for they might assume that my worried face requires assistance, but I have a permanently worried face! Also some people don't like putting their hands up so that gives them a chance to say "yes I'm not OK", but as I said, once or twice is OK).

You see what's the point in doing a maths problem without any struggle. I only like to ask for help as a last resort, but sometimes during example classes I find that they are opportunity for me to avoid that struggle.

Don't get me wrong, if I attempt the questions before hand and take my issues then they are great! Well that's what I found with Dr. Coleman's example classes for sequence and series and Real Analysis, because I always enjoyed them. (Ha, that was perhaps the only course that I actually worked hard in, which maybe explains why I always had problems!)

Anyway, this isn't a very good thing that I do because I don't benefit from the classes if I have fallen behind in the module. For them to be useful I need to be on top of my studies which is never the case.

5) Do students learn from each other in problem solving classes?

Possibly. I hate being told the answer and sometimes in a group, it is very easy for someone to tell you what to do. But what exactly does it mean by "learn"? "Learn" what? Working with others is a good way to check your answer and perhaps discover another method of solution. (Its best purpose is that someone can tell you that you've copied the question out incorrectly!)


6) What are problem solving classes for?

To do problems? (Oh and talk to the lecturers and "persuade" them to attend a Galois Group lecture!)

7) How do "able" and "less able" students tackle problem solving?

I would say that I'm a middle type of student, and that I can't answer this question! Fine I lied, but once again it depends on the problem we're working on. Sometimes I try to specialise or generalise the question to something I am familiar with to see if I can get elsewhere. I always try to start by writing down what we have and what we want. Then I write the "what we have" line out again and try to make deductions.

A picture ALWAYS helps me so I try to sketch things out. Another thing I sometimes do is to actually answer the question in a long winded and tedious way, just to make sure that my answer is right, and then write the short cut down.

If I see inequalities, I first have a cry to myself and then as I have learnt, I stick blimmin' values inside the daft things to make sure the signs are the right way round! Yes, I'm not the best of students but this semester it has all been my fault.

Oh yeah, and thanks to certain lecturers I try to ask questions or question every step I do. (If I can't answer a question I use one of 36 methods of proof to convince myself, but it doesn't seem to work on others...)


8) How can problem solving be taught?

Well I think reading books like Polya and the one by John Mason on my to read list, are quite beneficial. Although I sometimes did "specialise" or "generalise" I wasn't properly aware of that "technique" until I read about it in a book. I also think you can learn a lot from your tutors. My original PT and Dr. C have moulded me into the annoying git I am. Well you'll have to thank Dr. Coleman for the way I write basically every step out on most occasions, and that I try to explain next to everything. I still can't prove things, but it will dodgily come together I hope. (It's a shame that Dr. C and PS will no longer be teaching me. :( )

9) How do "able" students read mathematical texts?

NA on both parts! But perhaps I could say something on the second part. If I am stuck on a topic and my notes are hazy too, I look through more than one book from the library and try to make sense of the topic. It always has to be at least two books, and sometimes I am lucky to discover a really nice book this way. Sadly one thing I haven't done at university (which I used to do at school and college) is work through problems in the text books. That's the most important thing and I'm not doing it! There is no sense in reading the books if you can't answer the darn questions. And NO, I'm not going to say that hopefully next year it will be different.

10) How can one improve a student's reading skills in mathematics?

Erm design mini projects on small topics like the Euclidean Algorithm, where a student has to read about the subject and hand a written report in. A bit like our workshop module but for that we were already given knowledge of the topic and didn't have to do much reading ourselves. Our module was namely about solving problems in groups, but it would be more worthwhile if had been sent on missions to explore certain topics further. (I would have enjoyed that!) I guess I still could have read into the topic at hand, but the problems were demanding!

Alternatively, we have supervisions in our first year which only consist of eight students and a lecturer. If individual students were given a topic to read about and then later present to the class, it would be very beneficial. Once again, it could be something as trivial as numbers in different bases but students would have to read about this themselves. This would also give the students to present in front of an audience. Actually I like this idea and might run it past someone at University. I mean the "presentation" element in the workshop was sort of ridiculous but that I already posted about last year.

11) How can one improve the study and learning skills of students?

I need to think about this but I think I have sort of answered it in my answers above. Students need to be made aware of how they can help themselves to improve. Watching videos like the one on the Internet on by Jean-Pierre Serre, and reading other study guides can be useful. We are very very naive (with the two dots on top!) when we start university and some of us are seriously clueless about Mathematics. It is a steep gradient that we must climb and help would be useful.

Perhaps there could be an element of "oral exams" in each module which requires students to actually do some reading themselves. This assessment won't be based on answering questions but on how well students are able to communicate mathematical ideas that they have read about.

Our lecturers are gifted mathematically and it is obviously hard for some to understand what it's like for us dodos. (Or they understand but find it hard to empathise). However, the great story tellers are those who are able to communicate effectively with us and students should be given the opportunity to do this too. Some students understand things straight away but are unable to communicate their methods to others.

I don't really know what I'm getting at here but communicating maths is very helpful for students. I found that when I blogged about "proper maths" (once upon a time!) it actually was useful. Hmm, perhaps students should create blogs to help them?

Anyway I'm going to shut up now because I am being called, but there is a follow up to this post soon. (Oh - I forgot about the different colours!)

Friday, July 04, 2008

Me me me

I have learnt a lot about myself these past few days, which is rather unfortunate. I would have preferred learning about something more interesting, say Maths, but I have been unable to do so.

Sitting in one place for most of day and being unable to move is very restricting. I learnt that I am perhaps a tad impatient. Well if you have three letters that require posting (by recorded delivery) and you find that they are not being posted what can one do? I have sat and endured the trash TV. I have sat and endured the laughter and comments such as "good you needed the rest". But what I can't endure is depending on people to post my three letters, which by the way still haven't been posted. (I even asked nicely).

I did comment last week that I didn't like it when people depended too much on others, and I think that's because I don't like doing the same myself. My fuse has become very short these days, and I admit to have become a very different bean. I saw this week as "my week". The week where I tied loose ends.

Imagine you're a cop and you have to close a case down and tie loose ends (I haven't just watched The Departed!). Now further imagine that you have an accident and you find yourself stranded and unable to complete your work. Also no one else is there to continue your work because no one was on your case to start with. Now wouldn't you be one very annoyed and frustrated copper? Whose going to catch the bad guys?

Sigh. Yes I need to be patient, but for how long?! Just give me my five million cats and leave me alone, is what I've been feeling like.

Another thing I've learnt. I'm not as lazy as I sometimes claim to be. Yes, I'm lazy when it comes to certain things, but when there is something there that I want to do then I'll try my hardest to do it. At this moment I want to do a lot but because I'm on a short fuse and this damn hopping is getting on my nerves, I just do nothing...

I see them all running and groan inwardly. Then I do something foolish like try to walk and suffer the consequences. I'm going to post my three letters myself, and from this we learn that I can be a very stubborn git. (I sometimes blame maths on that "quality" shall we say!)

Honestly speaking I can't understand how people can sit watching TV for hours on end, but then I understand how it's possible. I disappear to my room sometimes and they say I'm a hermit. Well I would rather be that than a couch potato! (At least in my room I will be able to keep a tighter lid on the growing fire within me).

Actually I am lazy. But wait, I don't know. I have cancelled my driving lessons but my instructor told me to get the theory test out of the way now. I had six weeks but four of those remain. And guess what---I can't be bothered and have yet to do any reading. I like driving but the theory? No thank you. I don't think I'll ever pass because all I keep on hearing is "either you're a rubbish driver or your instructor is rubbish." I can hold my hand up and say that I'm not too great, but I don't really have that drive to pass just yet. I just like driving even though it's costing a fortune...

Consider this post an outburst of some sort. The only place I can actually read maths books and do "proper work" is at my desk. Don't ask how that happened, but because I can't get to my desk I haven't been doing anything. I've lost my wallet too, but that's because I can't look in all the usual places at this moment in time. Laugh while you can, I tell them, but i I will be walking and running again soon.

The one positive that I actually wanted this post to be about, was this deadline that I was working towards. The deadline is today (Friday) but I have submitted everything yesterday. I am slightly nervous but in a months time we'll see if I should have been worried.

Apologies for "letting steam out" here. I have controlled myself for three days but alas, sometimes things get the better of us.

For the time being, I think I'm going to conclude with "I'm lazy".

Wednesday, July 02, 2008

Fractal Science Kit

I received the following email, which I would like to share with you.

Hi Beans,

I have just released the
Fractal Science Kit 1.0 and thought you might be interested in taking a look. The Fractal Science Kit provides an interactive programming environment with windows for viewing the fractal image, modifying the properties that define the fractal, examining the data behind the fractal, and viewing/editing the programs, macros (inline functions/methods), and color gradients, used by the Fractal Science Kit to produce the final image.

The programming language you use to develop your programs, supports a complete set of control structures including if statements, while loops, for loops, switch statements, inline functions/methods, arrays, and user defined objects. The complex data type is the fundamental variable type, and arithmetic operators and functions handle complex operands/arguments. A rich set of built-in functions/methods are included, and you can develop your own library of functions/methods for use throughout the application.

During the development of the application, I developed 100s of sample programs to illustrate how the application can be used to generate many different types of fractals including: Mandelbrot, Julia, Convergent, Newton, Orbit Traps, Sierpinski Triangle, IFS, Strange Attractors, Rep-N Tiles, Symmetric Icons, Apollonian Gasket, Circle Inversion, Schottky Group, Kleinian Group, L-System and many more.

For additional details visit the web site at www.fractalsciencekit.com. The web site contains a complete description of the product and provides the full documentation, galleries, and tutorials.

Please help support my work by linking to my site!
Thanks,
Ross Hilbert

Be sure to check out the gallery on the site for there are some cool images! Apart from that I can't really comment on the product, but if anyone has tired to it out, feel free to comment.

Tuesday, July 01, 2008

Using LaTeX in Blogger

Many \sout{people} mathematicians tend to use Wordpress to blog due to the simplicity of using LaTeX to type maths. I obviously don't post that much maths (!) but whenever I do, it is not as difficult as it once used to be.

I started of by using the TeXer to create images, which I then would upload into the post. This wasn't a particularly good method because firstly I didn't know much about LaTeX, and secondly the images didn't look too good when inserted into the posts.

There then came a time when I had my formal introduction to LaTeX--the start of a new relation! (Slightly rocky at the moment, but we will work it out as always... with Steve's help of course!) However this new relations didn't help my posts look good because I was still inserting images.

Now the master of LaTeX, Steve, enters the equation who set me up with a really easy way to insert mathematics into my posts (probably in the hope that I will write more stuff about maths! :p)

What is this easy way you ask? That's the reason behind this post you see, for as I was surfing through Blogistan today I noticed that many people weren't aware of this beautiful resource that Steve has cooked up.

So here is a step by step guide (you better strap in though for it's going to be a long ride!)

1) Follow this link which will take you to a post on Steve's page on "Using LaTeX in Wordpress".

2) Scroll down until you find download math Tex helper.

3) Click on the link and download the winzip file by saving it where you normally would; the desktop in my case . (Note: if you couldn't find the link in the above post then I have linked it above!)

4) Open the Zip file (mathtex_images.zip) and extract the file inside (only one) onto the desktop.

5) Double click on the extracted file and you are done.


OK fine, it wasn't really five steps--I was just jesting with you! I didn't even have to post a "step by step" guide but hey, you can't now complain about not knowing how to use LaTeX in blogger! By the way, after step five I am hoping that it is obvious as to what you have to do next.

Don't forget to thank Steve. :)