Wednesday, March 28, 2007

Low on inspiration!

Yes, it's true, I've done ...... all! (insert colourful word where appropriate ;)). Crap all was what came to mind, but then I decided that sentence would not have been well defined, so left it blank!

'Maybe tomorrow' is what I keep telling myself, maybe tomorrow I'll get myself into gear that is. Then again on the other hand, maybe the five days of doing ..... all is what I needed? The semester so far has been pretty stressful and fast, maybe I needed to 'not' do anything? As always, when you find yourself in a position in which you didn't see yourself in, you tend to 'panic'. Or is that just me? My theory is that I'll do my Linear Algebra revision like I would for the end of year exam. I know that this coursework test is only 15% (did I say only!), but we don't exactly get a lot of time afterwards for revision (unlike the Christmas holidays). You see I tend to talk a lot of ...... . I say I'm going to do one thing and end up doing something else.

Today I had decided to invite the Tweenies over to my house. Well those who hadn't gone home for Easter. Well really Milo, but since Bella lives about 20 minutes away, I invited her as well. Milo couldn't go home because it's too much of a hassle, so I thought it made sense that he got a tour of my home town, which is really cool^(infinity), if you're wondering! Obviously you mathematicians are not going to believe that. You want me to 'prove' it! Well I will refer you to this post, and, well you can choose whichever proof method you find most fitting! (Intimidation could get interesting!). I can't even leave it as an exercise, which I would have probably done, since you don't where 'home' is. Ok, now that's out of the way (any disputes can be mentioned in the comments section) I'll move on.

Milo lives in Manchester (duh), and since Milo is from down South, he didn't really know how to get to my house. So using this as an excuse to go the library, I got up super early (read 8:15am!) and got to Manchester 9:30ish. I wanted to really get some mechanics books out from the library, but once I got there, I was soon wishing that I could take more than three books out. The maximum number of books I can have is 20, so yeah, I now have 20 books! They're not all maths books before you get worried! I erm ... well would you class books like 'Nature's Numbers' and 'How to Solve it' as Maths books? They're for the general audience are they not? The thing is that I still have quite a few books which I got during the first semester that need returning. I have a reason for keeping these, since sometimes I erm.. do tend to look over the stuff that we did during the first semester. Just briefly I suppose, nothing too heavy on the grey matter. (where the heck did that phrase come from anyway?!).

Oops rambling again! Anyway, the mechanics books were next to the physics ones. That once again made me remember why I don't particularly like mechanics- it bleeding sits right next to Physics! (Note to school physics teacher- I'm blaming you for this. muhahaha!). I really had no idea which book to get. 'Classical mechanics', 'dynamics' etc were words flying of the shelves. The book recommend was not to be found. I couldn't even bring myself to look through a few to see if they had anything 'relevant' in them! So has anyone got any good mechanics books which they'd recommend? I finally got this one (had the word 'Newton' in the contents). After I got these books I then met up with Milo so we could go to my house together. [just remembered that in the book 'Beaver Towers' there used to be three 'mechanics' who were called 'Mick' 'Ann' and 'Nick', can't remember the author but we read it in Year 6 in primary school!]

The funny(well not so funny) thing is that the night before I had 'hidden' the other 17 books, and some others which I have! Haha, trust me it was for the best. Also the small post it notes that i have stuck on my wall, with the quotes that I post had to go! They're back in their normal places now, but Milo and Bella would have probably fainted upon seeing the books. I had just left the course books which we all 'had to' buy on the floor and they were pretty amused at that as well. Just because I have them books doesn't mean I use them all the time. They're there for when I get stuck or need to quickly look up something, and since I have more than one in each 'subject' I get a good overall understanding of what I'm after (hopefully).

Eventually we got to my house, and it was good. Maybe for a second I did think- aaah need to start working, or was it a minute, but overall the time pleasantly passed by. I showed them bits and pieces of the 'coolest' town, and then they went. If anyone else wants a tour then I'm afraid they no longer operate. You'll have to wait for the summer holidays now. Only special circumstances would allow me to give another tour in the next few weeks (email me ;) ). OK, I'm chatting...... again. I tend to do a lot, but today seems a special case of this.

I played cricket again today, but I was well behaved and didn't ball. I obviously wasn't too pleased at this since I tend to get 'bored' with batting - especially since it's pretty restrictive playing in the back yard. You see I can't exactly feel the ball hitting the middle of the bat and going out 'of the ground' so to speak. We have to be more reserved, and guide the ball nicely along the ground. Pfft. I really need to get a new football! (my old one is a bit under the weather, and I have no pump).

Now I had intended to post another 'neat' ickle theorem, but I'm just going to make another post for that. However, I'm going to resist the temptations of this blog for the next few days and see whether I can concentrate on getting some work done. (so if you're going to lose some light entertainment I'm sorry). It's not really this blog that is distracting me, but because of this blog I have a 'need' to go on the computer, after which I waste too much time. Now there's a prize available to anyone who could thing of a cool way to write something like what I'm going to write in a minute, but it has to be about computers, the net and time wasting etc.

All men are mortal.
Socrates is a man.

Socrates is mortal.

It's known as 'syllogism' and, well I said I was short on inspiration, but tomorrow I'll see what I can muster. (mystery prize- doesn't that tickle your pickle? :D) I don't know why, but I see this as 'poetry'! Now we were told in my FIRST EVER lecture (I remember it like it was yesterday- infinity was mentioned!), that Math's is like a language and imagine that you have to go to Russia and live there without knowing any Russian. Thus, you eventually pick up 'Russian' or learn it to live there. Maths at university is a slightly similar experience. You know nothing, but to survive you have to train yourself to know certain things and the rest hopefully follows. Damn that was another aside, but I might as well try to say what I want by having a lame attempt at the syllogism thingy.

All languages have an element of poetry.
Maths is a 'language'.
Maths has an element of poetry?


If you're really feeling sick after reading that, then I'm sorry! But if you're having a good old chuckle then I don't mind. I was trying to say that we study languages at school. English is a language that we study at school. In English we study poetry. Maths is another 'language' you study at school, so maths has poetry. OK I'll stop now before I embarrass myself further. All I flippin want to say is that I find syllogism like poetry! There I said it. They're like mathematical poems. I never understood poetry hence I'll probably never understand this. That wasn't too hard was it! Hmpf.

I can't believe where I started and where I ended up. I'm just going to resist the temptation of writing any new posts, life-threatening situations might be given special circumstances, but I'm going to restrict myself to comments only. I hope your Easter holidays are going better than mine.

Tuesday, March 27, 2007

'Me & My Maths'

I don't know when you actually started reading my blog, but if it was from the very beginning then you may or may not remember that I had naively called my blog 'Me & My Maths'. As you can tell this was a very silly thing to do, that's why I promptly changed it to 'Me Or My Maths'!

Some of you may be wondering what's the difference, so here's the explanation!

Given two sets 'Me' and 'My Maths' we can form the set of elements which lie in both 'Me' and 'My Maths'. This is called the intersection of 'Me' and 'My Maths' and is denoted: . Thus,

(you read this as, 'x such that, x belongs to Me and x belongs to My maths.)

Where x is probably the posts that I make. Since there have been things which I have posted that only belong to the set 'Me', then the initial name would have a been a lie. (I've got to stop doing that!). You only need one counter-example to prove something is false, and I can think of a few posts which would do the job. Hence, that is the reason why my blog got its new and cooler name!

You see given two sets 'Me' and 'My Maths' we can form the set of elements which lie in 'Me' or lie in 'My Maths'. This is called the union of 'Me' and 'My Maths' and is denoted: . Thus,


I'm sure you'd agree that this describes the content of my posts to a better degree! If you still need convincing then we can also use truth tables!
'Me' or 'My Maths' is called the disjunction of the two statements Me and My Maths. In everyday speech we often use 'or' in the exclusive sense. However, in mathematics we always use 'or' in the inclusive sense (to avoid ambiguity) determined by the above truth table (on the left). On the other hand, 'Me' and 'My Maths' is called the conjunction of the two statements Me and My Maths (table on the right). So if for instance, looking on the table on the right, for my post to be a 'true statement' I would always have had to write something about 'Me' and 'My Maths'. If I only wrote about 'Me' and not about 'My Maths' then the post would be false! That's why the or option is 'nicer', since if I wrote about 'Me' but not about 'My Maths' then the post would still be a true 'statement'. Obviously if I don't write about 'Me' or 'My Maths' then the post is false in both cases. (so my posts have been 'true statements!).

[I'm being a little 'cheeky' here, since these truth tables tend to deal with statements in general. Statements generally either denote predicates or propositions. A proposition is a 'sentence' which is either true of false, so 1+1=3 is a proposition. Whereas a predicate is of the type: m < n. They involve free variables, and once these are given values they become propositions. ]

So yes, some thought had gone into naming my blog! Since I've gone this far, I'm tempted to go slightly further! Intersections and unions are operations on sets, and you've probably come across them in stats (hmpf), and truth tables are about the basics of the language of maths (they can get ugly when you get more than two statements!).

Alas, I can't control myself! Given sets 'Me' and 'My Maths' we say that 'My Maths' is a subset of 'Me', written or , when every element of My Maths, is an element of Me, i.e. .(I don't suppose the converse is true!). If Me and My Maths are in addition unequal, so that Me contains some element not contained in My Maths then we say that My Maths is a a proper subset of Me and write:.

So that's the mathematics behind my blogs name (there will probably be more stuff when I move onto other topics, or when I really should be revising but rather think of stuff like this!). Now I don't really understand proper subsets, and well you've probably figured that I used my notes in order to create this post (but do tell if I made any errors). Like I said this is the 'language of set theory' and I don't particularly like it! I get confused when to use 'the proper subset' notation or just the 'subset' one. However, let's not get distracted about what I can or can't do.

I hope that I've now convinced you about why 'or' is ultimately the better word to use in my blog title. When someone offers you an 'apple' or 'banana' (could be anything in general), you could be cheeky and take both, and then innocently say, 'I thought you meant the inclusive or!'. This could either result in physical abuse or weird looks and someone who clearly is not amused! (although I would recommend trying it, just to amuse yourself if not for anything else.):D

Don't worry if this mumbo jumbo doesn't make sense, I was just erm.. amusing myself, but later I'll insert links of the 'mathematical' stuff that I've mentioned in case it's confusing. :) Oh and you're not allowed to give me them 'weird' looks, if you're a mathematician you should deal with the inclusive or at all times. That is all. No ifs or buts. Sacrifices have been made and more have to be made! Look at the big picture. (I'll stop now, in case I risk scaring you for life!).

(You've probably figured that the Internet is working and are hopefully relieved of this fact! It was the darn router).

Monday, March 26, 2007

Another 'erm' type of post...

... so you can't say that you weren't warned. If you're still 'eagerly' waiting for the posts that I keep saying that I'll post, then the only thing I have to say is that 'good things come to those who wait'. OK that sounds like a load of 'codswallop' but I couldn't think of anything better. You see I have three weeks of holidays, which if I'm lucky, will be filled by me trying to squeeze as much maths into the small thing that is known as a brain. So that's why I'm going to nicely space the posts out. They're not that big of deal, but they've got a topic unlike random posts like this!

Today was(is) a Monday. I had to state that because most of the times that I have holidays, I lose track of time, which isn't very good. I've got a feeling that the more determined I am to do some work, the less I'm going to get done. Call that Bean's 'amount of work done is inversely proportional to the square root of your determination' law or something like that. (Well Newton can have laws which sound cool, but make no sense whatsoever, (to me) so why can't I?!) The proof of that (if it's required) is obvious, and if you still reading that again with raised eyebrows then you'll know for sure in three weeks time. (BTW it wasn't really meant to make sense, but if it does then blame egm for linking this ! ~evil laugh~).

You've probably noticed that today wasn't a normal day, or that I actually might have done as the song suggested and beat my 'brain' against the wall. This wasn't so. It seems that I've gone into holiday mode again. It's only the first day of the holiday, but I went to sleep at some weird (read: early!) time. I previously commented on wanting to have approximately 8 hours of sleep, but another one of them weird laws, (which I shall not give a fancy name to ) is that the later you sleep, the later you wake up. Today I could blame the fact that I hadn't changed the time on my phone, so when I did wake up I thought I had another hour That's really a pathetic excuse, but I'm blaming the change in sleeping pattern for my headache, which I've had all day. (Or could that be due to the fact that I'm having withdrawal symptoms already, because I had no lectures today! aaah- what's going to happen to me in the summer holidays...!).

OK, enough of the dramatics (for now!), although I had a headache I decided to slowly ease myself into an ideal pattern for revision. If you're wondering whether I have anything else better to do with my time, then I don't blame you. I do do other stuff, but what I can say- I'm consumed by maths! (Not that I mind). So, obviously since I was taking things nice and slowly I chose to do the first chapter from the Linear Algebra book on vectors. Opening the book I was greeted with this:

"Where shall I begin, please your Majesty?" he asked. "
Begin at the beginning," the King said, gravely, "and go on till you come to the end: then stop."

-Lewis Caroll
Alice's Adventures in Wonderland. 1865


So that is what I hopefully intend to do. However, I don't see the 'end point' in my case, but I will assume that for Linear Algebra the end is the end of the book. Now I didn't get very far in this chapter, although I had hoped to, but I came across this neat proof. I have decided to post it here, since it's to do with maths(duh) and this also gives me another chance to mess around with LaTeX. Now at this moment in time, at the bottom of m
y screen it says 'could not connect to blogger.com.... etc'. I'm taking it that my Internet connection is somehow not working, although my computer is telling me otherwise. Another reason for me to believe this is that I can't seem to access the AoPS site! So indeed my Internet has gone 'kaput', but I will finish typing this post up before heading off to bed. (Indeed in a very annoyed manner- my previous disjointness has now vanished, and boy am I mad!). Now, you may notice a change in my tone- so I apologise before hand for sounding like a sulky teenager (6 year old!) but I'm not too happy! :(

The other reason for including this proof (which took longer than anticipated to type up, because of no net) is to show that although it may be obvious, that u+v= v+ u (i.e. vector addition is commutative) but to prove this is another matter. The proof isn't too difficult, although I would never have thought of it myself, but I like how 'sim
ple' it is. Although I didn't have to use LaTeX, I did:Neat. May I also point out that writing this post at 00.00am and knowing that I will not post it for maybe a couple of days is making life difficult. I can't exactly go and wake my dad up and shout the Internet isn't working! He'll just reply that it might work in the morning or he'll have a look at it then. What am I then meant to do? Shout 'Dad, you don't understand, I have to post this post on my .... oops... erm no it's ok. We'll see what you can make of it in the morning! Night.' Sigh. It's funny how much I rely on the Internet! I don't exactly rely on it, but it's always there so to speak, and I'd gotten 'used' to 'surfing' it and checking various things out! Noddy seems to think that maybe it's not working for a good reason! Humbug :D

A short laugh surfaced for a second, whilst I remembered what initial random mumbo jumbo I was going to post! I might as well continue with that now, but if you're already asleep at this point or sick and tired of my moaning, then it's best you don't read on. I'm going to give somewhat of a boring history lesson, although it's more of a case of writing what's currently on my mind.(not sure whether to write this now, but I can always 'get rid of it' later I suppose!)

In year 8 (that was when I was about 13 I think), I noticed that I had back problems. I obviously went to the doctor, got a blood test done etc. and the Dr said that there was nothing wrong with me. I didn't really care at the time, but since my Dad has a bad back he was a bit worried. The problem continued to exist, but it didn't change my life in any way. I forgot about this and a few years passed by with me not caring too much and it was in year 11 (I think) when things changed. You see I acknowledged that my back was higgidly piggedly (new word!), but for some reason this made me more determined to overcome this fact. You could say I was stupid, and still am stupid as a matter of fact, but I deliberately pushed myself harder.

Same as when I sprained my ankle. That didn't stop me from playing football, although initially I did move very gingerly (it was painful!) but I felt that by playing with my bad ankle, it'd get better. There's no logic in that thought process, but even today as I go to uni I 'choose' to carry a back pack which weighs roughly 5-6kg. This is silly, but I don't really know why I do it. Maybe I could not take my water bottle, or leave a book at home, but I don't. There is one possible reason that I do this, but I can't put it into words. I guess it's a bit like people telling me to change my degree- that made me more determined to struggle on, and the same thing sort of applies to my back.

What's actually got me thinking about 'why' is that today, whilst I was doing some 'revision' I heard my brother playing cricket outside. My attention was slowly diverting from my books, and once the neighbours dog started to bark I realised that revision was pointless and headed outside. I've not played cricket in a while so I obviously decided to bat first. I was slowly getting into the swing of things, and after my brother had gotten me out three times I decided to let him bat. (I wasn't initially planning on bowling since my backs being a 'pain' :D ). Bowling is what I love doing in cricket. Batting is great when you want to vent your frustration, but if you don't bat 'calmly' more often then not you get out! You only get one chance, whereas with bowling you get more than one chance. I'm a medium/fast pacer, and like to pitch it up sometimes, but mostly I like to bowl a good length. (extra info if you're interested!)

It's pretty restrictive playing in the garden, but I bowled some loose deliveries to start of with. I knew that I shouldn't overdo it. I knew that I should continue bowling slowly to him. I knew this, yet I couldn't help myself and slowly started bowling slightly faster and faster. Now when you bowl you have to put your back into it, however like all other times, I don't realise that I'm overdoing it. You could say it's adrenaline, but even when I'd helped Milo move his stuff back into his university room in January, I didn't realise that I should 'chill out' for a second. It was painful then, as it is now. I've come to the conclusion that my back is funny shaped (or that I don't stand up straight all the time?), that is why I'm probably more susceptible to back problems. That's why I'm more determined to not let them affect me too much.

Ok I'm getting sidetracked here (again). I'm basically trying to say that although I haven't been nice to my back, but I adopt the same mentality in my maths and other aspects of my life! You could say that I see my back as a 'weakness' and so try to overcome it by using it to do what a normal person can do with their back, but slightly pushing it harder. Now in maths, this is obviously different, since when I face a difficulty and persist in trying to overcome it, the only harm it could do me is cause me great frustration and I could probably become hulk-like! I guess it's also because I don't like 'not' being able to do something, which I know that I can and should be able to do. (I could name a few maths topics here!) Weird!

Now this post is becoming longer than anticipated, but I guess the delay of no Internet is to blame for that. However, today I've realised that I'm 18 and playing this 'game' with my back is a serious game. If you ever get hurt take it easy. You see writing this down has me feeling very stupid indeed (I normally keep this to myself :o ). I know that after today's cricket game, tomorrow morning is going to be painful (that's why you should stick to football folks)! Lecture over. I hope I didn't scare you guys, and I don't get them everyday like it may seem. (At random times, like today, it plays up a bit, but apart from these times it's not too bad.)

Oh and I've calmed down after the Internet mess up- let's hope, for my sake(!) that's it not too long before it's working!

Sunday, March 25, 2007

Pi(e) day?

I've been having one of them days, in which there's this annoying song tune playing in your head but you CAN'T remember which song it is!! Obviously You Tube seems the natural option, to help you to control your frustration and figure out the tune. However in this case You Tube didn't exactly help at all. Instead it introduced me to Pi(e) Day. It may be a bit late to 'celebrate' this day, but when I had initially read about it somewhere else or was told about it (can't remember properly) I thought it was to do with pies (i.e. food). But today, thanks to You Tube I learnt otherwise!



You probably already knew this, but there's no harm in me celebrating -day again! (Any guesses on what the right answer might be?!)

And to continue this celebration, here's something which might amuse you, found whilst 'googling'. (note: if you're not amused, you might want to try checking this post next year, on -day!)
But is it worth circling this day on my calendar for the year 2008? I mean it's not really that big a deal is it? Otherwise we might have been given the day off from our lectures, and made to learn as many digits of as we can! (3.14 is a safe answer when asked how many digits you know, well in my case anyway!)

How I got LaTeX.

Well I though that I'd write down exactly what I did to get LaTeX on my computer. It was by no means difficult, but I have the unique ability of making even the simplest things difficult!

I followed the link that Steve gave me, and started reading the installation documents linked on the left.
I read them twice maybe thrice, and then tried clicking on:
But this resulted in:
Yes, it wouldn't let me install it! I probably hadn't read the instructions properly, was my initial reaction, but no matter what I did the same error message cropped up! I went back to the link that Steve provided and clicked on the link that took me to the home page. From there I clicked on another link which took me too:
The file that I downloaded was pretty big (about 500 mb to be precise). Anyway, from the page shown above I clicked on, 'ProTeXt-2.-.exe 536108 KB 06/03/2007 23:52:00' (i.e the link on the top!). Clicking this will ask you to 'save file' (I used FireFox), click save and then wait. (I'm guessing that you'll know where it's being saved to!). The only reason I chose this one was because of it's size! I don't really know what clicking the others will do, but do feel free to try. (I'm not responsible for anything wrong that might happen).

(If you are using Internet explorer, after clicking on the above link, you'll be asked whether you want to 'run' or 'save' the file. Select save and choose a location to save (make sure you remember this).

Now when I said wait, I don't really know how long you'll be waiting for. You could do what I did, and leave it running overnight (FireFox said it'll take two hours and IE6 is saying 5!). How long it takes obviously depends on your system I suppose, and your Internet connection, so just sit back and relax/sleep.

Anyway, when you wake up in the morning and find the installation has been completed, we can move onto the next step.

I saved the file onto the desktop, so in the morning I found the file 'ProTeXt-2.0.exe' sitting there ever so nicely. When you (double!) click on that, the following screen will appear:
You might need WinRar for this, or some sort of 'winzip' type of softrware. (You can get it free from the internet I think). The directory where you extract this is not important, but remember where you extract it to. (I just extracted it to the desktop). Click on install and let it do it's stuff (shouldn't take too long, but then again it won't exactly take a minute!). When this has finished, find where you had extracted the file to and open the file. The following files will be displayed in the folder. You could explore them further, but to get LaTeX on your machine first click on the file which I have made a red box around:
Now after clicking this, click 'next' on the box that appears. This will open up this document, from which I'd previously encountered a problem. However, now (after reading the instructions of course) you can safely click: When it asks you to open the file, select open and then follow the instructions of the manual to get MikTeX onto your system. However, you may find the downloading guide from AoPS useful as well. After the setup is complete, you will have safely loaded MiK TeX onto your computer. (I loaded it into c:\program files\miktext).

Following on from the instructions in the pdf file (note: make sure you use the pdf file which opened after clicking 'setup' and not the one I've linked!), you will now install TeXnic Center. Once again click on the blue writing which says, 'Click Here to Install TeXnix Center'. Select open when asked, and follow the instructions (using the pdf file or the AoPS guide). This is pretty straight forward, but if like me you get slightly confused and wonder which directory to install this in, then don't worry. You can install it in the default directory which it provides you i.e. c\Program Files\TeXnicCenter\.

After this setup has been complete, you now are ready to use TeXnicCenter. If you selected to have a shortcut on the desktop, then click it to load TeXnic, if not then go to start>program >TeXnicCenter>TeXnicCenter. The first time you run this a 'configuration wizard' will appear. I suggest following the instructions on the AoPS website (6-7), to get this sorted. And then there you have it-LaTeX on your computer.

It's not that difficult, and I'm sure there's other ways of installing it. However this is the way I did it, and it worked (woo hoo). In the pdf document there is an extension section at the end, but I'm ignoring this for the time being! Seems like a safe option at the moment, but obviously once you're more familiar with things then you can venture further. There are also links for alternative text editors, however like the author of the instructions said, that depends on personal choice. (TexCenter is free whereas WinEdt is shareware, however WinEdt does seem popular.)

Nope, I've not finished yet! I then proceeded by installing the 'Ghost' thingies, however that was just for the sake of completeness. I don't really know what they're about (the word post script crops up a lot), but will probably soon find out I suppose! So I guess they're optional, and you don't have to install them.

That's it after that you're done! Now obviously, I had no idea what to do after this, but once again the AoPS guide to creating your first document came to the rescue. (The pdf instructions show images of what to click, so using both you'll be ok). The AoPS site has many more information about LaTeX and I'm currently working through the basics on maths etc. If there is something unclear about anything I've written, then please do let me know. And if you are brave enough to follow what I did, then feel free to ask any questions. (although I may not always be able to answer them, I'm sure someone will :) ).

Saturday, March 24, 2007

Sleep

How many hours of sleep do you have on a normal day, and what time do you normally get too bed? (That's a serious question if you're wondering!)

The time's going forward one hour, if I remember correctly, but why does this suddenly have me worried? It just doesn't seem right. Maybe I'm so worried because it's an indication of how fast time has passed by! It's already the end of March. It seemed like we started the second semester just the other day. What's more worrying is the amount of work that I should have done already, but haven't. Worrying is a natural thing for me, but I seriously can't think of anything 'productive' which I've done during the second semester. I've done what had I had do to. Nothing more, which is what I should be doing.

Now is a good time to really reflect on what I haven't done, and what I now must do. I know that I had decided to really have a go at Linear Algebra during the Easter holidays, so maybe that caused me to slacken slightly. A change in lecturer had me shifting up a gear, but then when we started subspaces I slowed down again. We have a coursework test worth 15% for Linear Algebra after the holidays, which is enough reason to 'revise'. So maybe all is not lost.

For Calculus I kind of 'get' the ODE bit, like finding the characteristic equation etc. The only bit that stinks of that part is the 'graph' questions, and existence and uniqueness. Oh and how can I forget stinking oscillations and the 'perturbation' method. The mechanics bit is just evil. I went to the library to see if the book recommended by the lecturer was available, but sadly the library only had one copy which has been taken by someone else. (I was going to see if it was any good before buying it, but might just buy it now!). I don't really want to spend time on mechanics, but have a coursework due in after the holidays. So this will give me a chance to get myself informed on what's happening! If you're wondering why I'm so relaxed about this module, then I'm afraid even I can't answer that question. But this 'relaxed' attitude has warning signs all over it! (I'll have to squeeze some mechanics in somehow).

Finally to sequence and series. You take one step forward in this subject and a further three backwards. So how many steps do I have to eventually take to get to the end? (too many to count!). As I've previously stated, I get bogged down by little things, which bugging me for days. I'm not sure whether I should be worrying about trying to understand the proofs, since this is taking far too long, or whether I should be doing more questions. I don't really want to write this since it's 'painful' but I'm still on convergent sequences! I've got divergent ones left, the ratio test and a million other tests as well! On top of this we have now started series, so yes, I'm really behind in this subject. I'm not sure how long my Linear Algebra revision is going to take, so I can't really say for definite about how much time I'll be spending on this subject. Sigh.

The real reason I'm moaning about this is so that it can give me the kick that I need. You could say that I've been in 'denial' about how much work I've been doing this semester. Putting it all down really weighs it up.

Now the question of sleep comes into the picture. Today was the first time in ages that I didn't have the alarm clock on. I was really testing to see, after how many hours of sleep would I wake up without any external influence. I woke up after 8/8.5 hours (but then thought it's a Saturday, so turned over and went back to sleep!). Now having too much sleep is not good for you (trust me on this!) and too little is not enough. So what's the optimum amount of sleep one should be having? I've been reading 7hrs on some certain sites, but should you always use an alarm clock to wake you up, or let yourself wake up when you're ready?

Having the right amount of sleep makes a big difference in your concentration levels. During the last few weeks of the first semester I had got into a good routine in which I was sleeping well. Consequently, I never dozed off in my lectures (shockingly) and always felt wide awake, ready for anything that was to be thrown at me. This post has really come because during the second semester that has not been the case. During the holidays, I'm aiming to wake up early-ish and do some work then. When you wake up at erm... 12ish your whole morning has disappeared and so you don't feel that you can accomplish anything during the day! So I wouldn't mind your comments on what time you tend to go sleep and wake up. On a normal day I'd say I aim to be asleep by 12am, and wake up at 8ish. (most times out of ten this never happens!)

You've probably already figured that today has been a so and so day (I should really have woken up the first time round). England drew in football and won in cricket. Which would I have preferred? I'm not complaining about the win in cricket, but my main passion is football. I really do sometimes wonder what the result would have been if I was managing England. (That's another thing for the 'to do list'! :D) Just really been watching football and cricket for most of the day, but I did one thing which I'm proud of! I cleaned my room. Yes, it was tedious, painful and no Mum to help me, but it had to be done. My mum stopped cleaning my room the day I threw a huge tantrum after she had put the millions of separate piles of papers that I had, into one huge pile! That was painful.

Anyway, the real reason for sorting my room out was so that I could get into my 'revision' mood. Tomorrow is also going to be a day of doing 'nothing' probably, since I need to first 'de-stress' myself. Oh, and I could always play around with LaTeX! (my first ever document, this is a day to remember indeed! You don't have to download it, but I didn't know any other way in which I could link it. BTW thanks for the links Steve :) ).

Friday, March 23, 2007

Pin drop silence.

Once again two posts in a day, but I didn't want to 'spoil' the other posts with snippets of my day. You're all probably shocked that the title doesn't mention the word 'oscillations'! To be honest, I was a bit sick of that word so decided to go for something new.

The two hour calculus lecture went surprisingly ok! Thankfully, much to my relief, the lecturer switched the lights on full upon entering the lecture room. ( I had an issue with this last Friday, although I had a plan for this week!). Now, there is something fishy about 'mechanics' which is bugging me, but I can't seem to place my finger on it. Whilst we were doing the ODE stuff and integration etc. I was ok. However, as soon as the 'mechanicy' explanation was brought into the picture, my brain suddenly lost it's ability to understand what was being said. I obviously muttered, 'yeah, that's ok' when the lecturer asked if things were OK, but like I said it was slightly fishy.

Whenever the word 'ultimately' was said by the lecturer, I couldn't but help remember Ultimate Muscle! Don't shoot me, but it was hard to keep a straight face when all I could think about was Kid Muscle!! Oh, and if you've heard of the 'myth' that if you throw a coin down, from the empire state building (I think), it'll kill whoever it hits, then that's rubbish. Although, it'd be pretty interesting to see what life would be like if that wasn't the case! Imagine throwing a coin down and then being charged for murder- how many years would you get for that? OK, I'm sure that Dr H didn't have them things in mind when telling this to us, but I wouldn't mind actually testing this 'myth', you know finding a 'counter example'!

Another something which I found funny was that 'life could get exponentially complicated'. You can't hate that comment! It's just so funny. (well I found it funny, and still do :D )

Moving on, after this rather pleasant lecture, it was time for Linear Algebra! This time Prof S didn't put any question on the board. He began his lecture like normal, and today I had trouble keeping up with him. I put it down to the fact that it was Friday, and that I don't like vector subspaces and showing whether a subspace is closed under addition, and scalar multiplication. Although I did manage to follow one of the proofs! Once again, let's not get sidetracked. If you were 'on the ball' you might have wondered why Prof S didn't put a problem on the board. Obviously that can't have been because we were all quiet- that's the empty set! Today was the 'day' that Prof. S asked two people to leave. It happened quite rapidly. He turned around and told two guys that their Easter break was starting a little sooner, so please leave. One of them protested that his friend couldn't read the board because he'd not got his glasses but Prof. S wasn't having any of it! He waited for them to leave, and then carried on normally. After this no one dared utter a word. People didn't know whether they should laugh, or to be afraid. No one dared breathe loudly. I even thought twice before clicking my pen. Fizz though twice before whispering something to Milo! The lecture continued in silence, with only Prof. S talking. Just the way it should be, was what I thought. But I shudder to think how I would have reacted if he'd chucked me out!

Normally after this lecture, we have an hour for lunch after which we have Sequence and Series. But that lecture had been cancelled, so we now had two hours before the example class. Now I thought this was great- I could do the stats coursework and hopefully finish most of it before the end of the day! However, things didn't go entirely to plan. My mood did oscillate today, but I seem to notice a pattern in it oscillating between me wanting solitude and the opposite. Now I think, no I know, that I this want for solitude will never go. It's going to with me forever. I don't mind this, since I'm understanding why. Since I've been more determined to get work done at University, I welcomed these two hours with open arms. However, when you do math's work inevitably you sometimes want to be on your own.

Now the problem for me is that these feelings seem to be 'intruding' on my time in university. Seriously, I don't know what came over me, but I was slightly annoyed because we ended up doing a million and one things which didn't include going to the mss building to do Matlab. So, yes you got it. Them two hours went down the drain. Thankfully I did manage to have some lunch so all wasn't as bad as it seemed. Now I seem to be jumping from point to point (brain= disjoint), but I keep going back to the thought of being wanting to be on my. You see I don't want to sound like an ungrateful idiot, because I do value the difference that the Tweenies have made in my 'uni experience'. However, sometimes there's a conflict of interest. Now I could be a party pooper and suggest to them that 'I'll meet them at x-place, after they've finished', or I could just not go and watch the two hours tick by. I did a bit of both today, however I don't want to ruin the Tweenies fun. Gah, I wish that I could think more clearly about this, because like I said I don't want to not have the Tweenies around.

I've always been able to go off on my own and do my own thing, even if I was in a group. In school, I always used to 'disappear' (not go missing, but my friends weren't always with me). The same happened in college. Our timetables were slightly different, so I inevitably had time alone. I'm a free spirit so to speak, and need this 'free time' I guess. You know, I like going for walks (sometimes with people), pushing myself physically and mulling over random stuff. I person needs 'alone time' I guess, but I've gotten used to 'drifting away' without people really asking me where I'm going. Hence why I've said this type of behaviour is oscillating! Thankfully it's the Easter Holiday's now, so I'll be able to have that 'solitude' and re-charge my batteries!

I do get carried away when I'm typing, but things come to me in random bursts! Today's example class, once again shook me out of any troubles I was having (not just mental ones!). I had gone prepared with my 'Standard List of Questions' and after realising that I'd made some dumb mistakes, and had forgotten log rules (which didn't come as a surprise to the staff present!), I was pretty pleased with having the list of questions answered! It was a pleasant atmosphere as usual, and the time really did fly! Milo did later point out that we might slowly be getting the 'swing' of things, but I think it's best if we didn't get too ahead of ourselves!

Something interesting was pointed out to me, so I thought of sharing it (gives me another excuse to use LaTeX I suppose!):(a_n=log(n)\quad a_n\rightarrow\infty\: \mathrm{as}\: n\rightarrow\infty):
(a_{n+1}-a_n\rightarrow0 \: \mathrm{as}\: n\rightarrow\infty)

Oh and: ((2^n+3^n)^\frac{1}{n} \: \nrightarrow 1 \; \mathrm{as}\; n\rightarrow \infty)

That was my big stupid mistake in case you're wondering, I'll leave that as an exercise shall I. (sorry, can't help but say stuff like that!)

After the example class, I had another go with Matlab but I reckon I might just leave it till after Easter now. Oh and I didn't climb up the stairs today! I was really 'not in the mood' but the main reason shall be discussed later. Although I did compensate by running to catch the bus- felt great! I think it's best if I shut up now. (I can hear you know!) Sleep doesn't seem the natural thing at the moment, so I'll just have to busy myself in something or other.

Maths: Reason 2

Here is a question which I will ask you to do, although you can obviously choose not to do it! The question is find the length of x. Now you must excuse my useless excuse for a diagram - MS paint and myself have had a falling out!However if you persist, I will explain the problem using words! You are given an isosceles triangle, with the equal sides length 10, and the other side length twelve. Unfortunately now I must make reference to the diagram, since my brain is slightly more disjoint than normal! So the line, length x, is right angle to the line length 10 (if you couldn't tell :o ). So there's the problem. However, I'm going to be nice and tell you something which wasn't told to me before I was 'given' this problem. I was in my 'ickle' zone, attempting this problem, when suddenly I asked for a calculator. 'It's a 'non-calculator' question', was the painful reply. So no calculators allowed. Obviously you may have already solved this problem, and are wondering what I'm rattling on about (or you may have read my previous comment about the state of my brain and understood!), but if you're still getting your hands warm, then here's a hint for you. (I think it's fair that you are at least provided with the information I was). And this question was from the chapter on Pythagoras's Theorem.



So, what's this got to do with any thing? Well yesterday, when I eventually got home, my sister who is in Year 10 (secondary school) asked me to help her on a question she was stuck on. My sister was born in 1992, but it seems that I'm not capable of doing arithmetic in my head, so I'll say that it's 'obvious' how old she is! So fair enough, I tell her to show me the question, and give me some paper and a pen. I sit patiently whilst she fetches her big maths book, which she had been reluctant to buy, and opens it on chapter 6. Supposedly she had asked me have a look at this question before- I have no memory of this. This could be either due to the fact that I hadn't been able to do it last time, so was actually playing dumb. Or that I had actually forgotten about it. I had actually forgotten about.

But that doesn't matter of course. If I had managed to solve it before, then it should be easier this time round. So now I had pen and paper. I was was armed. Due to my supervisor, who I am now ever so grateful towards, I have to write proper sentences in my maths work. I understand the importance of this, since if someone was to read your work and they couldn't follow what mumbo jumbo you'd written then that'd be pointless. So I obviously wrote what I was doing whilst solving the above problem properly, much to the annoyance of my sister. She's young and doesn't know any better, I thought, so I was patient and explained to her why what I'm doing is good. She obviously didn't care- the solution was more important. Now at this stage, she hadn't told me the hint written in the margin. So I'd worked with two triangles, relabelled one side as 'a' and the other as '10-a', done a bit of fiddling and then stopped.

Yes, I needed the blimmin calculator, but she annoyingly pointed it out to me that I couldn't use it! 'Can't you do flippin square roots in your head?', I retorted, obviously annoyed. But not to worry, she now told me the hint. I don't know whether she had planned the motion of events to make me suffer, but nevertheless she'd done a good job! Armed with this new information I turned the paper over to start fresh. Got distracted for a while (food time) but then was back at it. Now this was where things could have become nasty. I have another sister (grrr) who I will be calling 'La La' as in the teletubby La La. Anyway, La La was mocking me about doing maths, and how I would never be able to solve this problem. I was a bit short on motivation at the moment, since I couldn't see how it was to be done without using the bleeding calculator! However I was patient, and mentioned to 'Po' (the maths one) that La La is treading a fine line. Also that I will return to her problem later, since I had some of my own work to do.

This was obviously a lie. At that moment in time I didn't have any intention of doing my own work, but such is the case with maths problems that sometimes you need to come back to them after a while. You see we had the answer from the back of the back (which did make life easier one could say) but that was all there was. So the night progressed and I had forgotten about this 'trivial' question, as had Po. I actually then did some of my own homework, however I once again somehow managed to overlook doing the Linear Algebra work! It was 00:33am and I decided to get some sleep, since Friday's do take a lot out of me. I turned my light of and lay in bed. Obviously one doesn't fall asleep straight away, and suddenly I remembered telling Po that I'd do the question before going to sleep! I'd forgotten.

So, whilst lying in the dark I mulled over the question once again. What was I not doing? What's the hint got to with anything? Yes, I've tried that but it's not worked, so what shall I try next? These questions continued for a while, until I suddenly sat up in bed! I quickly switched the light on, and found some paper! Damn it, where's the bleeding pen when you need it! I located one under some books, and rushed to write down my solution. Obviously when I say rushed, I mean I wrote it as fast as possible but using sentences! I must confess that I did actually use the calculator, but in my defence it was to check the answer!

Satisfied with the solution, I went to sleep. Now that is a pretty empty statement. I considered writing about the euphoria that I was feeling at that time, but you obviously know what came before sleep! I wanted to wake Po at that time and excitedly tell her that I'd got the answer, and I wanted to ask La La what she'd been muttering about before! I didn't do either of these, but went to sleep a happy bean. (after the victory dance of course!).

There's reason 2. Maybe not such a big reason, but how many times have you fallen asleep before solving the problem? That's only the second time I remember doing that. Normally I tend to 'sleep on it', and hope to tackle the question in the morning. Obviously when I say 'sleep on it' I mean, lie awake in my bed thinking about what avenues I need to explore and then suddenly jump out of bed after discovering something. Most times the avenues are dead ends, and after shouting at myself I try to go back to sleep. Now the number of times this happens is indefinite, but in the morning when I woke up and remembered the solution- it was a 'kerching' moment!

I didn't tell Po the answer, but gave her another hint! She obviously wasn't pleased about this, and it seems that after I left, she took the solution from my desk. Po was convinced that her math's teacher would not be able to solve the question, and I'm glad that he did solve it! :D

So anyone managed to solve it? (gosh saying that made me laugh! You're probably shouting the answer out at the screen).

Thursday, March 22, 2007

'Analysis'

I don't know whether you recall my lame reference, of the number of people attending the sequence and series lecture being a 'null sequence', however today the lecturer seemed to make the same link. I'd estimate that about 70 people turned up today. However, this reference can only get better. Tomorrow no one is going to come to it. 0 people. I'd say QED rather cheaply, but that's not my style! (QED= Quite Easily Done!). Although, don't naively think that after tomorrow's lecture, the sequence is going to be constant. Tomorrow's lecture has been cancelled I believe (I wasn't the only one shocked to hear this!). I don't really care about this, because during the first semester Prof D had to go to a conference, so he had cancelled his lecture. (You could say I'm somewhat relieved, since then I won't have to walk up the stairs in the mss building twice in a day!)

I'm guessing that you could call 'sequence and series' analysis, (correct me if I'm wrong) hence the title of this post. Today in the Linear Algebra lecture, after someone had asked a question, Prof S told us about how they used to ask questions in lectures whilst he was an undergrad in Russia. You wrote your question on a slip of paper and folded it. You then passed it to someone in the row in front of you, and they then passed it to the person in the row below them. This happened until the paper with the question reached the front table, so then the lecturer opened it up and answered the question. The student's used to sometimes try to write difficult questions to 'test' their lecturers I suppose, but the lecturers were great so of course they always answered correctly. Apart from the analysis lecture (I think so anyway). I don't want to quote the great man, since I'll be then risking misquoting him. But he said something along the lines that his analysis lecture was not a very good lecturer. (I'll refrain from using the exact word he said! :D) It was the 1970's and rather than using the 'brilliant' blackboards they had (unlike the crappy Schuster Building ones) he used to write on the OHP thingies!! That is why Prof S is an algebraist, I suppose.

I got a bit sidetracked then, but I found the idea of writing the questions on paper, and passing them down pretty cool! Anyway, Prof S also mentioned that Analysis is a delicate subject. It teaches you how to properly appreciate maths, it's proofs and so on. I agree with him on this. Analysis is a 'tricky' subject, but once you look at it with a good understanding it does look pretty neat. Some bits are subtle, but overall you get to see it's value. Now you see, in maths if I can't understand something I tend to become 'angry', but not quite like the hulk, but annoyed. It's more of being frustrated I suppose, but don't get me wrong, I don't expect to get stuff straight away!! No sir, I know that I'm slightly slow so have to work harder than most people. This is where my 'slight' (ok maybe high) dependence on teacher's comes in.

I really have to say that no matter how great I say Dr Coleman is, his greatness continues to 'diverge' without a bound. It 'tends to infinity'! When Prof S was talking about his own 'accident' with Analysis, I couldn't help but feel that I had been saved from this very 'accident'. And the reason for that is Dr C. He doesn't get half as much credit as he deserves, but seriously I really do value and appreciate all the help he's given me in the example classes and his own time. If it hadn't been for him then maybe I'd still be whinging about 'sequences and series' and 'winding' myself up over this. You see it could be said that I could try and learn the stuff from a book, and self-teach myself I suppose. However what a book doesn't give you is motivation. What it doesn't give you is inspiration. It does provide you with alternatives, but it's no substitute for a teacher. I could read my notes, but does that mean I'll always understand them? What about the little tricks that seem to be found most of the times?

I don't know what I'm currently feeling, but I know that no matter how much I thank Dr. C I'll always feel it's not enough. He's really been the difference in my university education. He always has a way of explaining things to you, in more than one ways if there is a need. And the bonus is that you don't feel 'dumb' asking him for help. You know that no matter what help you ask for, he's most likely to provide it, or present an alternative way in which you can get the answer. Previously my school maths teacher had been my motivation in doing maths, and possibly maths teaching but now it's Dr C. Sigh. That was a sigh of relief, in case you're wondering. Relief that I was saved from an accident, which I know would have had nasty outcome. And possibly a sigh of gratefulness that once again, when I needed that motivation and inspiration the most- I found it. I think you all know what type of posts to expect on Thursdays and Fridays!

I'm not complaining so to speak, it's just that in my heart I believe something, and this something is what causes me annoyance. I'd rather this keep this belief to myself for the moment, but I'm feeling both optimistic and pessimistic at the same time. However, I really can't say why!! You see, like I said about being a PASS mentor, I want to do things properly so they're with me 'forever' so to speak. I don't want to forget any maths!

I seem to be rambling again, and have lost sense of direction. Such is how I'm feeling at the moment. I don't really have a conclusion on this bit of the post, but I can't really describe what state of mind I'm in. You already know that I have a screw loose, so there's no sense in using that as an excuse. Let's just hope that I'm able to somehow survive any more accidents which are to come!

So now I shall return to preparing my 'Standard List of questions' for the example class. Don't really want to mention my ongoing love-hate relationship with Matlab (oops), but Dr Yuan is great as well!


PS: Sorry just remembered something else which HAS to be mentioned! In the Linear Algebra lecture, two girls were 'caught' talking by Prof S. He decided to give them a question to do during the lecture, and proceeded by writing '9:2' on the board. That was it. However, whilst he was cleaning the board later he asked us if anyone had solved it. No one had obviously solved it, but he told us it has nothing to do with sports. He then went and said that for the past 16 years he used to write something on the board and ask the students what it was. No one had got this in the last sixteen years apart from some student last year (it was to do with the 1966 World Cup). Anyway, towards the end of the lecture he again asked us if we'd figured it out.

Bemused expressions were to be found and people were quizzically looking at him. So he then proceeded to write 10:1 underneath 9:2. At this moment I whispered to Milo, that it's probably something to do with the number of lectures that we've had, and how many have we had! (I'd lost count!) I then thought nah, we've only probably had seven so it can't be that. However Prof S, said that 9 was the number of lectures we'd previously had and two were how many were left before Easter. So 10:1 meant we'd had 10 and one was left! So yes, I was chuffed so to speak :D (had a big grin on my face for most of the walk to the mss building!) Small things do tend to please me, but I thought it was pretty cool! (I'll stop typing before I break into a silly song!).

I've also taken the time to insert links this time!

Wednesday, March 21, 2007

I'm famous?

Now if everyones in the same dopey mood as me, then you'll probably be wondering, 'Really, how come I've never heard of you then?'. Seriously, staying up till the early hours of the day for two days in a week is not good for you! Last night was just stupid, because after I'd finished typing most of the coursework, I did some other questions!?! And then looked over some Linear Algebra stuff, whilst everyone else was probably sleeping.

I'm guessing that you're not in a dopey mood, and probably had spotted the question mark. I think I should change my name to 'dopey' for a while, as in one of them dwarfs, or 'dopey mathmo', but that's a bit too long. Nah, beans it is for now! So, if you did notice the question mark, take a Freddo.If you go to the Student Union shop tomorrow and find that there aren't any Freddo's left, you know who ate the last three. (That is, the people who spotted the question mark!)

So back to being famous. You know sometimes when you sit and ponder on life, you have brief bursts of 'inspiration'. Today, as I was pondering, not necessarily on life, I decided to Google my full name! Obviously not beans, but my real name (oooh). Yes I do possess one of them, although I'm one of them few lucky people you'll meet, that possess more than one name! Ask the staff at the example class, and a few lecturers. I'm sure they'll enlighten you with my other names (apart from 'the' real one! :p). I wasn't really expecting any results, but was shocked (and secretly pleased of course) to find that my name had a hit! The top most result was about me- hurrah! It wasn't about something wacky I've done, but it was just my college's homepage. Still though, I got a result. I decided to Google the Tweenies real name's as well and it seems like Milo is the only one who got a result.

So it's been a productive day I guess, I'll just have to wait for the queues of people who want to know what I'm famous for! I could keep the suspense going, and make people think I actually did something big, but then you'll be disappointed when you hear the truth. I was merely a student council member in college, and hence that's one of the reason's I could find my name! (that wasn't on page 1). Next year, it'll disappear so I might as well enjoy the few months I have this 'fame' I suppose. Don't worry, I won't let this fame get to my head! Come on now, it's not like I have much of a head (it's the weird types) and why would I make a big deal out of something this small. Actually why am I still talking about it?... :p

So are you famous? Or how famous are you? Google is your friend.

BTW: I TAKE EVERYTHING NICE I SAID ABOUT MATLAB BACK! I HATE IT, HATE IT MORE THAN BEFORE! THE SECOND COURSEWORK IS WORSE THAN THE FIRST ONE. IT'S EVIL. THAT IS ALL- MATLAB IS NOT NICE!

LaTeX and a few other snippets.

It's a weird coincidence that today, when I went to Dr C for some help we started talking about LaTeX. I had actually wanted to ask him how he got his notes into the PDF format, but I'd forgotten. But thanks to my 'typed' sequences coursework I was kindly reminded of this question. (which had stupidly been printed out more than once!). I've gotten used to typing my coursework on word, but you can't always find the right symbols for certain things, like the Natural numbers. (I had used the online texer and copied pasted the symbol into my document). This coursework actually didn't take that long to type, but I'm always up for a new challenge. Dr C had this big book on LaTeX, (would look pretty cool on my shelf I reckon, so he best be careful! ;) ) which looked useful. He told me that if I read what people had typed into LaTeX then that'd be a good way to pick it up and learn it. (since it does look daunting at first). So that's what I've been doing, well trying to.

Dr. C suggesting googling LaTeX (I didn't know that it was pronounced Latec!), however upon checking the comments on this post, I don't think that is required. I have a pretty fast computer at home, which has a lot of memory (I thought I'd be using it a lot for games, but alas don't have the time for that!), so I'm going to give it a go. As always, I get worried about loading software from the Internet, so erm ... I'm going to load it on my Dad's computer first!! (without him obviously knowing!).

Here's what Steve posted, if you've not been following the comments:

'Mathematicians use LaTeX in a te
xt editor then compile to various formats including pdf.

Unfortunately LaTeX requires a huge download though it is free. On Windows a good system for beginners that guides you through it all is ProTeXt.

Alternatively, you can use a slower online compiler such as LaTeX-Online-Compiler or Web LaTeX and a good text editor is TeXnicCenter.

That's for your own computer but the university is bound to have a LaTeX system installed which you may be able to use.'

I asked Dr. C whether the unive
rsity has a LaTeX system but it seems they don't. Something about staff getting it but I don't think it's available for students. I have been looking through the directories and this seems to be the case. But going to get more feedback on what to do.

So do I have time to 'waste' learning LaTeX? Not really no, but I'm rising to the challenge. I'm very determined to actually get this thing working on my computer, and being able to use it will be a bonus! As you've probably realised, I do tend to have silly goals and ideals, but I really want to be able to use LaTeX. I had teething problems with Matlab, but now whilst I'm at home and sometimes need it, I cry! (well not really, but you know what I meant didn't you??). The problem with us using Matlab in univ
ersity was that we only ever used it for about 3 weeks in the first semester, and that was it. Then we never touched it again, until now. So obviously, since I'd never got acquainted to it the first time around, the second time was a disaster!

I will keep you posted on my 'adventures with LaTeC' (!) , and here's what I have just done now (for the sake of it obviously!):

'100^n \le n! \quad\forall n_0' gives you

You use \le for less than or equal to, and you'll soon realise that it's pointless pressing the space bar, so \quad gives the space between the two things, and the '_' is used to denote a subscript. (That's what I was helped on today, amongst other things like a strategy for determining limits of sequences! Note to self: look up Stirlings formula )

So once again, let me say that this may be one of the stupidest things I've done, but it's a challenge. Not against someone else though, but against myself, which makes it even more better. I'm feeling quite restless though, since I know I shouldn't be drawn into this challenge right at this moment. I shouldn't prioritise this, but it seems to be pushing itself up the pecking order. We'll wait and see what happens.

So on to the other snippets- what, you didn't think I'd forget did you! Wednesday's don't seem to be good days for me anymore. Today morning was one of them days, when you wonder whether if you were to go back to sleep and wake up again, would things be better? Why is that when you're running late every bleeding traffic light has to turn red. And as soon as you're out of the car and walking to cross the road, they never turn red! At this stage I knew it was going to be one of them days where everything went horribly wrong.

Someone must have been feeling sorry for me, since I managed to get into Manchester at the intended time (thankfully) however, don't get distracted by this one positive. I obviously walked it to n13, with my 6kg bag (yes I had brought the two damn books with me again!) and this was painful. But I needed to clear my head so I didn't mind the pain. Then I did other bits of stuff like sorted the coursework out, did a few questions and life was good. I got the problems that I was having sorted out as well, so all was good. I stupidly decided to walk down the stairs to go to the lab session for stats. Not a problem, was just out of breath!

The lab was ok this time around, since we didn't really have to make any stuff up ourselves, rather we had to input certain things into Matlab. After this I rushed of to the Lamb Building to hand my coursework in. Once again I was stupid and didn't consider the time. I got to the Lamb building and there I bumped into the Tweenies who were also handing there coursework in, but taking there sweet time. I handed it in and said to them I'm heading of to the lecture. Milo decided to come with me. I hate going to lectures late, and I had a sinking feeling that Prof S had started already. Sometimes when you come late it's hard to get into the lecture, so I try to be there on time! So we walked 'as fast as we could' to the lecture. Obviously we got there late, and Prof. S had already started. (I got pretty annoyed at myself for this).

The lecture was good, and well I don't really need to mention every cool thing that Prof S does, do I? Although today I realised that it's good to talk to ones self! Prof S does it (somewhere ;)) and well then that means I can do it as well! Although, he doesn't do it in public. What brought this up was the fact that the word fundamental, has the word mental in it! Ok, ok let's not get sidetracked again. We're doing Vector subspaces at the moment, and my brain's in first gear at the moment. (Can't wait for the Easter Break).

After this lecture it was the PASS meeting that I mentioned yesterday. Quite a few people turned up to this meeting and it was good. We were just basically told about what it'd involve and that we'd have to be trained up etc.

You see there is a reason why I don't like telling other students my grades. When you tell a teacher it's different. You know from the bottom of your heart that your teacher will have no hard feelings towards you. But when say a classmate knows what results you got, they no longer see you as you, but rather as what grade you got. Also other people knowing your grades, can put extra 'unwanted' pressure on a person. This works in both way. For example say I got all E's in my A levels. I tell someone this, and the transformation on their face is pretty much what you expect. Now this is just an example, you'll probably get consoled and told it doesn't matter, but what if them grades mean the world to me!

The other extreme is to say I got all A's. Now there's a different transformation in this person. He could either be the type of student who goes, 'oh you genius, you swot! blah blah blah' without thinking that maybe I worked hard for them grades and putting it down to the fact that I was a 'swot'. Or he could be the type of student who sits quietly, and makes a rude remark and then tells your results to everyone. I don't really want to go on about this, but this second type of student then is no longer your 'friend'.

I don't want people to know my results, so then they won't have to go through any of the transformations that I mentioned above. People should see me for who I am, not see my results when they see me! I don't want them to see a letter on my forehead. My results are a result of 'hard word' (sometimes!) and they're not anyone else's to disclose. Sigh. I also decided to walk up the stairs in the mss building again! I'm actually noticing an improvement in the amount of time it takes before my shins start hurting (or is that my imagination!).

Second coursework for stats is up now, let's see what I can make of this. Hopefully it'll be less painful than the first one.

Tuesday, March 20, 2007

'The best way to learn/understand maths...

... is too teach it.'

That's another quote from Prof. S and I agree with him. I think you can generalize that statement and say that the best way to learn and to properly understand something is by teaching it. (Although there may be a few exceptions!). My recent posts have been more of my day to day business, and I keep on mentioning posts that I am going to write about. I thank you for your patience (if indeed you are waiting) but I'm waiting for the Easter Holidays, truth be told. Them post require a lot more thought, and as you've probably gathered a few of the previous posts have been slightly random. The posts that I have in mind are not such a big deal, but they're more about 'me and my maths!'.

Back to the quote. Now this wasn't a random quote by Prof. S. He said it at the end of last Wednesday's lecture, after two students and Dr. W had finished talking to us. Basically, the University's Maths department runs a 'PASS' scheme, which I believe has been ran for the past 10 years. Obviously they don't want to break tradition, so they are going to be continuing it next year. However, for this to happen they 'need' (I think) first or second year students to volunteer an hour of their time a week. Hence why we were being invited along to a meeting- tomorrow.

So what exactly is PASS? (I have to spoil this 'formal' post by saying- wow!:o).

'The School of Mathematics runs a Peer Mentoring Scheme and a Peer Assisted Study Scheme (PASS).

The PASS Scheme consists of weekly sessions, which give First Year students a chance to share ideas with Second and Third year students in the School. The Second and Third year students have invaluable experience of course units and life as a student in Manchester, and they can help First Year students to learn how to study. The mentors are there to provide support and advice, and although our academic staff are very (trust me they are) friendly sometimes it's easier to talk to another student who's just been through the same experience.

The student mentors are not necessarily expert mathematicians, but they have developed strategies for succeeding on our degree programme, and they can pass on their experience to help you improve your study skills.

The aims of the PASS scheme are

  • To enhance the quality, quantity and diversity of student learning within the school.
  • To provide you with a supportive environment to work through issues relating to your academic course.'
And a load more mumbo jumbo about it looking good on you CV etc etc. As you've gathered, I just got that chunk from my student handbook, otherwise I wouldn't have been able to give a proper description of it!

So I'm a first year student, do I go to these PASS sessions? Or how many have I been to? OK, I'll confess, after the first session that I went to I learnt it was optional to attend them. So that was obviously my first and last session. I have a few things to say in my defence, however I'm ashamed to admit that one reason for not going was because the Tweenies weren't going. I've since learnt from that. Another reason was that on Monday morning's last semester we had a 9am Sets, Numbers and Functions lecture in the Renold Building. (Surprisingly I didn't mind the 9am start!). Now the PASS sessions are in the Newman Building, which I don't particularly like. It's only a whisker away, but during the first semester I was a lazy so and so who used to bus it everywhere. The prospect of walking to the Newman building and then back to the UMIST campus was frightening. (gosh I could have said that liked I meant it!) The PASS session was at 11am so I really had no excuses.

Another reason for not going to them was that the 9am lecture was our only lecture on Monday, and after that we had a whole day of doing nothing (till 3pm I think because Milo had a supervision then). In the beginning, when I wasn't particularly acquainted with the Tweenies, I used to spend some of this time in the library. However soon we went through a phase of not doing anything during this time. (Either used to watch movies, or general stuff if we didn't have any assignments to hand in).

I never really felt 'guilty' of not going to these PASS sessions, but I have another 'excuse' for that. You see when I first started- fresh from the holidays, excited about university, crying about how hard the work etc etc, I was a 'goody too shoes'. I felt that since PASS was on the timetable, we should at least attend it. It's a good scheme as well ~tiptoes~

OK, I'll stop beating around the bush and get to the point. My first session was actually an introductory one (so that means I went to two sessions!), in which we met with our mentors and they arranged a time for us to have the sessions. We agreed to stick to the 11am slot, and after getting some contact details we were out of there. Next week was the actual session. I decided to do the problem sheet in this hour, because I felt that was a productive use of my time. We had two mentors. If we had a pure problem we went to A, and if it was a calculus problem we went to B. This wasn't a strict policy, we could talk to them about anything I suppose. The hour session was also another good opportunity to talk to other maths students on your course and to get to know more people. I had gone to A, since I was doing the first problem sheet which Nige had set us. So we talked, did some maths, and talked some more.

I obviously did become stuck (duh!) and asked for assistance. This is where my excuse comes in. You see A and B told us that they couldn't really remember any of the stuff that they'd done during the first year properly! I wasn't very enthusiastic' after learning this. I'm particularly stubborn in the sense, that I only ever ask for help if it's the last resort. There's one question that I'm currently doing (but can't), but I'm not asking for assistance because I obviously want to do it myself. Now this stubbornness only applies to certain cases. When it comes to me wanting to understand a concept which I obviously find difficulty in, then I naturally seek help (probably of Dr C in uni!). However if it's a question then I feel that I should be able to do. I battle with the question, until well my frustration gets the better of me and I am left with no inspiration. When this is the case I reluctantly ask for help. (and then feel like banging my head against the wall, thinking why the heck could I not do that!). This, isn't always a good quality to possess, because sometimes my stubbornness is seen as something else by people. Can't really find the right for exactly what.

Anyway, I'll stop there before I go of another tangent. Back to PASS. Now I'm not going to expand much about the next few sentences, because they're what I'm going to write about during the Easter Holidays. When you have a teacher or mentors or basically anyone who teaches you in one way or another, then you have a special relation with this person. That of trust. You trust to be guided along the 'right' way and when you do deviate slightly you get a nudge towards the 'right' direction. You place an enormous amount of trust in these special people. When that trust is slightly broken, or when it's never there then you don't really feel that you'll be given that nudge or slight push into the the 'right' direction. I never really got to build this trust with my PASS mentors, and maybe I didn't give them chance. But I was really put of by the fact that they didn't really have the 'solutions' to my problems. I didn't really want to know much about the university experience, since I've not really come to university with that being my main motivation. I felt that rather than going to PASS, I would find it a more valuable use of my time to sit at home or somewhere else, and struggle away.

Like I said, I can't really expand on this and 'blame' the mentors since I'm guilty of not attending the sessions. I'm a different type of learner. I prefer struggling. Then crying. And crying some more. Cry... ah you get the picture! But then finally asking for help. (You'll be hearing more of this next week).

Now the question begging to be asked, is why do I care about PASS? Well I'm going to go for it. Tomorrow (if I remember!) I am going to the PASS meeting in the Newman Building at one, after my Linear Algebra lecture. Milo's not coming but Bella and Fizz might be going as well. Not only will this give me experience of 'teaching' it will also help me many more ways.

You see I sometimes I sit and think about what I did during my first semester (everything apart from stats that is!) and actually mull over the work we did. Unfortunately, there are certain things which I've forgotten and other things which I never really learnt properly since I never understood them. (Sets!) I do look over my last semester files, and sometimes do a quick question here and another there, but like I said my memory is like a sieve. (Wow, just remembered the sieve method for prime numbers!). Anyway, I obviously don't have much time to make sure that I remember all my first semester stuff, because of the new content this semester. However I now have a reason to actually make sure that I go back and make sure that I understand what's happening.

I want to be a PASS mentor who knows what the students are on about, and can actually help them. I'm pretty determined to do this, although if I do do this then I'm going to pull a sicky when it gets to the set bit! And going back to the quote, by doing this I will inevitably be helping myself. I'm one of them sad students who was thinking about spending my summer holidays, getting books about the modules which I'll (hopefully) be doing next year, and looking over them. But now I'm going to make sure that I fully get the first semester stuff so that, if life turns out all rosy and I pass my first year, then I'll be able to help others. I still want to be a teacher, at the moment anyway, so this will also provide a good experience for me. I don't really want to forget anything I've done, this may be inevitable but I was in such awe of my personal tutor, and other lecturers when they used to be able to help me in other fields of maths. I guess they've been doing it for much longer than students, but it was still cool! My PT just looks at the question and knows what to do, as with the staff at the example class! Cool. (There you have my motivation and inspiration).

I got distracted half way through this post, but the things I tiptoed around will definitely be discussed some other time. I'll conclude by saying that PASS is a good scheme. I do regret not going to any more sessions, because even though my mentors couldn't help me all the time, it would have been good getting to know them and they would have given me a chance to learn from their experiences. It's a bit late to start attending now, but hopefully I'll be over to 'get over it' so to speak by being a mentor myself! (Don't worry, I won't be telling them about the weird experiments that I do, and definitely won't be recommending them!).