Wednesday, September 16, 2009

Children in school are like children at the doctor's...

When I was a child (and even now), I loved going to school. I enjoyed learning (most subjects) and had a great time at all the institutions that I have attended. Now some of my siblings were the complete opposite to me. They hated going to school to learn. Nunu who is now in year 8 is the same - school is attended for socialising, not really for learning. (Unless of course it’s the favourite subject being taught or a “nice” teacher’s class).

Whilst commuting to University, I was hit by a sudden realisation as I read “How Children Fail” (J. Holt). I had naturally assumed that the students I will teach would want to learn; that they would share my enthusiasm as I took them down the wonderful path of Mathematics. Of course, from the little teaching experience I have, I knew that a lot of students hated Mathematics but I was challenged by this thought. I felt that I could change the student’s perception of Mathematics and make them want to learn it and enjoy doing so.

Now Holt mentioned the fact that students are in school because they have to be there. They couldn’t care less about how the lessons go, but that they make it to the end of the day. So automatically I am fighting a losing battle.

“Children in school are like children at the doctor’s. He can talk himself blue in the face about how much good his medicine is going to do them; all they think of is how much it will hurt or how bad it will taste. Given their own way, they would have none of it.” (Holt, 1982)

I particularly like that quote for it’s made me think that although it’s good to be enthusiastic, I shouldn’t set myself up for a big fall. I shouldn’t exceed the students’ expectations of themselves (if that makes sense). Yes it’s good to push at boundaries but miracles shouldn’t be expected. I need to check back on my optimism whilst making sure the learners have at least a positive mathematical experience. That sounds quite hard too. Perhaps I need to spend a little more time thinking about what I need to expect of the students when I’m teaching them. Is it right to have any expectations?

My post was meant to be about the scripted lesson sessions I had, but in this break I can’t discuss them (no time). I find myself in bed by 10-11pm would you believe it, and am completely exhausted when I get home. The above had to be posted before I forget about it you see (!), but I do hope to post again, tonight or early morning (for I have something to do for tomorrow which I can’t imagine competing over night). And perhaps I will edit this post when I read it again, for I have four minutes to get back so no time to proof read.

Monday, September 14, 2009

Week One Review (and Family Feuds)

I'll be doing this post in chronological order for a change, as I'm pressed for time. You see I haven't got into a routine for doing "homework" which consists of "reading" so I'm awake at some unusual time trying to finish things off!

The first word that comes to mind when I think about my first week on the PGCE course is tiring. Both mentally and physically I'm afraid. Unfortunately my health is not what it used to be (perhaps due to laziness) and I find myself tiring very easily. On the other hand I've been a lazy slob for the past three months so I'm not used to the increase in physical activity, so I'm hoping this is only temporary! Mentally though, I feel like my brain is being ripped apart and broken into epsilon sized pieces. These pieces are then being put through their paces before coming together in a completely different and new way. I feel like I have a new outlook on Mathematics now. It's no longer about ME (well humour me for a second!) but it's about CHILDREN.

But hey, isn't that what teaching is all about, you ask? The children and getting the point across? Well I have to disagree slightly with that you see, and that's what this PGCE has made me realise. It is a lot about ME but not about MY MATHS. There I said it. This blog will be sucked into nothingness now - apologies! The PGCE makes you realise a lot about yourself as a person and what you tend to do a lot. Hopefully it will allow me to improve on certain things, like slowing down whilst talking perhaps. This whole "ME-ness" and trying to get a control over myself and being accountable for myself is somewhat scary. I'm not always immature etc but 30 children gazing at you with expectancy, can be quite nerving. I don't think a lot of ME is going to change, but I am on this occasion making more of an effort to smarten up!

By the way, I'm not suggesting that I shouldn't know the Maths or take an interest in it anymore. I'm merely commenting on the brain being broken up process and how it seems slightly disorientating at the moment. With time this will change, but doing a year 9 SATS paper was a shock to the system, especially when I answered "don't know" on a ratio question!

Yep - that was my homework for the weekend: answer a SATS paper correctly in the way I would, and then incorrectly in the way I think students would answer it. It was enjoyable enough, but on certain questions I was intrigued as to how anyone could possibly get them wrong. That's the gap that has to be bridged now, for one thing I have learnt is that most students don't see words but just numbers. Another thing which struck out to me was that (in my opinion) secondary school kids haven't been taught to CHECK their work. I did a question wrong at first attempt, but I always review my answers and thus realised an error. It was actually my Dad who first stressed to me the importance of checking that my answers were sensible, and later in year 10 I can recall my Maths teacher doing the same. I realise it's all about finishing the work as soon as possible and moving on to the next question, but checking and reviewing is such a powerful tool in helping ones understanding that students sometimes lose out on.

Enough of my personal rumblings. Apart from the (painful!) process of having my brain ripped apart, I have enjoyed the challenge this week has presented me. The challenge of adapting my thinking and applying it to a different situation. I have some teaching experience but it's a giant grey slab. In the same way that my brain is being broken into bits and joined again, I have to do this to my own experience to be able to teach a class of 30 kids. I am very apprehensive, as from past occasions I am known to be given a lot of "crap" from the students. Certain family members don't help by actually imitating what they think students would say to me! Meh.

I missed the first day back (due to timetable mix up) which consisted of being taught starters - i.e. what's done in the first five or ten minutes of the lesson. This is meant to an activity which brings pupils attention to maths from whatever lesson they had. You can do whatever you want in it - recap previous lesson, play maths logic game etc. As I missed this day I was in for a shock, when on Tuesday we were put into groups and asked to prepare starters to do in front of everyone! What made this doubly worse was that everyone else already seemed to know each other, and I would be making a fool out of myself in front of random people. Thankfully though I spotted someone I knew which has changed my experience a heck of a lot. (The table I was sat on didn't seem to want to engage me in their group, as of course they all were knew one another).

My post on starters is non-existent yet, as although time thankfully ran out so I didn't have to do my starter, I have yet to find "the starter" that I like very much. I have made a note of a few interesting ones, but nothing different. However I have some questions though: Should students be divided "boys vs girls" if you play a game? The competition is already there, but should you enhance that? If not boys vs. girls, how would you divide a class into two (apart from down the middle)? I mean in the mathematical sense? It might not end up being a fair test, for eg, you could say, "one team is of people whose birthday is an odd number?".

Moving on, as I said above, I have found it very difficult to answer questions incorrectly. I have a been given six questions to take to my placements to give to students to do. I can't teach them how to answer them correctly, but just note what they do and see what goes through their heads when they're doing them. This is quite challenging and I will invite your opinions on what you think students would do, when I get a moment.

Hmmm - this is going on isn't it? A quick summary of a few other things then. We had a brilliant session on data handling and it's amazing how visualising data can make a difference. Also having some comparative data and putting it into context makes a heck of a difference. One thing I learnt from this is DON'T force my understanding on students. For example when teaching mean, mode and median. Instead work on what the students know and take them slowly to my understanding.

We had a session on Professional Studies but it was mostly a recap for me as I had gone through a similar study when I did the Student Associates Scheme (link?). The key thing is not to answer any personal questions whatsoever the students might say or do. Full stop. Not even a nod of the head is acceptable. As politely as possible tell the students to "butt out"! I think that's the best advice anyone can give for as a naive Teaching Assistant, when I was a lot younger, I responded to questions and later on regretted it as the students wouldn't stop harassing me for more information. Nevertheless the discussions we had on this topic were very interesting, and trainee teachers just have to make sure that they're professional all the time.

Overall it was a very knackering week and the weekend has flown. My bones are protesting and concern is beginning to shadow my thoughts. This week will be my last week in University before I go out on a small placement. I worry about this placement because I am out of my comfort zone. I normally decided where I did placements etc. so always chose safe-ish options you see! I do welcome this challenge, but nevertheless it does worry me.

I've met a lot of really nice and friendly people on the course, and sharing our experiences and thoughts has been a very good thing. Although I do disagree heartily with what a few people say, it's still good.

I have just bracketed the title as I can't afford to diverge into that topic. It's suffices to say that I am surrounded by a lot of people who can't be happy for me. My Dads family especially. This stinks as some dislike me by "association" and others just like to create situations for me that suggest I am unhappy at how my life is. Yesterday for the first time in my life perhaps, I stayed upstairs to try and avoid everyone. I had to come downstairs to eat, which was a big mistake, but still these things happen right? I'll say it again - A I have been quite lucky in life. Certain opportunities have come to me at good times and I've tried to take them (the tutoring for example). Bitter people just annoy the life outta me - GET A HOBBY (which doesn't involve being bitter). I didn't even want to play Pro Evo for a change! At least we won't be having a family reunion for some time now. (We all get together on the day my Grandad passed away, but not for the same reasons anymore...).

Alas, I better get going now!

Friday, September 11, 2009

PGCE Secondary Mathematics (G1X1)

This week I have started the PGCE Secondary Mathematics course. The course is indeed quite challenging, though not in the same sense as the Maths degree was. The first thing I have realised is that the PGCE is somewhat harder than the Maths degree. You see when I was studying Maths, it was all about my perception and mental issues with concepts, and how I dealt with trying to understand topics. However now it is no longer about how I deal with the Maths but how I make Maths accessible for younger people. This is a damn hard thing to do! Words like social development floated in one session really made me think.

It wasn't too long ago that I was a student, but even so, I am still amazed at what wonderful beings children are (not when they're being monsters obviously!). Their capacity to learn, how they interact in certain environments, what makes them tick are a few of the things that have been brought to attention. Previously I was aware that all students have different abilities, but with children ability isn't always what influences how they respond to your teaching. There are a million and one other pressures that a child might be going through as she walks into your classroom. Gah. It's horribly scary at the moment for although I love reading about "effective teaching and learning methods", being in the classroom is another story. Will I be an effective teacher?

This post has come at the end of the week for a very good reason, as we have to write a reflective piece of work every week. Most of you would have seen past my blatant excuse for you all know too well that I will write more posts than one a week, as I am bursting to share what I'm learning! (Honestly speaking - some stuff we've touched upon has been fascinating). This week has been absolutely knackering and I confess to leaving the task I had to hand in today to the last minute. (Thus I was awake at 5am finishing it off!) Reflecting writing isn't too hard I suppose, for I do it all the time whilst blogging. However what I worry about is how "formal" they want the reflection to be. I mean, could I just print my posts (with some editing of course!) and hand them in? I suppose not for the assignments are meant to prepare us when we have to hand in work that will actually be graded. Hmmm - they use the Harvard referencing system here too, which I have yet to read up. (Wikipedia to the rescue... but on the weekend).

Now this post is very rushed as I have been desperate to post something all week, and finished early today and got home at 3:50pm as opposed to the usual 5:30/6pm. (The timetable is not very flexible). Thus I have half an hour to give you a brief summary about what to expect the next few weeks. My main "reflection on the week" post will be on the weekend, which will obviously contribute to what I end up handing in.

By the way, I accepted a bunch of comments today and I will respond to them in due course (i.e. when I'm next posting - as I've got to run now!). However a childish part of me insists on writing "who the heck is aryabhatta and what the heck has he done?" (If you follow the comments on the side it might become apparent as to why I wrote that). I am suffering from lack of sleep and if my common sense didn't save me, I would have wrote a lot more than that! Anyway, the change of routine has been hard to accommodate but give me four weeks and I should be okay.

I'll be back!

Monday, August 17, 2009

What next?

This question has been looming over my shoulders since I graduated - what next? However I have been doing a very good job at avoiding any attempts at answering this question by reading a lot of fiction. Well without the Internet to distract me, and the fact that my controller for the PS3 got "misplaced" (according to my mum!) during the building work, I needed something to do. And so in approximately three weeks I managed to reread all seven Harry Potter books again! They were a jolly good distraction I must say, and I still can't believe the lame ending of book seven. I will refrain from mentioning any other comments on them books as that will probably take over the whole post! (And this is meant to be me finally answering the question above.)

I considered taking a year out to do nothing, but that was roughly pushed aside by the powers that be. Taking a year out would just make me an even more lazier git, and thus I shouldn't postpone anything that I want to do. (You can tell that's my mum speaking again!). So teaching it hopefully will be for the immediate future, during which I hope to "self study" Maths.

There I have said it. I haven't deliberately done any maths for a long time, and now my brain is trying to pull me towards the books. (By the way - my glorious shelf, stacked with Maths book broke during the time I have been away!) I realise that in my third year, a lot of the modules I took weren't properly understood by me. I'm not going to study them again, but I'm going to try and get rid of my Algebra bug. I'm hoping to actually read the fourth year modules that I would have taken and other random bits of Maths that I enjoy.

You see there are some things which I have avoided mentioning in this post, and that is sadly due to the fact that I haven't spent time working on them. My desk should be with me soon and it is then that I hope to sort some unfinished business! (I use a laptop, and for some weird reason, I only ever work productively in front of it when I'm seated at my desk or some table. When I'm lying/sat in bed I don't really do much...).

Sometimes things happen and we wonder what would we have done had we gone back in time. I always believe that if something happened, then no matter how many times I go back in the Tardis, the same thing would occur again and again. This in one sense gives me some consolation, and indeed tells me to stop dwelling on what has happened. Now I'm keeping this post short as I don't want to ponder on the above question for much longer. You see I once posted about "karma" aka one of Newton's laws (!) and mentioned whether it was worth knowing someone's reality? You see would people think differently of the decisions that I made, if I told them the whole story? A few people do know my reasons, and Dr. Eccles knows everything hence why they are all somewhat understanding.

However my reasons are not any form of excuse. I could have still done four years for example, but I decided not to. I'm going to miss not going back to the Maths department next year, but if the Ollernshaw lectures show an appearance I might just drop by...

Sigh. Money has never motivated me. I just like having enough to get by. But somehow money seems very important to everyone else in my whole generation. You see tinky winky graduated too and will be earning more money than me. I'm happy for TW but all I hear is "you shouldn't have done Maths" from everyone else. Thankfully they don't know how I did, otherwise they would probably bury me alive.... They don't see teaching as a good money making career and are suggesting all sorts of silly jobs I should do. The reason I did a maths degree is because I knew that although I love to teach, it is never going to be a permanent career choice. Lets leave the future where it is!

I can't think of a mathematical way to end this post, so back to some quote it is:

Where all think alike, no one thinks very much.
- Walter Lippmann

Thursday, July 16, 2009

Graduation - A Memorable Day

Monday 13th July 2009 was the day my graduation ceremony was scheduled for, starting at 10am. Sunday night though, you could find me pulling my hair out from one side and my mother pulling it from the other! Yes - she was insisting that I "look smart" and gave me a huge complex about it all, and that too the night before the ceremony. I understood where she was coming from (whilst being deeply offended of course, at her suggestions about how I normally appear) but it didn't help. I ended up asking Dr. Eccles opinion on this in an email I was writing to him!

You see I have a "healthy sized" family and wanted extra tickets for my graduation, thus my email to Dr. E thanking him for his help. I had asked him if he could do me this other massive favour you see, and thankfully he knew a graduate student who didn't need the two tickets that he was allocated so I got them. (We were all given two tickets and had to ask for more if needed).
Anyway, I didn't sleep very well on Sunday and dreamt of deliberately falling of the stage to upset proceedings! (That might be because Bella had spoken to me earlier and had expressed her fear of falling down the stairs). {\aside this is more of a case to remember this for the future than anything else, but in one of the Galois Theory example classes, Bella was asked to go to the board to answer a question and she tripped on her way! Thus she was worried about repeating this in front of a lot more people}.

My ceremony started at 10am so I had to be seated about 30 or 40 minutes before hand, and the guests had to be there 15 minutes or so before the start. I stupidly didn't realise that you could be seated any time you went, and assumed that guests should be there for 9:45am. We live quite near to Manchester, so myself and one M.Hatter got to Manchester at 8:30am by train. I had to get there earlier to get all robed up and collect my tickets. The night before I had also given clear instructions to my parents, informing then that the ceremony starts at 10am, so they should leave the house at 9am. I had also found the post code of the car park (for my Dad) so he wouldn't have any problems - how very thoughtful of me I had assumed.

The idea was that I would get robed up and collect my tickets, which I would then give to M.Hatter who I had dragged along with me (at that ridiculous time!). M.Hatter would then wait for the others whilst I went inside Whitworth Hall. Brilliant plan in theory, you would have to agree...

On to the robing room it was then, where thankfully we also collected the tickets. However straight away a problem occured - my hat was too big. I politely asked for a smaller one, but still it kept on falling off! Now rather than feeling wonderful at the fact that I had now proven everyone who thought I had a big head wrong, I began to worry. The woman who had helped me with the gown was started to become creased around her eyes. I asked a third time and still the hat kept on sliding down to my eye brows. I'm not known as a pest for nothing though, and asked again and again and again.... until I found a half-decent hat! (It slid down but not drastically). Thinking about it now, when I had hired my gown I'm sure that I had measured my head wrong, thus the hat problem. Sadly though, the woman had the last laugh as the top of my hat was slightly damaged, which I noticed quite later.

All robed up I strolled in the sunshine and had a few photos taken. I honestly can't describe how cool it felt wearing the gown and hat. It was going to be a great day, I sensed. It also so happened that the car park where my Dad was going to park was a stone throw away from the AT Building, so it was quite close to where the ceremony was.

9am: I rang my mum enquiring as to their position and a mild panic started to build inside me. They hadn't set off yet. Not to worry I thought, they'll be here. So I then proceeded to make sure that M.Hatter knew the way to Whitworth Hall from the car park (which wasn't too problematic as we'd been there before in June).

9:13am: I spotted Milo with her family. I was also borderline hysteria now. My parents had only just set off. I didn't know what to do. We decided to walk to Whitworth Hall and hang around outside for a while, before heading in. I gave my backpack and the tickets to M.Hatter, and panic rising in my heart, we went separate ways.

I did one stupid thing though - my phone was left with M.Hatter and all my other things. I had no way of knowing where my parents were or whether or not they had arrived with Nuno.

The hall was ginormous and full to the brim with students and guests. I spotted Fizz's parents sat near the front and thought bitterly about where mine would be seated (no where....). As it was nearing 9:30am we had to be seated so had found our seats near the front. Now it so happens that the Powers that Be felt sorry for me as I was seated next to a friend who had her phone with her! But woe and woe again - I only knew my own mobile number and the house number! Nobody at home was picking up, and M.Hatter simply refused to pick up my phone (as it said my friends name on it - someone who wasn't recognised).

9:45am - I walked towards the back of the hall to a woman in charge. "If my family come five or ten minutes late can you please let them in? Can I wait outside for them? Please...".

But we weren't allowed out. The prefects were very strict with us and wouldn't let us leave our seats. This was Hogwarts readers! Witches and wizards in their robes and hats - yet I was still not taken in by this magical atmosphere. I had one last option: attempt to guess my Dad's mobile number. (If I say it in a certain way I know it, but otherwise I always forget a zero in the middle). Ring ring.....


They wouldn't be able to make it for 10am he told me. The motorway was very busy, and they might be five or ten minutes late. I sat back dejected. Hollow. Honestly speaking, sharing the experience with my family was what this was meant to be about. As my friend had free minutes (and she thankfully permitted me to use them) I rang my own mobile again hoping against hope that M.Hatter would pick the phone up. Ring ring...


I told M.Hatter to remain outside the car park (as the tickets had to be passed on to everyone else) and to inform me when they arrived on this number. Everything was going wrong. I enviously watched all the excitement around me, wondering who to blame! Ring ring...

It was my Dad - ringing on my friends phone. He wanted to know what building the ceremony was in as he had decided to drop my Mum and Nuno directly outside and come back later after parking the car. It was 9:53ish. I told my Dad that he had to get the tickets first so head to the car park as instructed. The phone had disconnected. I rang my own mobile again. The tickets were no longer outside the car park. They were on the move. What the heck was happening!

Now I don't know what happened next properly (as I was in a very bad state and hadn't had any breakfast too), but according to the myth, M.Hatter had decided to walk towards Oxford Road as my Dad had told him to do so. The plan being that everyone but my Dad would be dropped off directly outside Whitworth Hall.

At 10am the ceremony had started. We stood as the procession walked in, but I without a clue whether or not my Mum, Nuno and M.Hatter had arrived in time, was preoccupied. I solemnly sat, craning my neck towards the doors and balcony every five seconds, praying like mad. And then a miracle happened! My Dad appeared on the balcony directly in front of me and grinned down at me. Relief flooded me as I knew that my Mum, Nuno and M.Hatter had to be there too. Sitting back with ease for the first time, I smiled and let the magical feeling take over me.

The rest of the ceremony went smoothly (in contrast to earlier!) and I didn't fall down any stairs as I collected my certificate. It was only then that it hit me properly - I had got the degree I had wanted. My work in my first two years had definitely paid off. I carried a stupid grin on my face for a very long time afterwards too - just enjoying the sense of having achieved something. Even now I can't believe the dramatic change in fortune! How my Dad entered late I don't know; but the myth continues that my Dad had taken the graduand entrance, flashing his ticket to everyone around, wanting to know where to go. Thus he was ushered to the balcony where upon seeing him, I relaxed.

After the ceremony a lot of photos were taken after which the maths building had invited us for nibbles and snacks. This was great (although I was slightly late!) and it gave me a chance to talk to lecturers and other students, who I won't be seeing for a while now. They even had graduate hat cakes there! I hung around till 2pm-ish I think, after which I trudged home, having returned books that had been loaned to me.

Yes - this is the very long tale of my graduation. I think my Dad being late (though my Mum and Dad blamed each other) made the day all the more memorable. Wearing the robes had also felt great, and a part of me was actually wishing that I had bought them instead!

I started this post in July - and today on 15th August I finish it. Why? Well due to the building work I didn't have internet access for some time, and then I went away for a while. Upon returning it has taken a few days to sort things out (as the building work left a big mess) but hopefully normality is returning. I haven't checked my blog emails for quite a while as when I was at the computer I just checked my normal account; thus upon checking I was surprised to see a few serious emails about this blog amongst the spammy ones! This motivated me to finish this post, and since it is 2:34am I have decided to reply to all emails after some sleep.

I also think an update on my current position is best left for another post... :p

Monday, July 13, 2009

Hats, Gowns and Graduating!

Today at 10am I will graduate with a BSc (Hons) in Mathematics.

It feels slightly weird though. My graduation signals an end to my undergraduate days - an end to a certain chaos I lived in; however I don't feel "bad" or regret how things have turned out. I am to be honest mostly relieved that I managed to get a decent grade, for in my third year life went topsy turvy and my University studies suffered very badly. My worst University result was in "An Introduction to Algebraic Geometry" (no surprises there!) and my best was in my first year module "Sequences and Series"! Yes the very same module which, three years ago, I had hated and complained about till I went blue in the face.

I haven't thought about the major question "what next then?" just yet though. Thoughts of it flit through my mind sometimes, when I lose guard, but my problem is that there's too many things that I want to do but they all can't be done at once. Dr. Eccles best understands my situation at the moment, and once again I have to say that he's a great guy. Tinky Winky tried to give me advice the other day, but I don't know how many balls I can juggle.

This problem is closely linked with me studying Maths further. Before I would have loved to do the MMath course, but then I started struggling to pass my exams, hence that was out of the picture. Next comes doing the MSc, which is what I think I will do before considering a PhD. Yes - a lot of people are pulling their hair out at what I'm writing, since I was told that this is the best time to study what I like and get it over and done with. I recognise that my "mathematical ability" might be at its highest point at the moment, but my interest in Maths will continue to grow. Thus that gives me enough encouragement to not give up my hope of studying Maths further. I know that I have disappointed someone by my decision, and that hurts me deeply. However, other things in life are more important for me at the moment, and I wish to accomplish them first. The Maths will follow.

On Friday 19th June 2009 I was humbled by the University for some strange reason! I was told it was to do with The Galois Group, but on that Friday I had felt slightly out of place... This brings us to my next dilemma - TGG. I have two student volunteers for next semester, and lots of lecturers, but its students which we need. My summer holidays have been very "bad". I haven't been feeling well for a while (and my Dad dare joke about Swine Flu!), and this renovation work is just not finishing. Banging my head on the car's frame also didn't help... Anyway, I intend to get working on TGG in the summer once I have graduated and things calm down.

This is going to be a jumpy post so please bare with me! My results had gone online on Friday 26th June 2009 and I find it amusing to recall how nervous and twitchy my parents had been! My mum and dad had kept on ringing me asking "are they online yet?" and they didn't like hearing my dull no! The University did seem to enjoy torturing us, for they came up after 5pm I think which didn't help anyone's nerves.

There's a lot more that I want to post about, but I have to go to sleep now as my graduation is first thing in the morning. Humbug. I have got used to sleeping very late (or early!) you see, so I'm confident of looking like a zombie tomorrow. I actually can't wait for tomorrow now! I promise that I will resist the urge to throw my hat... (Like that's ever going to happen).

On a final note (!), this blog will continue as the Maths hasn't died yet, and of course shouldn't die. Yes - it has shrivelled up a lot, but as I said, the more I studied the more I posted (so you get the idea of when things went pair shaped!). I would once again like to thank everyone who commented and helped me to graduate tomorrow -- it has been greatly appreciated. :)

Friday, May 08, 2009

End of an Era

Today is officially the last day, and indeed my last lecture of my University "career". Next week is a revision week, after which my exams will begin.

How am I feeling about this? Well yesterday during Hyperbolic Geometry, it seemed to hit home that everything is coming to an end. Today it feels slightly worse, but I know in my heart, that I am making the right decision.

At the moment I have one foot in one boat, and the other foot in another . Both these vessels are travelling at very fast speeds, and it is inevitable that I fall, as I have poor balance as it is. Thus both boats end up crashing. I propose that it is better for me to travel in one boat first, "become an expert" in guiding it, and then slowly make the jump again.

This decision may harm my mathematical aspirations, people claim, and I will become dumb in the subject which I already struggle with. However, I disagree. I won't lose my passion for Mathematics which is enough for me.

This will be a short post as I will leave the house in the next five minutes. I don't think that I could have wished for a better three years at Manchester. Yes, things did get hard for a while as I wasn't able to cope with sudden changes. However, that was part of my experience and hey, I'm smiling now! I don't really want to leave the people behind you see.

Last night, the teletubbies claimed that I was the worst Mathematician they knew (!) as I kept on saying that Maths was greater than Physics (and every other subject on the planet). I couldn't make F'(S) equal to zero, so was already frustrated, after which I deliberately annoyed Po and Tinky Winky, as they were revising Physics! I think I'm the only Mathematician that they know...

Anyway 10:45am means I must leave for the bus stop now!

Sunday, May 03, 2009

Nonsensical Theorem and Proof

Today I was in the mood for some Maths; and as I am home alone, I had no distractions etc. First up it was the Euler Product for the zeta function. I understood the sieve process, until the very two last lines which complete the proof. We take the sup and limits and then draw a nice black square. Well not very nice in my case, but at least I followed the main idea I consoled myself.

Next came lecture five - Derivatives of Infinite Product.

I understood the first paragraph, but then came the Theorem and its proof. Some generous lecturers offer rewards if students spot any mistakes in their notes. Although this proof and theorem is not something I originally wrote, I too will be generous and offer a reward if anyone can point out any corrections. However... to claim your reward, you have to ask for it in person! By the way I can on this occasion say that I copied exactly what was on the black board, as I remember the lecture very well (due to a small hiccup). So here goes:

Let f= \prod g_j with g_j \in Hol(U), f \neq 0, g_j \neq 0 in U, and f = \prod g_{\lambda} (L.U). Then

\frac{f'}{f} = \sum \frac{g_n'}{g}.


f_n = g_1 ... g_n \Rightarrow \frac{f_n'}{f} = \frac{g_1'}{g_1} + ... + \frac{g_n'}{g_n}.

But f \in Hol(U) and f_n' \to f' by convergence lemma (2.2).

Let C be a circle in U, then \exists \delta : | f(z)| \ge \delta "more than" 0,

\exists N \text{ st } n \ge N \Rightarrow |f_n(z) | \ge \frac{\delta}{2}.

\Rightarrow | \frac{1}{f_n(z)} - \frac{1}{f(z)} | = \frac{|f_n(z) - f(z)|}{|f_n(z) f(z)| } \le \frac{2}{\delta^2} |f_n(z) - f(z)|.

\Rightarrow \frac{1}{f_n} \to \frac{1}{f} uniformly on C

Therefore \frac{1}{f_n} \to \frac{1}{f} uniformly on each compact disc.

Therefore \frac{1}{f_n} \to \frac{1}{f} (LU) \Rightarrow \frac{f_n'}{f_n} \to \frac{f'}{f}.

If you can't find any errors and understand the proof, some help would be nice! I'm being dumb, I know, but how does the conclusion in the proof help us?

Anyway, it's food time now! Erm - not fast food again... Pizza is quite healthy in my opinion, especially if it has some pineapples on it!

Sunday, April 26, 2009

Brain food, Insults, and Kiddy parties

I bought 10 Ruth Rendell (Inspector Wexford mysteries) for £7.50 recently, and they are inspiringly quite "thin". Well they are not your normal John Grisham sized book you see, and they're equally good to read. They're stacked next to my bed in the correct order, waited to be gobbled through by myself.

Now you might recall that I once stated that I never read fiction during term time, as it sometimes stresses the point that I am not studying, hence I stress out! Well I am happy to announce that I am cured of that bug! (Not for the next billion and one...).

Yesterday it was my cousin's sons birthday, and naturally she had to hold a birthday party (for him I think...). I obviously didn't expect to be invited, but unfortunately I happened to pick the phone up when she rang, and so ended up promising that I would attend. (They want me behind the camera you see!).

The house was full of loud, noisy and sometimes annoying children, as well as their equally loud, noisy and .... (!) parents! I had a good time I must admit, as I ended up taking a few decent shots behind the camera which obviously put me into a better mood. However I chanced upon someone who has a disliking towards me. Milo once said to me that I sometimes don't really get it when people say "evil" comments to me, and just act normal. Milo doesn't know that I let people say what they want to because it shows me a bit of their character. I don't really get why people like to throw superiority (of any nature) onto others.

I know y'all are probably annoyed about me continuously mentioning that my planet Earth has changed and stopping there; but I would rather not say any more. The key fact is that I happy on the planet I am standing on at this moment in time. I am slightly stressed about a lots of things (due to jumping through space and time in my Tardis *cough*), but I have this small hope that I have started walking down that yellow brick road. I just don't know where it will lead me too.

Due to the fact that I'm not miserable, unhappy etc. a few people seem unhappy. Perhaps this is why I'm currently really enjoying the book "Shake Hands for Ever". There's an old woman called Mrs Hathall who revels in other peoples misfortune (and she's quite a character). It saddens me to say that I know a few Mrs Hathall's. Firstly, whatever I do is for myself, and once I'm Prime Minister (!) that's when they can say that I have achieved something! You see parties like this are a chance for everyone to get together and catch up. I haven't got any catching up to do and would rather prefer being told to just go and play football on the X-box (but alas the seats have already been taken... and nobody wants to risk being embarrassed by an amateur).

I hate people who want their egos pampering. Sigh. I am still annoyed, but it's more to do with my expectations of certain people. Thankfully it's another couple of months before someone else has a birthday!

I want to be an inventor and want to invent something cool. But what to invent, I don't know! I have been thinking deeply (which means for more than a minute of course!) about doing something drastic. At the moment I am drawing blanks... . I will keep you updated of course, if I think of something!

The title was misleading I'm afraid. Well I tried to work my way backwards, and was now meant to talk about all the junk food I am eating and how I need proper meals, as I am quite unhealthy. However, that would make me feel guilty and instead of phoning my sister for a lift, I would walk towards my destination! That's not going to happen thought... well I hope not.

I have a coursework in Geometry for next Thursday and and and I hate that module, so naturally I hate anything associated with it, which includes the coursework. I will go and study now (ha!) and see if my hate decreases for it. Ah this reminds me - I was supposed to search the net for some decent Intro. to Algebraic Geometry notes. (Anything to delay the studying....)

Saturday, April 25, 2009

Final Galois Group lectures of the semester

Dear All,

You are invited to attend the last Galois Group lectures of the semester (and maybe my last one too!). Two lectures will be given next Wednesday (29th April) at 1:10pm in room G.205 by Speaker 1 - Linux for Mathematicians - a simple introduction; and by Speaker 2 - A "Group Calculator" to help in learning group theory. (Abstracts below).

The lectures are open to everyone, and registration is not required. Please do come along and make this event a success. Free refreshments will also be available at the end

For further information or any queries, please feel free to contact Dr. M.D Coleman or myself.

See you all there!

Best wishes, Beans
Wednesday 29th April 2009 - 1:10 - 2pm
Alan Turing Building room G.205

Speaker 1
Abstract - Linux for Mathematicians ? a simple introduction
Drawing on approximately twenty years experience in writing and maintaining software in various aircraft stress offices, I intend to discuss why I believe programming skills are likely to be very useful to any mathematician who works with numbers.

I shall consider a few topics which are of interest to individuals rather than to employers, and show that computers allow mathematicians to get results which, a few years ago, would have needed large teams of people.

I shall also discuss the Linux operating system, and its support groups, as I believe this provides a suitable environment for people wishing to develop computer skills without relying on an employer.


Speaker 2
Abstract - A "Group Calculator" to help in learning group theory
As an undergrad trying to grasp what symmetry groups are all about, I would have found it useful to have an easy "group theory calculator" to experiment with simple examples of groups. When I could not find a suitable program on the Internet, I set about writing one to teach myself basic group theory. Other students might find this a helpful study aid, so the talk will outline what the Calculator does. You can download it, plus fully worked examples, from

Friday, April 24, 2009

I Dreamed a Dream

I haven't blogged for a very good reason. I call it escapism. Blogging makes me ask questions about what I will be doing next year. Blogging forces me to address issues that I do not have the guts to face.

I have been a massive chicken, I confess. However today, as the Tweenies enjoyed a cup of tea (and some sushi!) we all reflected on our three years at University and how only a month or so remains. It was sobering. Fizz (I think) commented that we shouldn't think of what we will be leaving behind, but take what we can with us. (Or something like that...).

I don't want to leave. I don't want it to end. But that is what will happen, I know.

My reluctance to accept that I will be leaving soon is due to many reasons. I want to remain unburdened by certain responsibilities which are a natural process of life, and which I fear will come across my path once I graduate. Namely "growing up". I don't mean becoming maturer - for I can't see that ever happening. A certain freedom is associated to being a student. We have disorder - chaos - in our orderly lives. But we get along just fine. We like the chaos.

I resent (to a certain degree) "unchaotic" systems. Things that force a stopper on human creativity and natural flare. University though, doesn't do that.

I know that I am "young and foolish" and I don't really know what lies ahead until I have taken a bite of the apple; but still my heart is restless.

Motivation is another thing which I am very low on at the moment. Exams are my worst enemy. The prospect of yet another year of exams is definitely making the fourth year look like the empty set. My circumstance have also changed - in all senses - financial etc.

But then I wonder how life modulo (human baggage) would be.

I feel sad because there is so much more that I want to do whilst at University, and I feel that everything is going to prematurely end.

Maths I still love (if you will humour me for a second!). However, I must confess that since the balance of my life shifted, I can't find the time to focus on studying maths. Hence I wonder, if I do four years, would it all end in tears?

I chose cool modules but I must say that I am disappointed with two of them - those which I expected to be more better. Namely, Number Theory and Algebraic Geometry. The course content in Number Theory seems yucky (!) - I know prime numbers are the goal, but it seems like another course on series - which I can't manipulate of course! Silly Von Mongoldt. Meh.

And the geometry course - well let me just say that I really miss Dr. Eccles' lectures.

I know that I like a certain type of lecturers, but if you ever study Maths at Manchester University, be sure to attend courses lectured by Dr. Eccles, Dr. Coleman, Prof. Stohr, Prof. Sharp, Dr. Walkden, Prof. Prest, Prof. Heil, Dr. Hewitt, Prof. Dold, Dr. Khudaverdian and Prof. Rowley (in no particular order - and I hope not to have missed anyone out!).

The above lecturers are all awesome and really friendly as well. Sigh.

Sadly, I can't even answer the question: What do you want to do next year?

Nothing. Maths. Nothing. Teaching. Nothing. Win the lottery. Nothing.

I know I'm not alone in my worries, for many other students are probably experiencing similar issues, but gosh does it feel lonely. I need to do something though. How can I leave?

All good things must come to an end? I think that's what Bella said to reassure the rest of us!

By the way, you are all invited to attend the last Galois Group lectures of the semester next Wednesday 29th April 2009, and perhaps my last one too. (Kill me now! ;) ). Well at this moment in time it is my last Galois Group lecture, hence why I am being forced to do the introductions, even when it's not my turn! It's been good though - The Galois Group. And when the second speaker of next weeks lectures asked me: "Have you enjoyed it?"- "Too much" was my reply.

I'm sad that I couldn't get the mugs produced though - and I'm desperately trying to think of something to give to the volunteers. (Whilst trying to pass my exams!)

Whoops - I'm running out of steam now. The title of this post and indeed this post came after I watched Susan Boyle (yes everyone's talking about her!) on YouTube. It was her song (lyrics below) which seemed to cry out for attention:

I dreamed a dream in time gone by
When hope was high,
And life worth living
I dreamed that love would never die
I dreamed that God would be forgiving.

Then I was young and unafraid
When dreams were made and used,
And wasted
There was no ransom to be paid
No song unsung,
No wine untasted.

But the tigers come at night
With their voices soft as thunder
As they tear your hopes apart
As they turn your dreams to shame.

And still I dream he'll come to me
And we will live our lives together
But there are dreams that cannot be
And there are storms
We cannot weather...

I had a dream my life would be
So different from this hell I'm living
So different now from what it seems
Now life has killed
The dream I dreamed

I'll have TGG post up soon as well. Hopefully I can stop avoiding this blog too. *Tries to end on positive note *

It's the weekend! Woohoo!

Tuesday, March 17, 2009

Oh How I Hate Revising

Especially at this time! Yes tis my fault, but my Number Theory course has been very uninspiring up till this point. The inspiration being that I have a test today at 9am which I am going to do very badly in.

I honestly don't know how I can get a grip of my motivation and study! And another funny figure is the amount of third year students who I have heard say: "I hate Maths".

I don't hate the maths, but I hate exams. Oh and I hate the fact that I need to make a decision as soon as possible about next year. By the way, Dr. Eccles is one great guy. I liked what he said to me today: I should make a decision which is best for me, and not what other people would like me to do. He said that it will be sad to see me go, but I shouldn't stay for that reason etc etc. But you get the idea. That has taken a load of my mind though, as one reason as to why I am was "forcing myself" (perhaps) to stay was The Galois Group.

I don't think I'll ever lose my interest in maths when I leave, which is what I'm clinging onto at the moment. But tick tock.

Back to the BORING old Riemann Zeta function. Gah. I might write too much but it's better than writing too less in my humble opinion!

Monday, March 16, 2009

Galois Group lecture on Paradoxical Decompositions

Dear All,

You are invited to attend Professor Richard Sharp's Galois Group lecture about 'Paradoxical Decompositions' this Wednesday 18th March 2009, at 1:10pm in the Alan Turing Building Room G.207. Free refreshments will be available at the end. (You would be mad to miss this lecture!)

Please feel free to email me if you have any questions or comments.

Best wishes, Beans

Wednesday 18th March 2009 at 1:10-2pm
Alan Turing Building, room G.207

Professor Richard Sharp

Abstract - Paradoxical Decompositions

It is possible to decompose a solid sphere into a finite number of pieces, which may be rearranged to make two spheres each with the same volume as the original one. Put more informally, it is possible to cut an orange into a finite number of pieces and reassemble them into two oranges of the same size. This is called the Banach-Tarski paradox and is perhaps the most counterintuitive of a family of so-called "paradoxical decompositions".

This talk will explain some of the mathematics involved, exploring concepts of volume, non-measurability and self-similarity.

PS: I'm still alive - but I've lost my voice and memory it seems, as I have no idea whatsoever as to what I did this Saturday! I'm straining to remember but my minds drawing blanks! (On Sunday some cousins came over though...).

Monday, March 02, 2009

Mondays can KILL

Mondays are very dangerous. Especially when one has six hours of Maths lecture, namely: Number Theory, Commutative Algebra, Algebraic Geometry, Galois Theory (x2) and finally Hyperbolic Geometry.

What also makes matters worse is that I'm not allowed to go to sleep yet as it is too early, and that I have a lot of work to do. I also have a test on Thursday which I am not particularly looking forward too.

From the modules that I'm taking this semester, I have to say that Algebraic Geometry is one which I hate the most at the moment as I don't have a clue as to what's going on. Then I next suck at Galois Theory (sadly) as it is very hard in my opinion, and I am lazy and I do not like Algebra!

The good thing is though, that my algebra modules do over lap which is helpful at times. You see Galois Theory is a fourth year module so to us third years everything is NEW, but not for the fourth year students. (As in Commutative Algebra Eisenstein's Criteria for the irreducibility of a polynomial in Z[X] was mentioned, which we covered in Galois Theory the other week.)

Deep breaths Beans. Results should be out on Friday. I have actually been having nightmares about them. I have been reduced to using short, disjoint sentences - you'll have to forgive me!

I feel that I am fast losing patience with a few things at University, but I need to find some discipline as fast as I can. Namely because I'm not studying at all as my routine has been completely disrupted, and this is beginning to show now!

Anyway - going to keep this short as I am going to try and sneak myself to sleep! By the way, there are Student Galois Group lectures this Wednesday (4th March!), which I will post more about tomorrow.

Saturday, February 28, 2009

This Blog is Not Dead

Well not yet anyway! I might have died for 2.5 months, but that's because the Internet... my life source (!) was gone. It finally returned last night at 7pm, but you will have to forgive me for not posting then as I was too busy celebrating!

Don't shake your heads in disgust - surely you were missing my lame jokes and comments? No? Or you don't want to confess?!

Anyway, this is going to be a shortish post as I have a million other bookmarks to organise (delete!) and as I have a test next week, I'm not going to get carried away today.

Surprisingly, not having the Internet was quite great in one sense, however I really did miss my blogging, and not being able to check what the binomial distribution was during revision was very annoying! (Well when you have negative powers...).

You could say a lot has happened in the time I haven't been waffling about things. Too much for my pea sized brain to comprehend at times, but then that's what makes us human.

This could potentially be my last semester at University as well! How did that happen, you ask? Well the exams I sat in January were the worst I have sat in a long while. I am absolutely sick to death of exams and the prospect of doing another year with more exams makes me cringe. So it's either a PhD or teaching. I have been told that it is frowned upon to do a PhD without having done four years, but I could always do a part time PhD. I sort of want a break from it all. The maths, the Galois Group, Univeristy, working, needing money etc. I want a state of dynamic equilibrium, but I'm struggling. I do worry though, about what the end of the semester will bring. I wanted a good degree - too badly - I had things to prove. However perhaps it will be me with egg on my face... again.

Ah well, I better not make this "back from the dead" post too dramatic, lest you all smack your forehead and shout "WHY?"! Yes that was lame again, but hey I'm back! (For now anyway...).