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. :)

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!

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:

Theorem
Let with in U, and (L.U). Then

Proof



But Hol(U) and by convergence lemma (2.2).

Let C be a circle in U, then "more than" 0,

.



uniformly on C

Therefore uniformly on each compact disc.

Therefore (LU) .

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!

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....)

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.

AND

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 mathstudio.co.uk.

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!

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!

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...).

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.

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...).

All Burnt Out

Today I am exhausted. There is no other way to describe me. I am one of them stupid people who have the habit of 'wanting to put my foot into everything'.

It was the student Galois Group lecture today, which although I didn't understand parts of, was very well delivered and the turnout was equally great. I did something to make sure that we had a good turnout, which I will mention in a minute, but the lecture was a fantastic way to end the semester. During the lecture I also took back what I said about TGG in my previous post, for these Wednesdays are honestly worth it. As I have said on numerous occasions, I only wish that I could spend more time trying to take the Galois Group further. (Well at the moment I do spend 98% of my time on TGG, so the other 2% would definitely do some good!)

You see the final week of term is always a dodgy time for a lecture, and considering the fact that I have been shirking my responsibilities for the past week or so, I was worried about the attendance. (The student was very keen on a big audience you see). The lecture was titled Maths and Philosophy, and a natural part of me wanted to advertise in the Philosophy department, but I just never got round to it. However last Thursday, by chance I bumped into a lecturer from Manchester who I had spoken to briefly during the Philosophy workshop organised by Professor Borovik, and he gave me his email address as he was in a rush. I emailed him and asked him if he could advertise the lecture amongst students in his department and that seemed to have done the trick!

The lecture finished at 1:45pm which sent me into a mini-panic, as if we had all started piling out of the room, the refreshments would not have been set out - my friends normally get started at 1:45pm! What I didn't know was that the student had intentionally finished early as he had expected lots of questions. The following fifteen minutes were indeed filled with questions and discussions, which made me deduce that the lecture was more of a philosophical one than a mathematical one! I honestly felt a lot of the philosophical jargon go over my head, but as the student said, the idea is that I now read up more into this topic, which I will (eventually!).

Dr. E kindly did the conclusions etc. and he pointed out the fact that a lot of Physicists and "third floor" people of our building had ventured down for the lecture, which was nice to see. You see if I had the other 2% of time and effort, then I could work harder whilst advertising these lectures and always get 50+ attendance. I got lucky this time round (i.e. the powers that be feel sorry for me!) but the lectures are not just for the maths department - they're for everyone who is interested by what will be said! I just wish that I could find the time to get the stupid website online so everything was more accessible.

Indeed, I wish for a lot of things. I can't recall mentioning this on my blog before, but if I had another me, life would be complicatingly simpler!

Today I am unable to stand on my feet at the moment, as for the past week or so my food intake dramatically decreased, due to my stupid immune system playing up. I've been feeling slightly better so I have wanted to stuff my face with whatever I can get my hands on, but my body disagrees with this. Today I had to skip breakfast, so I have only eaten an apple, a wispa, a jaffa cake, some pringles and drank two cups of tea. That explains my exhaustion as today I have also ran more times than I can count. I had to run in the morning to make sure I wasn't late, and then I had to run to get the milk, and then I had to run when I saw Jerry and .... and yes I actually do run, as opposed to walking fast. Don't get me wrong, I love sprinting, but the stupid adrenaline kick that I get on Wednesday makes me feel invincible which doesn't help! I honestly don't know how I managed to stay standing today.

You see straight after the lecture at 2pm, I had this meeting to attend which I ended up going slightly late to. I "sit" on various committees in the Maths department and this happens to have its uses (note - I did say I am one of them 'gits' who like to dabble my hands into everything..). Initially, perhaps naively, I only actually volunteered as I thought that by doing so I could put forward the case of TGG, so the people who sit on comfy chairs above us would take it seriously. Yes that was very naive of me, but I enjoy these meetings (at times!) so everything is good. The Galois Group has actually benefited, but I think I have personally benefited too.

Today the meeting went past 4:15pm (hence my tiredness!) and parts of it did drag. You always have your "nap time" in meetings and towards the end I had mine but it was a nice nap, as 'Peter' who was sat opposite me did something that amused me. I sat chuckling to myself, not as discreetly as I would have liked, but there you have it!

Anyway - I digress. Two days left till freedom/doomsday/exams! More on that later, but I got the time to sit at the computer so I thought I would type whatever randomness came to mind, and to thank all the people who have made an effort to attend Galois Group lectures this semester, and who have helped to keep me sane! Thank you. :) If you have any feedback on how things went this semester, and how I can improve, please do let me know. I value any constructive feedback.