Wednesday, October 29, 2008

Crikey - it's snowing!

I just woke up a while ago and noticed the snow as I walked downstairs. I didn't believe my eyes at first, but the dream that I had been enduring just before I woke i.e. being late for my 11am lecture, was enough to convince me!

Last night I had gone to sleep fairly early (in my books!) and thus, I was supposed to wake up earlier than now to "not do some maths". I suppose that was rather hopeful of me; so instead of trying to do anything at home now, it would be in the interest of my 11am lecture to get into Manchester as soon as possible! Roll on Calculating Careers... .

PS: I am normally quite a fan of snow, but since college it has been quite the disruptive thing.... . I fondly remember "pretending to be ill" in my Chemistry lesson in college just so I could join a snow ball fight with friends! Everyone else had been in lesson apart from the group of us so it was an open playing field! The lesson was one in which everyone did their individual revision and called upon the teacher when stuck, so I wasn't missing out on anything (although I'm always reminded of my crime).

Tuesday, October 28, 2008

Calculating Careers

There's nothing like "advertising things" at the last minute! Unfortunately though, for those interested, I believe tomorrows event (advertised below) is for Manchester students only. Well the email did say "Although you will not need to pre-register, you will need to show your university student card to enter Calculating Careers and gain a student information pack." but I'm not sure if you can pop by and make do without the pack?
A year or two ago I would have attended the teaching panel at 3:15pm but tomorrow (if I stick around for that long), I will most likely attend the other talk at 3:15pm!

By the way, it may seem that I have very nasty feelings towards this event but that is not the case - I think it will prove to be quite useful for many students. My problem was that whilst organising the event, every single room on the ground floor of the AT building was booked by the organisers, when clearly most rooms will be utilised after 2pm. I have made my peace now though (!) for we have rooms for the lectures in week 7, 10 and 12 and I also have abstracts, pictures and nearly complete posters. I realise that it is better to wait for the above event to finish before letting my posters show the department how things should be done!!

[The department were naughty and didn't speak to George and crew you see, and the poster you see above wasn't on the wall for very long! As I was speaking to George today, a woman named Bev (I think) walked past into the lifts. She knew George and gave me an interesting piece of advice on how I could go about getting George to turn a blind eye. (Nothing violent of course....)!]

Now I am brain dead today and will remain so for a very long time (you will be happy to hear, thus a shorter post!). My day was mathematically quite nice. Well group and coding theory was not very appetising, and then applied complex analysis was too filling, which left Measure Theory to do the digesting! Sweet. Complex analysis had too much going on and my stomach was bursting with lots of disjoint information which I should have connected by now. Note: remember to take complex notes in tomorrow.

I don't feel like an undergraduate student at times, and today happened to be one of them occasions. Why do I say that? Well *whispers* I crossed the atrium bridge today! ;)

Haha - normally I prefer to do a u-turn, but today there were only a few people about and my energy levels were running dangerously low. I wish that I don't study any maths tomorrow. (Let's see how sod's law likes that then!) You all should know what I meant by that (if not feel free to ask) so if you get a minute please ask my "well-wishers" to send some help.... . I need to stop trying to end this post with a lame sentence.

Monday, October 27, 2008

Least Unsatisfying

It seems that the powers that be either felt sorry for me today, or they want to keep me alive long enough to throw other misfortunes onto me! Everyone seemed to be very nice to me today, well apart from when Dr. C was being mean but he said that I was misunderstanding his humour (fair enough I replied, tis a Monday after all!).

Well actually Dr. C might have been mean twice come to think of it! It goes without saying that I often say a lot about not a lot, and an easy way to distract me is to get me started on a completely different topic about which I can say a lot. (I now know his plan and will not fall into this trap again!) Anyway politicians are famous for saying a lot about not a lot, but is suggesting that I be a politician an insult?! I didn't take it as one (you'll be relieved to hear so Dr. Coleman is perfectly fine and healthy...) but this did distract me from interrogating him about the email he was supposed to have sent to all undergraduates, and instead I went of on the road about when I was interested in politics!

Anyway, let us move onto the nicenesses of today for it is rare for one to ever say "I had a nice Monday". I was four lines and a diagram late for my 9am lecture but that was due to bad judgement from a fellow Mathematician and myself, when "choosing" which bus to catch. (One often does not have the liberty of choice in such matters, which is how it should be...!).

The lecture had an involved proof which did not involve me (!) but when a little bit of group theory was mentioned, I was relieved that it made sense. Come now it was only about cosets, you mutter, and basic properties about them! That being so, the lecturer did give me a heart attack when he made a typo and wrote Ha = {ha | h \in H} as the left coset of H in G! Having done my group theory coursework test and defined that to be the right coset, I began to wonder whether I had just lost 10 whole percent of that module. Fishing my group theory notes out I relaxed for the remainder of the lecture.

I stayed for half of the example class as I had posters to make! This is when the stormy clouds came out of no where. The computers in the cluster are the most disgraceful invention to mankind, well maths students in particular. I have been disgusted for quite some time to note that TeXnic Centre is no longer installed on them, whereas it was available last year. Today however, my issue was with open office. You spend 5 minutes finding a computer which actually logs you in but then you find that the blimmin software won't open. I had 15 minutes until the Topology lecture and try what I may, I just couldn't get the software to open.

Finally when I had had enough and decided to log off, it "installed". Pfft. The Topology lecture was better than last Mondays and I am happy to say that my incessant, unprovoked attacks on Dr. E (!) might have got me somewhere! One (!) of my complaints had been that we should continue the lecture in the first period of the example class, for then one could leave and not stay for the example class if one didn't want to. Unlike previously where I used to wait around and doodle during the eg class and then barely be concious when Dr. E finished the lecture. [I actually did stay for the eg class today, but at least I didn't have to be 100% awake for it.]

I'm actually quite pleased to report that I once again had some lunch today. Well I forced myself to ignore the posters and other TGG issues until after my last lecture of the day, and sat with the Tweenies for a bite and some tea. Hopefully I can keep this up!

It's funny, how us humans are built for survival, or perhaps how our survival instincts kick in. You see normally after lunch I have a further two hours of lectures. Normally I am able to struggle through the first hour and remain alive for complex analysis at the end of the day. Today however, after the group theory lecture, when I knew that I no longer had to keep my brain alive, I slumped exponentially! It was quite amazing how all of a sudden I lost the ability to speak and understand simple things, and could just mumble myself along to the computer room for my previously postponed activities!

At 3pm I was in the computer room and it was 3:20pm when open office finally opened. However after only five minutes of it opening the whole computer crashed! There's nothing like anger to get your brain charged again, and so, turning the computer off I stormed out of the cluster to find other computers. Well the ones in the Brian Hartley (BH) room to be precise. They're not for undergraduates but I had previously spoken to DW and she said that since I needed WinEdt for Infinite Descent, she was okay with me using them. It seemed however, that open office was not installed on them computers as well! Defeated and having wasted a lot of time chasing dead ends I decided to get to work on the magazine.

You won't be surprised to hear that I faced an equal amount of problems with WinEdt. I think once you get the hang of it, it doesn't look too bad; but how was I to know that the pdf file would be in my documents? They're meant to pop up automatically once compiled! Giving up, steam coming out of my ears, I decided to see if I could bug Dr. P (an IT genius) about the perfect solution floating in my head. This is when the clouds changed faces. I saw Dr. P crossing the atrium bridge and quickly tried to intercept his path. He saw me in the corner of his eyes and thus walked faster, but I did manage to catch up with him!

My problem: would it be possible to install TeXnic Centre on the cluster computers or get star office to work instantly on them? My solution (for the answer to my problem was obviously no!): install open office and texnic centre on one of the computers in the Brian Hartley room, which I could then use. My Monday morning well wishers were working hard at this point and Dr. P seemed to agree with my solution (but I left it till later to drop mention of TeXnic centre). So we strode to the BH room and he used his administrative powers to set me up with what I needed. It took a while so I went to complete other errands whilst it downloaded.

On my travels I first went to see DW, who has saved me a lot of embarrassment and trouble as I had wrongly assumed that the next Galois Group lecture is in room G.205, when it is in G.207! I also happened to bump into Professor Borovik (after some time) and at the end of our conversation I made the same mistake again: I said the "fingers crossed". For those who read Prof. Borovik's blog, you might recall an incident which involved his finger. I might one day report on the circumstances of that incident, but the magic words "fingers crossed" had been said by yours truly before the fatal injury. Thankfully though, I was happy to see the finger looking much better!

Back to the Brian Hartley room Dr. P was finishing up but I had enough time to ask him the burning questions which have been haunting me for my whole life! Well since I got started on TGG if you want to be fussy.... I tend to send an email to Dr. P or Rob or PG asking them to print the posters in colour for me, as the computers downstairs only print black and white things. Now this is quite a messy situation (and being the graph theorist I am!) I am trying to make the process more efficient. So can I not print the posters myself, I wondered loudly (and in the most "unobvious" manner of course!). It can be done it seems, but I will leave such matters to another Monday when my well wishers are hard at work again!

So I now have my own computer in the "post graduate" cluster - yes, the software (TeXnic Centre and open office) is only installed on one computer which will now support an "out of order sign" courtesy of yours truly - thus it's always going to be available when I need it. Muhahahaha. Don't go around telling anyone my cunning and discreet plans though for they might take this "privilege" away from me.... Well in my humble opinion, it's about time that I had epsilon benefits for working on TGG! So now I have my "own" computer and a nice little corner where I can sleep without being disturbed by anybody. Perhaps I won't have to do postgraduate studies after all? (And my Webmail account maintenance means I get 300MB instead of the current meagre 50MB) I did conjecture that perhaps the powers that be are giving me such perks for they are trying to tell me that I don't need to do post graduate studies after all!

I was quite lucky to bump into Dr. C today, for I was actually leaving the BH room to go home, when he walked into it. He did try his best to evade me but he can't always hide inside the TLO! I was also lucky to bump into Prof. S' whilst I waited for Dr. C to stop playing hide and seek. He was very kind in telling me something which he hopes to do at the start of tomorrows lecture. (By doing this he ensured that I won't be shell shocked during the lecture, which would have been a shame indeed!) Note: I actually informed him of something else (which he didn't know) without any hidden clauses! So I'm not such a git after all... . ;)

The calculating careers event is this Wednesday and obviously all the lecturers remember to remind the undergraduates about it at the start of their lectures. They even have a fancy acetate which they stick onto the OHP - how very thoughtful. This is a perfectly reasonable method of advertising, but it once again shows how many people actually read my emails, for I send separate emails specifically asking everyone to mention TGG lectures in a slightly similar\{ohp thingymajib} way. "Remark": cheers to all those people who do help me with advertising TGG lecture events, and you have my blessings to help promote this calculating careers event! Ha. :D [I saw George today and grudgingly thanked him for his consistency in taking certain posters off the walls! If anyone knows what George likes to eat, then please drop me an email. My next plan is to bribe him so he all of a sudden can't see my posters that might appear in the lifts....].

My eyes drift to the title of this post, which I must credit Dr. Coleman for. Isn't that such a brilliant way of confusing people when telling them something which you might like? I have to marvel in its brilliance and I must confess to having overused the title already, as Po is on the verge of insanity! (Two points for the Bean!) I don't mind it if you find my posts least unsatisfying... (Though I wonder how long I've gone on for as I typed most of this in word pad!)

I will end with something I read on a wall or other:

"The test of fairness is how fair you are to those who are not".

I really like that or should I say that I find it least unsatisfying! It makes sense in a weird way, and on that note I will retire to my slumber. (Tomorrow it is going to be more hectic than today...).

Sunday, October 26, 2008

An unproductive weekend

I have done nothing "mathematical" this weekend, which is quite the shame for I had every intention of being productive this weekend.

How do I measure my productivity? Well it seems that I only turned my computer on now, and for the whole weekend I haven't touched it.

Come now, doesn't that mean I must have been busy doing Maths then? you wonder. Ach, what can I say - not all is that simple with me!

Normally when I'm being "productive mathematically", I spend some time getting lost in my notes trying to make the nonsense appear sensible. Then when I have had enough I switch the computer on, check the emails and perhaps post something here about what mathematics is currently bugging me. It seems (looking at the frequency of my posts in certain months), that I post more when I'm more "mathematically active". That does sound quite strange to me but there is no denying it.

My weekend has been a very hungry weekend. I ate breakfast in the morning and a meal at night and that is all. My fault I know, but it is such weekends when tea seems to be a dominant feature, that I envisage being "rich" one day and having food given to me on a plate. Ahhh. Doesn't that sound just great? Or a Sainsbury next door would also be great....

I'm going to go to sleep early today for tomorrow is a Monday which spells bad news. I was going to try and do something "productive" on the computer (i.e. TGG stuff) but sadly I am not in the right mood or frame of mind to do so. Perhaps after my lectures are over tomrow, I will work on catching up with everything.

I will have to extend the deadline I feel, to this Wednesday for I can't seem to send emails out to all the students. My University email account is also going to be out for the count "overnight from 6pm on Tuesday the 28th October until 9am on Wednesday the 29th October" for upgrades.

By the way, it is change that I fear. I figured it out! I won't ever grow up (woohoo!) and responsibility is acquired through new experiences in life, which I can cope with. But drastic changes which can unbalance me, sometimes scare me. I can take things on board, but dealing with some changes is quite hard (for me). I don't imagine myself overcoming the challenges that are presented in such instances, but how such a such a thing will no longer happen (etc). The funny thing (but in a not so funny way) is that on occasions I know what I'm doing wrong and what I should do instead, but I don't. (Eg. driving - I know what the heck I should do and why I'm not doing what I should, but I still do what the heck I shouldn't, if you follow me!)

If only the weekend was to pity me and give me a chance to go back to Saturday. I'm actually nervous about Topology now for that is the only course (apart from Coding but that's so and so (!)) which I have yet to get started on. Ach, it's week five already but I'm still staying cool headed yet.

Mark this date in your diary for the two student Galois Group lectures: Wednesday 12th November 2008, 1:10-2pm, Alan Turing Building room G.205.

If I'm lucky and not lazy, the posters should all be up by this Wednesday and down by Thursday! Ha - well Thursday 13th November if I'm very very lucky... . Time shouldn't be allowed to move forward or backwards - it messes with my routine.

I got my annual statement from the SLC (student loan company) the other day and currently I am owing someone at least £12,000. Wow - I could buy a lot of things with that much money, and if I was being a so and so, the cost of my education shouldn't be that much.

It's really 11:36pm and I have been refusing to change the time on my phone. So if I was to wake up at 7am tomorrow, would that mean I'm going to be late for lectures, or early? Late would not be very nice as the doors for the graph theory lecture room are at the front and walking late is quite disruptive. That being said, whatever I do decide to do, I should now go to sleep for this post is not going to get any more lively!

Friday, October 24, 2008

A Hasty Mathematician

Yesterday was a Thursday and I had a Measure Theory lecture from 3-4pm. (Technically speaking it is 3-3:50pm, but that just doesn't look right!) I had mentioned that I was looking forward to the lecture as we would be continuing the proof of a Theorem stated on Tuesday. It was one of them "Andrew Wile's Fermat's Last Theorem Proof Lecture" if I may say so myself! The build up and excitement were all there, all we had to do was follow what was being said "without being expected to guess what was coming next". That sounded like a good plan to me....

NOTE: I will edit this post tomorrow with the maths symbols inserted, so please endure the TeXing. (I'm feeling too lazy today...)
The Theorem was that M - the set of all Lebesgue measurable subsets of \mathbb{R} was a \sigma - algebra. [This means that we have to prove (1) that \emptyset \in M; (2) If E \in M then its complement is in M; (3) If {E_j}_{j=1}^{\ifty} \contained M then the union of the E_j's is in M].

Proving (1) and (2) was somewhat trivial (two lines only...), but proving (3) is the fun part. We first consider two sets E_1, E_2 \in M and show that E_1 U E_2 \in M. To do this we have been given this sparkling, out of the box definition and we don't know how it works, but it works which is what matters! (The definition is about when a set E \contained in \mathbb{R} is said to be measurable).

I shan't be throwing any equations into this post, but consider this a preview of what's "coming up" (soon....).

So we first started by proving that the union of two sets is measurable. This seemed to take a while, but I was following the game so that was nice. However then something bad happened. Prof S' made the mistake of saying "Aha". The "aha" had been said. I hurriedly wrote the last line of the proof and drew my black square (as always) to signal the end of proceedings. I even took a moment to flex my muscles and prep myself for the remainder of the lecture.

How very silly I had been, but I will cover my naiveness by blaming the false "aha". (In my book they are strictly relegated and said at the end of proofs). We had proven the case for two sets (and an induction argument can extend this to n sets), but that's not what the third condition of a \sigma algebra is! The "note" that followed my black square didn't make me realise that I was being very silly, but when Prof. S' said that we now suppose that we have a countable collection of sets, I felt the egg on my face. Quickly crossing my small black square out, I pretended as if nothing had just happened.

This proof had just got better - Andrew Wiles eat your heart out.

So we continued with the proof and I wondered whether we would complete it by the end of the lecture, as I couldn't begin to start planning my weekend otherwise! I got lost somewhere in the argument of the next part but quickly found my feet again. I don't think that I would have pointed out the missing lambda to Prof. S' had it not been for the student sitting on my right. The student had not noticed it missing and her neighbour too had not noticed anything amiss, which was all I needed to open my big mouth.

The lecture was drawing to an end and we only had one inequality. Internally I knew that this proof would continue onto Tuesday, because to prove equality we have to prove that the inequality holds in both directions.

But then the tides changed direction: Prof. S' seemed to be smiling! He also looked to be saying that we only needed to prove the inequality in one direction to prove that the countable union is measurable. Where he got that from I had no idea, but hey, the proof was complete! A cheer ran through the room (although perhaps only near where I was sat...), but nevertheless the delight on everyone's face was undeniable. Prof. S' was so taken back with the atmosphere of the room that he awarded the proof with a very big black square of his own, which was a treat in itself!

Limbs were now stretched and smiles were plastered on everyone's faces - we had completed the proof in two days!

I must say, for those who might think that they're detecting sarcasm, there is none in the above. I was honestly really into the lecture and it was quite a sense of achievement when the big black square was drawn at the end.

This takes us to my next topic: Prof. S's lectures. Prof. S' is a great lecturer. Honestly speaking he's been telling a brilliant story about Measure Theory so far, and I know that it will remain this way until I have to read up on chapter 2 by myself! He's quite a brilliant story teller and after one comment he made about definitions and tea, my friends seemed to think that it came out of my mouth! (Although mention of tea did score him extra points). His lectures have a certain "casualness" and "mathematical drive" at the same time which is quite cool. I have yet to leave planet earth for long periods of time during his lectures, and even when I'm having a long and tiring day, I am alert for Measure Theory.

Once again, boy am I glad to have done Measure Theory this year, and if I'm lucky Prof. S' might be lecturing me next year too.

By the way - I did it again - I asked advice because I wanted an accomplice. I'm still not convinced about how far I want to take my mathematical education, but the fourth year has to be a must now.

I had left at the end of the lecture but sneakily sneaked back to the example class in the last five minutes, to enquire about the inequality of the proof. (My notes are disjoint and I had misplaced one set of lecture notes which answered my question.)

After this I spoke to Prof. S' about TGG and other things. He's quite a busy man it seems and has been an unbelievable help for TGG (he saved me from my despairs last week). He also might possibly be able to help me with a speaker for the second semester, but most importantly I feel that someone's working with me and not against me. He kindly shattered my bubble about being clever and booking rooms for next semester now, as it is not allowed. Teaching rooms for next semester timetable have to be booked first and then it's our turn. Nevertheless, hopefully this means that other "people" can't also book rooms and I can just play around with the dates I want to hold the lectures. (STUDENTS: Please volunteer to give a lecture. Don't think twice about it, just nod your heads and go for it!)

Go for it! Ha - that's exactly what I was told to do when discussing my silly indecisiveness about doing four years or more. We talked about quite a few many things, and then I finally asked Prof. S' about dynamical systems. (You see the dynamical systems seminars are on Wednesdays and were part of this week 7 clash). Going by Lagrange's definition yesterday, I would say that Prof. S''s "has thoroughly understood his work" (!) but then again I am not exactly an ordinary person on the street... Nevertheless, as I am exploring areas of maths which might interest me, dynamical systems has me asking more questions. It wasn't just mention of chaos which had me going wild (!), but the subject itself and how it's studied is quite interesting.

By the way, I officially hate the word colloquia for I always end up saying "British" before it. Pfft.

To conclude this post, I hereby remove the invisible clause which meant that Prof. S' had to attend all TGG lectures organised, for the rest of his life. (I would have told him the "rest of his life" part in due course....). He can attend whenever he wants to although I would obviously be a happier bean if he attended most times! This doesn't mean that all the other lecturers are off the hook though!

PS: The Topology lecture today happened to be a blur, but I was awake enough to hear Dr. E mention my name during the lecture. Now don't be hasty and assume that this bean has got a fantastic connection with Topology, resulting in a startling powerful discovery which Dr. E was exclaiming about. Alas no. Instead Dr. E was pointing out that he wasn't numbering something because "beans doesn't like it when I number things in this way". He just wanted to send the angry mass of students to me instead. Hmmm - second blood has been drawn, and this battle is going to get bloodier! Children - stay away from Topology, it's not the safest of subjects and believe me on that...

I drew first blood the other day (unintentionally of course) but my next move remains to be seen. Ideas are obviously welcome, but do keep in mind that Dr. E is a topologist. :D

If you have only just started to worry, or have just put the phone down after ringing the people in white coats, I can assure you that I will try to make my next move "mathematically painful". Happy? Alas, I have had a very busy week and need to sleep now, hence this nonsensical mess. You might be relieved to hear that I will be without the internet soon, and my blogging will most likely happen from the University cluster until rearrangements are made.

I thought this post had been very long so had published it but only to find it not very long. Now it should be very long and waffly so my work is done. Here's hoping for a mathematical weekend. (Now, now - don't laugh please! We can all live in hope...).

Sleeping in the AT Building

Apologies to those who were sitting expectantly at their computers, waiting for my post about "yesterday". Unfortunately I have developed a habit of falling asleep in the AT Building and today it wasn't just for 30-40 mins, but for at least 1hr and 30mins! How did I manage such a remarkable thing? you ask, without obviously being disturbed by the uproar of the mathematics department. Have the powers that be felt sorry for me all of a sudden, and allowed me to become invisible for the times I sleep?

Nah - the powers that be tried their best to wake me up, but they need to try harder next time. Unfortunately due to an old friends and my timetable, the only time I could see her was this morning at 8:30am! Obviously that's impossible for me so I had delayed this to 9am. Come 9am I am snoring like a baby and am rudely woken by my friends text asking where I am. (How can people wake up at 6am in the morning?)

Now I rushed out of bed and safely arrived at my friends house at 9:30am, blaming something or other for my lateness of course.I had a lecture at 12pm so we didn't have long catching up but it was still great. (This is another old friend and not the one I met on Thursday). My friend even taught me how to make breakfast for myself... (well how to use her toaster!).

Anyway, in the AT building I have found this brilliant place whose whereabouts I'm not going to tell you! This place is such that nobody goes there apart from myself since I found it. If I mention it then people will try to deliberately wake me up you see... It's not the most comfortable of places, but heck, I sleep on the floor so that's not an issue! At least now I don't have to restrict my naps to fifty minutes only. I don't have my own room to escape too, but that no longer bothers me.

I have woken up quite groggy though and I'm starving! The idea of the nap was to make sure that I actually pay attention in my imminent Topology lecture, but that remains to be seen.

Honestly speaking though, I have a corner of the AT Building which I can claim as my own now and where I can sit peacefully for five minutes at least, which makes me quite happy. Sometimes one has to escape from trivial conversations about trivial things and to obviously sleep! If you do ever come across my sleeping form then please be nice... . :D

Alas, Topology time. Perhaps I should have had two cups of tea instead of the one? I am honestly like a three year old when I wake up from my naps when I shouldn't have. I don't want to go to Toplogy! I want to sleep. Sleep, sleep and sleep.

Thursday, October 23, 2008

Three quotes

A lot I have to say today, but there's not a lot of time I'm afraid, hence why I will leave you with three "coolish quotes".

(1) Failure is not the only punishment for laziness; there is also the success of others.

- Jules Renard

(2) What a blessing it would be if we could open and shut our ears as easily as we open and shut our eyes!
- Georg Christoph Lichtenberg

(3) Realism...has no more to do with reality than anything else.
- Hob Broun

Number (1) is painfully true but not in a mean way. The success of others just reminds you on what you could have achieved modulo laziness! Meh. Number (2) is not very nice and I'm glad that such a thing is not the case. ;) You see I have to console myself with the fact that although people don't take in what I say, they can't exactly shut me out and ignore me! The best they can do is kick me out, which although painful at times (depends on whether I land on my head) is easy to recover from. (I can just imagine the number of people who read such quote with despair...). And number (3) I just pasted for it came after the first two...

My post about today (Thursday) will most likely be tomorrow during the time my Applied CA lecture would have been! Why? Well the lecture has been cancelled *cue evil laugh*!

A lot to say I have about certain things, but I shall resist and instead I will say that tea at Blackwell's is quite nice. You see it's 22:41 and I know that if I start typing a post on today and the Measure Theory lecture in particular, I will be here for a whole hour which is not a productive use of my time. (Not when there's Topology to be done!) It suffices to say that today's lecture was quite cool and I wasn't the chicken I normally am when I spot a "typo" on the board! (One nil to the bean...).

Okay it's 22:43, I better get going now... . Oh and did I mention how glad I am to have chosen Measure Theory as my third year module instead of fourth year one? (And that's thanks to Prof. S' too, which means that I probably owe him more than he owes me now! But we don't want to tell him that....).

Wednesday, October 22, 2008

Do you understand your own Maths work?

Joseph-Louis Lagrange was of the idea that:

"A mathematician has not thoroughly understood his own work till he has made is so clear that he can go out and explain it effectively to the first man he meets on the street."

Baby mathematicians (i.e. mathematicians who have not yet began their journey of research) are allowed to substitute "his own work" with "others work"!

So how many of you actually truly understand maths then? My lame explanation of Topology to the 'normal' person I met the other day seemed to make sense, so do I score some points?

That being said perhaps we should first consider general topics, say geometry and topology. If you can effectively explain what they are to someone else then you're a "growing mathematician". And if you can then go on to explain what a certain thing in them topics is, say what a tangent space is, then you're a 'slightly maturer' mathematician. The more mathematics you can effectively explain to somebody on the street, the more of a mathematician you are?

Well Lagrange probably wouldn't have allowed for such special cases, but this just means that he hasn't read the John Mason book which I have flicked through! (Perhaps he might have read it since his statement, but whose to know.... ;) ).

Now when I was googling for the above quote, I found another one by Lagrange:

"When we ask advice, we are usually looking for an accomplice."

How very true is that?!! I am pleasantly surprised to note that I have indeed been guilty of doing such things. When we ask for advice we are looking for people who agree with what we have suggested and for positive feedback, which then provides us with encouragement to 'go for it'. We know that we are probably going to go ahead with what we're asking about, however an accomplice in our plans makes the worry slightly less burdensome and more achievable.

I know that I bug the same people again and again for advice, but that's because I know that they will always say something which means that I worry less, and they also suggest great things that I would never have considered myself. I also know that people who I consult will motivate me further and make me more determined to forge ahead with my plans. The mysteries of life eh?!

I have a lot to say on "asking for advice" but I will leave that for another time and occasion.

Today was a very relaxing day - too relaxing - and it's not the weekend yet! I erm, was "fashionably" late for my 11am lecture (but thankfully not too late to have missed the first part of the lecture from the board) and spent the rest of the lecture in first gear. Well it was one of those lectures where one has already deduced a main result (max-flow-min cut theorem) and then considers other instances, which are easily proven by the main theorem. I mean one proof was very nice and small but I will definitely have to write a slightly longer version of it for I didn't follow something in the result it used.

After the lecture I made a to-do list with my cup of tea for company of course. You see I am going to try and book rooms for next semester in the coming week (don't tell anyone though!) and was trying to work out what weeks to have the lectures in. I'm quite reluctant to choose week 12 for that is is a "reading week" of some sort before the exam season starts in May, but I don't know yet. I also don't have any student volunteers at all for next semester (apart from students who want to give another lecture). This should be confirmed soon, but I need to consult others on this before doing anything. Hopefully once I have sorted the dates out I will send an email to all staff, asking them to have some compassion towards TGG if they're looking to arrange any thing.

I will most likely attend the 'stupid' calculating careers event in our building, but that doesn't make it any less stupid.... ;) [It's the first of such events I believe and I am going to be there to give a bad impression of Manchester students! You didn't hear that from me. :D]

Now I had written the next paragraph before but before it could stupidly save, I had to close the browser. Well what's forgotten is forgotten, but I had a pleasant day today which makes a nice change! I sadly didn't get the intended maths done, and Bella (as always) was quick to remind me that it's about time that I got working on my modules. She's quite pessimistic about the magazine, I must say, as is Milo.

Fizz though claimed that I'm an optimist, what with my endeavour with TGG and now the magazine, which shocked me slightly. I have always put myself down as a "realist" but I guess that could be changed to "optimistically realistic"? Ach - this is another discussion which requires more than a paragraph, and I have dragged this post out to 1am so won't bother with such discussions! (I expect the worst but hope for the best if you follow me.... and yes, that phrase is one which I seem to like using recently.)

Tomorrow is a busy busy day for me due to other commitments that I have. If I'm lucky I should be able to rush back to Manchester to meet a good old friend for lunch, after which it's Measure Theory. Strangely I have been looking forward to that lecture since yesterday! Well I should perhaps say thankfully, for it has been a while since I have looked forward to a module this much. *touch wood* (This is where I am now going to expect the worst. :D) We were doing this coolish proof which one would never be able to dream off, but we didn't manage to complete it so I haven't been able to sleep in peace. Thoughts of it torture me and are too painful for me to discuss!

Yes you got it - it's bed time. By the way, I'm ashamed to report that nobody noticed a "typo" in yesterdays post (well if you read it that is...). I don't have five coursework tests remaining but only four! The module which I have just been discussing above (Measure Theory) has no coursework but is 100% exam. That might prove to be a bad thing, but at this moment in time it's a good thing.

FINAL REMINDER: If you have anything at all (funny or not funny) that you would like to submit for the maths magazine, then please email me. If you have started to write something but feel you can't complete it by this Friday then please also get in touch with me. [Meh - they're a disappointing lot at Manchester! From the department I've received only one article each from staff, students and post grads, and a book review from staff! So that makes four submissions in total from Manchester - what joy. I'm hoping for another article but I don't know if that's going to surface at all, and then there's the interview... .]

Tuesday, October 21, 2008

An Unforgettable Tuesday

Today a lot of (countable?) things have happened, but enough to leave me in a haze of confusion and a small panic. This small panic I have disguised quite well for most of the day, and it's nothing really related to Maths or University. It's something to do with me and something that I although expected, wasn't really prepared for, if you follow me. It's like knowing that you have an exam but not revising for it. This panic isn't a pre-exam panic (thankfully), but a deep unrest is stirring within me. On one hand I am quite happy and over the moon, but on the other hand I'm nervous and slightly scared. Scared of what? I ask myself. There's nothing to be scared of but drastic changes I reply.

Changes that could and will change a lot of things in my life, but I have to be positive now and take things on board. If I'm being completely and brutally honest, I'm terrified. That's not very good though and I'm going to obviously bury everything away until it has been internally dealt with. (I worry about how long I have to process everything). On this occasion it is fear of the unknown and the fear of growing up.

Today, thankfully before the Measure Theory lecture, I happened to wake up from my previous zombie like state (resulting from messed up sleeping patterns). We happened to intersects paths with Prof. S' on the way to the lecture and I mentioned how I really enjoy the crunching feeling under my feet when I walk on the leaves. Prof. S' remarked that he too enjoyed doing such a thing but when he was eight!

I am eight though. But then I'm not. No - I am eight. Growing up implies responsibilities. Responsibilities of grown ups are not contained within me hence why I tend towards wanting to remain an eight year old. I don't know what I'm trying to say, I honestly don't.

I don't think one is ever old and that one ever stops enjoying (certain) childhood pleasures. In primary school during Autumn I had once collected a load of leaves, branches, twigs and stones to make a nest. Yes, that's what everyone used to do as rewards from teachers were involved, hence why I had made a massive nest near some trees away from everyone else. Another lad in my class then went and kicked my nest into smithereens and I was infuriated by this. He got into trouble but my desire to create another such nest has never been satisfied. The fantastic colours of Autumn fascinate me.

I don't want to grow up yet. I sometimes feel much older than my actual years, but that's only when I am tired of certain things. I'm not saying that "I'm 20 and it's the end of the world". No - the numerical value of my age has never determined how old I am.

Sigh - the above circular argument will go on forever as I'm not sure what it is that is actually worrying me. Is it responsibilities, growing up or change? Challenges are faced in our every day lives and that is how I will view everything now: a challenge. I can conquer this situation and I will do so. Hopefully!

After my post at around 4am I had looked over my algebra notes and then tried to sleep. Sleep came and went for an hour and I awoke feeling very groggy and not looking forward to the test. My final decision (after a cup of tea) was to just learn the dummy test, namely the proofs.

What stinks at times is when you wake up early and are still late for the blimmin' 9am lecture due to public transport. Everything seemed to be going backwards this morning, but I slept (with my eyes open!) during the first lecture so I'm not really going to complain about turning up late. The test was straight after the lecture and thankfully walking to the building woke me up slightly. I'm not an expert with Lagrange's Theorem, but if I ever forget it I deserve to be banished mathematically from ... mathematics! (How does one be banished mathematically I wonder?)

The test was okay apart from the last question which I made a mess off; but according to fellow Group Theorists on the course, I got the right answer in the end! That's one test down and five more to go - what joy.

Today I must confess that the second struggle of the day had to be the coding theory lecture. Straight after the test my brain went on a free fall and I could not for the life of me understand what the lecturer was saying. I got what we were trying to do but I just couldn't listen. Instead I busied myself in making sure that my hand writing was as "neat as possible" (pictures to follow soon! :D) .

After coding (I missed the example class....) The Tweenies and myself went for lunch in a nice place whose name I have forgotten. Well I only really was in the mood for tea, but nonetheless it was a nice relaxing place (perhaps too relaxing!) I desperately wanted to put my head down (as I do in the AT Building) but didn't manage to do so.

The measure theory lecture after lunch was quite cool in the sense that I only zoned our for an epsilon time. I know that I have promised to type my Measure Theory notes up (one day) but I'm first trying to work through them myself so they make sense to me! We have defined this strange thing called the Lebesgue Outer Measure and I was having trouble with the definition due to my naive understanding of collection of covers.

Well I don't get on too well with covers (and finite sub covers and lots of nasty topological things) which doesn't help. Prof. S' explained things in a neat way to me, but I've tried to cross reference the pictorial understanding I have with the mathematical one and it has been hard work.

Now with no mathematical symbols whatsoever, say that you have a set E and you have a cover for it (which is a collection of intervals covering E). We then compute the sum of the lengths of the intervals in this particular cover, which is a real number. Now say John Smith has another cover for the set E (which is a different collection from you), and once again we calculate the sum of the lengths of the intervals in this cover to get another real number. In this way we end up with lots of covers for the set E and lots of real numbers.

The Lebesgue outer measure takes the greatest lower bound of these real numbers I hope! [Well when I went to collect my money from Dr. C I got into a discussion with him about my pictorial representation of this definition. He did correct something I said about the infimum but I annoyingly can't remember what, and he also helped iron another crease or two out, though another one has just cropped back again.] I get confused by small things and it's this index j which is currently prickling me. (If only I wasn't this tired so I could insert some mathematical notation to make sense of this mess....).

Anyway, that's enough measure theory for now, and I have some slight good news. We have finally managed to get a room booked for the student lectures in week 7. I am waiting for the confirmation email but I was a brave knight and strode into the office to make "enquiries". Actually that's a lie - I squeaked like a mouse for the wrath of the office is one which I would rather avoid. [The office is actually quite nice to me and have yet to chuck me out * touch wood* but I have previously witnessed an office situation where things became mental in one second, due to someone like me! I see the hate for the extra work I bring bright in the eyes of the "officers" i.e. the people of the office! Officers sounds better so officers it its.]

More details about that lecture to follow (titles, abstracts etc). In an ideal world the UG SSLC meeting would start at 2pm, but if it starts at 1:30pm after the first student lecture, I will be happy. The magazine deadline looms and I am very annoyed to find that the University computers no longer have Texnic centre installed on them. Ah well - this means that I now have to annoy the computer "officers" who actually do get very annoyed by me. (It's ridiculous though, how the University thinks that they're making things better for us by upgrading the computers, when in actual fact things are horrible now.)

And I think that now is a good time to sleep.

Wakey Wakey Mr. Alex!

The title might ring a bell for those of you who have watched Madagascar, and if you haven't watched it then what are you doing reading this post?!

I know for a fact that I am going to have the lines from that movie in my head today, which isn't too bad a thing I suppose. Well rather than having silly group theoretical facts, at least the movie lines will keep me amused! (Yes, it seems I am easily amused at times...).

I did say I wasn't going to complain today and indeed I'm not going to "complain". Instead I'm going to make a few observations about Monday 20th October 2008. How does that sound?

Now I'm quite lucky to have made it on time in Manchester today, otherwise like Arthur I would have missed my first lecture. I say lucky for a very good reason as my 9am lecture happened to be the graph theory one. Last night, or indeed very early on Monday, I was struggling with the max-flow -min cut algorithm and mentioned my problem about the set S in yesterdays post.

I had to work hard to stop my mouth from flying open at 9am, and staying open, for the lecturer seemed to finish the example at the start of the lecture and he actually labeled the vertices that belonged to the sets S_1 etc (i.e. what I had been struggling with). I had my suspicions for a second but I'm quite sure that this lecturer has not come across my blog. Call it a Monday feeling, but for a very long time during the lecture I mused on how weird a coincident this was, for everything I had mentioned yesterday was now resolved. (I won't believe you if you say that this was no coincident...).

During the lecture I didn't sleep and during the example class I was also awake. You will be pleased to note that I had made a mistake in my calculations yesterday, well three mistakes to be precise, and 31 was the correct answer. I did check my answer before going to sleep last night but that is a lesson for me to learn: leave the checking of solutions till the morning.

I have now declared war with Dr. E due to his Topology lectures, but he doesn't know this. Dr. E is a cool lecturer and I have nothing against him. Topology is quite "cool" too and I have only slight reservations against it. What I have issues with is the example classes timetable and how it is utilised.

The Topology lecture was unfortunately the one in which I ended up sleeping. I don't mean eyes closed sleeping but eyes open sleeping. It wasn't the best of sleep I must say and I equally didn't get a word of the lecture. Hausdorff spaces were mentioned and I am meant to remember that it is spelt with one "s" and two "f"s, so I was awake for parts of the lecture in my defence! Actually that's a lie. I honestly can't seem to stay alert and concentrate for four hours in a row. Next week I am going to have six bloody hours in a row on Tuesdays! At least on Mondays I have four hours and then an hour for lunch before the final two hours, but next Tuesday it will be six hours in a row. (Which leads me to the decision that I won't ever be attending the Coding theory example class for I need a lunch break).

You see Dr. E always ends up using his example classes to continue the lecture, which I understand from his point of view is quite a good use of the time. However I think it is rather unfair for it forces one to stay for the example class, even though I don't want to because I haven't done any problem sheets yet. Yes example classes are "compulsory" so they say, but we all have our ways of learning and if I haven't attempted the problems before hand I don't like going to the classes. Sigh. I have to declare this mini battle for it is the only thing which will provide me with epsilon comfort. (Dr. E intends to continue with his "clever plan". Pfft). I wasn't grinning back when Dr. E was obviously amused at my shell shocked state today.

After Topology I had some lunch and then a 20 minute nap in the AT building cafe (I seem to making a habit out of this...). This was a very bad thing to do, for I woke up feeling worse than ever and with a very sore arm too. I don't know how exactly I had positioned my arm, but upon waking up I was a three year old wanting to go back to sleep. (And we all know how they tend to behave....). Group theory was a blur and Applied CA was once again a revision lecture which was great! (I actually remembered something from last years course so I didn't have to pay much attention...) :D

Now this post is sounding very "tired" to me. Am I allowed to forget trivial things when I'm tired, for it seems that I had forgotten something which I shouldn't have. I gave the receipts of the refreshments I bought to Dr. C on Thursday/Friday and had forgotten to pick the money up. He actually made me believe that I hadn't given him the receipts! This had sent me into a mini panic for upon invading my wallet, I could only find two receipts. Meh. I forgot this fact because I forgot whether it was Thursday or Friday. I'm sure it's Thursday which is why I had forgotten, but this doesn't mean that I'm going to let Dr. C of easily for this!

It seems that Dr. C and myself were waiting for the other to book a room for week 7 and neither of us did anything. Dr. W did leave a note at the office so I'm not going to panic just yet, however if we don't get a room then it's all Dr. Coleman's fault! (So I expect you to send not nice emails to him about why there are no student Galois Group lectures after week 6! I can help if you are stuck for not nice words... :p). I am beginning to worry that one of the students who has volunteered might let me down. Namely due to his comments about wanting to attend the UGSSLC meeting. I understand he has made a commitment towards that, but he also made a commitment last year to do a TGG lecture.

As soon as I got home today I went to sleep. No food and no emails but just sleep. I only slept from 5:30ish to 10:30pm (ish) as some people seemed to have forgotten that I sleep on the floor, as they eagerly increased the volume of the TV downstairs. Meh. I haven't actually done much revision since I've been awake for once again my other modules keep on calling out to me! I looked through my notes and saw a lot of ugly lemmas and proofs for things like the centraliser of the group etc.

Now what I need to remember is that Lagrange's Theorem says that the number of cosets of H (subgroup of G) in a group G is found by "order of G divided by order of H". And if that number is not an integer, then H is not a subgroup of G.

Now one natural coset is: e.H = H (as e is always an element of G by definition), and to calculate the other cosets we take an element g of G not in H (and not in any other cosets we already have) and calculate g.H. We do this because the union of all cosets of H in G is equal to the group G, and two cosets are either equal or disjoint.

Lots of messy stuff in the above sentences, but I'm having another nap now before I do the dummy test questions so I needed to see what I remember. By the way, I've been sloppy and not written what coset but the above is true for right and left cosets. Note to self: if g \in G is on the LEFT of H, i.e. g.H then this gives a LEFT coset! And if g \in G is on the right of H i.e. H.g then this gives a RIGHT coset. In all the questions that I do on cosets, I refuse to read the question and just calculate the left cosets!

That's enough actually. My heads starting to hurt. I am becoming quite good at not checking my emails anymore and not running around like a mad hatter around the AT building. Hey - I like that: mad hatter. Mad mad mad.

PS: More on the AT building tomorrow.

Monday, October 20, 2008

Sleepy Sunday

I hereby declare that I will not complain about being tired tomorrow after having six hours of Maths lectures, including a 9am start (which is followed by a further three hours!). However, I will most likely be complaining that Mathematics (Measure and Graph Theory in particular) are to blame for my current plight.

Today, Sunday, I have been very very sleepy and it's all because of a certain guests fault! Well one of my cousin (who I used to often see in my childhood) came for the weekend (from down South) to see how Pops was doing. Well that was the excuse that was used, but straight away I realised that my cousin just wanted to get away from the South and return to the Northern region of the country again!

I had promised myself a luxurious mathematical weekend (doesn't that sound amazing!) and was not surprised to find myself struggling to motivate myself into working. When I finally got rolling on Saturday, the GCSE student arrived after which my cousin came. Now my cousin isn't just related to myself (!) so I did escape for a while to do some Maths. The brilliant thing about the weekend is that when I do get "into the Maths", time just flies by and my stomach is the only thing that gives me an indication of how long I have been sat at the desk. I ended up working till 12am on Saturday, and leaving my room scattered I had gone downstairs for a cup of tea.

Downstairs the party was in full swing and I was very surprised to find everyone still hanging about and not sleeping! So what did I do? Well the cake that was fast disappearing was enough to make me park myself downstairs and join the conversation. It was nice to catch up with my cousin and indeed there was a lot of it to be done. We actually ended up watching the X-factor highlights and it was only when that finished that we noticed that we all should be getting to bed as our eyes were drooping.

Upstairs what did I do? Stinking, horrible graph theory of course! Isn't that a good thing you ask? NO, for I got into the "roll" again and it was suddenly 4am when I noticed that I had read a sentence more than five times and it was still not making sense! We had done the max-flow-min-cut theorem in the previous lecture and hadn't managed to finish the example of, which is what I was struggling with. We have an algorithm which gives us the answer and the lecturer had claimed that the answer was 31. I can't seem to understand the notation of the algorithm, hence why I didn't get far.

The idea is that we have a network (directed graph?) a source s, and a sink t, and for example we have to transport things from s to t along directed edges which have a (max) capacity of how many things can be transported at a certain "junction" (vertex?). That probably didn't make sense but I don't really get the problem myself. (There's this other thing called flow but I can't recall what exactly that is).

In the algorithm we first define the flow for each edge to be zero. We then construct a set S_1 (according to my notes) and "mess about" with it. I can't construct this set S_1 for my notes make no sense. The lecturer, when doing the beginning of the example didn't seem to construct the set S_1 and that's why I'm stuck. I don't know what he did. I have tried the damn problem from scratch but I get 41 for the max flow which is clearly not 31. If I knew how to construct this set I might just get 31... (roll on tomorrows example class).

So 4am was a bad time to sleep for it meant that I awoke today, Sunday, at a horrible and unreasonable time (which is not for the ears of children so I won't mention it here!) It was 4pm when I had my breakfast but that doesn't mean I woke up at 4pm! (I couldn't seem to eat anything up till that point, and even then my mum had to make me eat....).

Sadly the A Level student (ALS) that came today might have been disappointed. Well I think her emailing me three (somewhat long) questions during the week makes up for it! Domain and range are "okay" but we had inverse functions and I was trying to remember whether the domain of a function is the range of the inverse function. I couldn't remember that, although it still rings a bell, so I ended up drawing some horrible log graphs to convince us both. (Well she said she was struggling with transformations so that should have helped...). This is the first lesson which I hoped would finish early!

I have now figured out how to deduce when ALS doesn't understand something I have said. I mean to say that I now know the "AAAHHH I don't understand" look that the student gives! As I saw this look and said something to help, I mused about how my "AAAHHH - speak English please!" look looks like! I do have a very dumb look (as I have been told), and unfortunately my dumb look is very transparent. (I can't help but frown...).

It's two something am and this post doesn't make much sense to myself. I am awake now due to the silly graph theory problem I mentioned above. It's taken me two days to still get an incorrect answer and I still don't want to give up. After I had eventually put my graph theory things in a pile, I made my "to do list". Well tomorrow has to be devoted to Groups for my test on Tuesday, but after that I have to seriously do some topology and measure theory.

Ah-- measure theory. I'm too tired to say anything mean about that module, for stupidly, when making my to do list, I decided to get my measure theory notes out. And would you believe it, I got into another "roll" until I looked down on my paper to find too many questions that needed answering! I would definitely say that I'm probably the worst learner that you will ever encounter. You see at times some things might be skated over or not defined, and on most occasions I want to know why this is so. Perhaps this is why I'm disliking Topology?

Okay okay, that's enough from me. I am going to be a dead duck tomorrow. :( But on the plus side I haven't worried at all about TGG this weekend, and even a nice email today, which might be able to help me didn't make me worry. Tomorrow though will probably be a different story, which reminds me that at 11am I hope to find the Maths building in it's "raw beauty"! (I'm also going to perform a certain experiment this week - wish me luck).

Perhaps this post should be called Sleepy Monday...

Friday, October 17, 2008

A slow post

I realised today, that when one isn't feeling particularly happy, the world seems to slow down completely. The cars on the roads, people walking on the pavement, the lecturer's mouth talking in another language all seem to be happening in slow motion.

You hide this sadness quite well and no one knows how your insides shudder in turmoil, wondering what to do next. No one else sees this slowness. You stop caring for a day and promise yourself to deal with this problem tomorrow. You hide from the things that will remind you of your worries and your laughter might seem exaggerated. In fact, you're so relieved to find yourself laughing at a joke or something, that you end up laughing with relief! But then a reminder walks by. Emotions stir up inside you. Do you check your emails or continue eating your lunch, which will help cheer your insides up, whose pain is only visible to you?

I didn't check my emails this lunch time and for one moment I felt like I was forcing myself to keep sitting and eating. Lunch had been nice today, apart from the few times when certain things reminded me of my troubles, but I did good if I may say so myself.

Last night, after my post, there was nothing left for me to do but Maths. That was the only way in which I could stop worrying about something that shouldn't be having this effect on me. Perhaps fortunately at the time, I got drowned in group theory and lost track of time. I would say unfortunately because for most of the week I have been asleep by 2am, and last nights marathon ensured that my Friday lectures were very hazy and confusing.

It was 1:15am when I had had enough of the question I was doing and gave up. But before going to sleep I tentatively checked my emails, whilst sending my Group theory lecturer an email about what was troubling me! (That was the only way in which I could sleep peacefully...).

We have a coursework test next Tuesday you see and... well another unfortunate thing is that I seem to find one of the easiest modules difficult. (This is namely due to my attitude and my reluctance to believe that I can understand silly algebra - whoops I mean annoying algebra. Ach - you know what I mean!) I want to make more of an effort this semester but I can't ever prove things in Algebra which is annoying! I write the information that's given to me and what that implies, but then what? Well I am going to post more on Group theory soon due to my desire to revise!

I had to wake up early today so only got roughly seven hours of sleep, which further slowed everything down! Hmmm, so perhaps I was slow because I was tired and not because of the worries that I was trying to bury inside me?

I'm ashamed to say that whilst walking to the AT Building I came across a set of traffic lights. A car was clearly slowing down and I felt it safe to cross, but I didn't. The green man was still showing and I had to wait for the red man to come. The car came to a stop but the green man didn't disappear, so I decided to glance at the traffic lights instead. They were red! Confused I decided to cross the road wondering why the heck the green man hadn't changed. A second later my mouth flew open....

Coding theory was ahem and erm and linear! Ah right, that means we're going to do easy things now? Well that is what I'm hoping for! I have been told that coding theory is quite easy once you have "got it". Hence why I am leaving that module untouched for the moment, hoping that I will "get it" when I do look into it.

Applied complex analysis just reminded me of how much I hate the residue theorem. It's quite a fantastic result (I'll have you know!) but my problem since last year has been trying to find the damn residues of the singularities. I have found my complex analysis notes from last year and a quick skim through them has given them the thumbs up (they're good notes as they provide more motivation and explanation). Hopefully things will make more sense a second time round (but that's not always true, for I'm hoping that third time round algebra will make sense!)

After complex analysis I finally found the courage to check my emails. Thankfully I was greeted with positive news. Well I was expecting the worst so anything that wasn't bad was good! The relief that swam through my body actually recharged my batteries and allowed me to concentrate in Topology for 3o minutes at least. (Considering it's last thing on a Friday, that's pretty good in my books.) The email hasn't solved anything yet for I'm still waiting to hear if a room has been booked, but at least it has given me some hope that not everyone is out to get TGG or indeed myself! (It's quite amazing where ones imagination can sometimes carry you...)! Actually I'm quite naughty at times and "do a Godel".... .

The email has given me hope that if we get a room for our lectures, the clash might not affect the student who has volunteered to give a lecture (fingers crossed that we hear some more good news). I'm eternally grateful to Prof. S' for although he may not realise it, he has saved me from a potentially ugly disaster that could have resulted in no lecture in week 7, 8 and 9! He's also saved me from the depths of my despair and helped me to stop worrying about this too much. Perhaps I can have a weekend where I don't have to worry about TGG for once?

It's getting to me more than ever that I don't have a group. Every single problem always directly affects me to such an extent that I can't avoid it. I also can't pass the problems on to someone else for they would just disregard or ignore them. This year Dr. C is also very busy in his duties (teaching two big courses and other things), and I think I have already tested his patience on too many occasions this year so I am going to try and "bug him wisely" (rather than all the time "unnecessarily"). Well he shouldn't really have to endure my worries for that's what this blog is for. (I do need to see him about something else though, but that can wait).

Some times one needs constant reassurance I suppose, that one is capable of doing things and that one can cope with everything, no matter how depressing it is.

Today I witnessed something in the AT Building that I hope is not there on Monday. Mathematicians strive for consistency so if our building all of a sudden demonstrates inconsistency, what do we do? I won't say any more, but if on Monday I witness what I saw today I will be very annoyed.

To end this post I will narrate something that happened to me on my journey home today. I happened to bump into two student opticians that I know, and at the time I also happened to have a book on Topology in my hand. One of the to-be opticians asked me what the heck I was reading and what Topology was. I gave my friend the "piercing look" to decide whether or not she was taking the mick, but she seemed genuine so I then looked at the book for motivation to give some sort of answer! I mean the first thing that came to mind was "Topology is a lot of hand waving", but somehow that wouldn't make my chosen profession look particularly great against optometry!

I finally got inspiration from "the doughnut and the mug" thingymajib, and went on to explain how a doughnut and mug can essentially be seen as the same thing (for you can transform one to the other without any ripping or cutting). My friend found this particularly amusing but I made sure to "wave my hands around a lot" to convince her! (Mentioning "topological equivalence" might have scarred her so I avoided that). Boy am I glad that I'm doing Measure Theory as 15 credits for I although that is harder, at least it's more paper waving than hand waving.

It's time I stopped being lazy now.

Thursday, October 16, 2008

A despairing Bean

This is life, or so I'm told. You meet some dead ends, crash into everything and then face more bumps. But hey - the "life" bit tells us that we have to deal with such things and get on with it.

What happens though when you are not willing to deal with things any more? Does one stop "living"?

Or does the thing that you're struggling towards cease to exist? Does that venture die. And a part of you dies with it?

I have dealt with these bumps. I have met them head on. They took my posters down and I stuck more up. They took them down again and I devised a new ploy for advertising my lectures. I tried to build up contacts to spread the word. This worked it seems and yesterday was brilliant. It was one of them moments where you just have to stand back and watch the crowd - amazed at what's standing in front of you. But such moments are very rare like... I don't know - seeing a shooting star perhaps? They happen once and if you blink they're gone. You have to make sure you live that moment to its fullest at the time it happens.

I did that. Bella, Fizz and everyone who attended gave me that moment.

But then it disappeared just like that.

As you might have been reading, I am having a horrible time getting a room booked for the next student lectures. I feel that the next lectures are cursed (and that's not because I have read Memoirs of a Geisha recently). No matter what day it is going to happen it will be a disaster. Which leads us to the next question - will it ever happen?

NO. It's not going to happen. I am tired of this particular bump and I am feeling very weary. I have annoyed to many a people due to this damn room booking dilemma, and that is quite wrong of me. It is not my intention to cause others inconvenience but how else can I deal with this bump? What would you have me do?

I have one last hope and if that disappears then it is going be very hard to pick myself up. I can imagine how Wiles felt when his initial proof was found incorrect. I don't have an attic to lock myself in but I'm sure I can find something...

My last hope could decide if there will be a student Galois Group lecture next. Week 8 is all booked up, so it has to be week 7. We haven't got a room yet and if we don't then it's all over before the game started. If we do get the room though, we have a clash with the UG SSLC. Why' is it a clash? Well our student speaker is a member of that committee and although I have more to say on this than I will write, he wants to attend the first ever meeting of that committee this year. (I'm also on the UG SSLC but I will be turning up "late" which I have already mentioned to the chair).

Now would I be unreasonable to ask the student speaker to miss the first 30 minutes of the meeting? I don't want to go down that lane, hence my one hope. At this moment in time I feel like doing and saying a lot. I wish we had more student volunteers. I wish I could get a grip of myself too.

Sigh and sigh again. I honestly do not lie when I say that everything that could possibly go wrong has been doing so. Yesterdays lecture is the only joy I have felt about TGG for a long time, and even that was short lived. (My post about yesterdays proceedings remains incomplete for I do not have the heart to continue it.)

Sometimes I feel that I am not old enough to carry this burden. TGG has added a few years on my forehead. I'm not that particularly fussed about white hairs sprouting out but I have lost an inch which is what concerns me!

This probably seems like such a trivial issue and perhaps it is. I'm just looking at it from one side and not liking what I see. It's time like these that I honestly can't take positive comments about what I do seriously. Or is it true that all good things come to those who are patient?

I am being shockingly patient (if I may say so myself). Well last year when I hit a bump ( i.e. the first time my posters were attacked by the evil gits) I lost a slight control over myself and was quite angry. Perhaps anger would be nice now for that comes and goes instantly. It doesn't hang over my head like this predicament I'm in at the moment.

Times like this I really wish that The Galois Group was actually a group with more than one person. It's hard - carrying this load on my shoulders and not having anyone but Blogistan to share my problems with. That mental support is what's missing. I'm dreading checking my emails now, for I don't want to hear any more bad news.

Tuesday, October 14, 2008

A "to do list" whilst I can.

Someone rudely disturbed me whilst I was on planet Mars, having a nap. I have truly become a monster now - a very sleepy one. Muhahaha.

I left the AT building at some time after 5pm and got home at 7pm-ish. Did I mention that buses and public transport can be quite horrible at times? My best bet would have been to actually camp in the AT building today, for upon coming home tea is the only thing I have had. That's partly my fault, but because I got home late I ended up "not doing something" that I had said I would which meant that a lot of people were very annoyed with me. Call it foreshadowing, but Dr. C got it right when he said "poor Dad" but he forgot to add the word annoyed.

I was meant to help my Dad with this computer software he has bought and told him that I will be home earlier than usual. I can't remember what I was meant to have done for Po, but he better stay away from me if he can help it! You see I lost complete sense of time when my phone died and then everyone lost all contact with me! I didn't mind a dead phone - it's actually quite a relaxing feeling, unless of course you get to your destination and see unhappy faces wondering why they kept reaching your voice mail.

Ah well - although everyone is no longer annoyed, I still am! (Well with Po especially... ). Do recall that I was on Mars a minute or so ago.

Anyway, I forgot to mention the introductions to Dr. C today but an email will fix that. Apart from that here's what I have to do (this is to remind myself tomorrow when I will probably be going crazy and unable to think straight or remember anything):

1) Charge my camera and clear the memory card.
2)Buy the milk and Jaffa Cakes.
3) Check that the OHP is working in the lecture room.
4) Double check table arrangements.
5) Go to TLO about kitchen key and double check with Bella that she will do the refreshments.
6) Once number five's complete, dump the refreshments etc in the kitchen.

DAMN! I don't know if the kitchens going to have cups for tea and drinks! Meh - they had them last year due to open days etc. but I had stupidly assumed that they will still be there already. Ah well, this means I will have to get in early and try to get access to the kitchen to check things. If my fears are correct then I can always run to Spar (?) and buy some. (Or ask the "staff room" upstairs if worse comes to worse).

7) Ask Dr. C to print poster for door of lecture room.
8) Probably write a note or two for the introductions for I can imagine what Dr. C is going to say. PFT. Well I will definitely have to do the closing remarks...
9) Make sure I pass a register along.

Anything I've missed?

You are probably wondering why I am writing every single teeny thing out, but it has been five months since the last lecture and I'm out of form. I am growing nervous at the amount of things that can go wrong! But if we get the audience I will surely feel much better.

On a serious note, have I forgotten anything bleedingly obvious?

I don't like doing introductions because on Wednesdays like tomorrow I will lose any segment of calmness that I might claim of having. Thus I will speak super fast and put people off from attending future lectures.

Today it was brought to my attention, in the nicest way possible. that the school of Mathematics doesn't really give a damn about The Galois Group. This much I suspected anyway (namely due to the amount of needless problems that I have been encountering this year), but hearing the words from someone else drove the message home. I wouldn't expect them to really give a damn for it doesn't really benefit them in anyway, but then why make things harder?

If I was being a so and so, I would say that someone in the Mathsoc has infiltrated a higher power in the maths department, who have then gone on to conspire against TGG. I do have an over active imagination (how the heck do you think I've been surviving for the past few years?!) but I don't like the current climate of things. I suppose it is a little saddening to note that no one is really going to miss TGG if it suddenly disappears, but this has strangely motivated me even more. Previously I was dragging my feet along at everything (which could be because today's a Tuesday and I've had eleven hours of hard maths over the course of two days) but I suppose now we will have to pause a minute before we think any further on this topic.

Whatever you do though, please don't say that the Mathsoc don't have a higher power looking after them! Honestly, the "perks" they get are unbelievable; well enough to turn this bean green....

Ach - that's enough from me. I must return to Mars and get back into my fighting spirit! (I'll need it if I have to do the introductions. :( ).

Finally please make your way to AT. G.107 tomorrow at 1:10pm for Prof. Nige Ray's lecture on Categorification. Cheers.

Slowing down

I talk at an unnaturally fast speed and I always have done so. I have a perfectly "acceptable" excuse for this, but I'm not the in the "perfectly acceptable mood" to disclose it.

I'm still in the AT building waiting to dump the refreshments in Dr. C's office. He wasn't in before but I do hope he sends me an email when he's free (as unlikely as that sounds).

As you can tell (perhaps) from my "short paragraphs", I'm not amused... . Frowning deeply is something I am an expert at, and this moment in time is no different.

I don't want tomorrow to come. It feels wrong. The Galois Group just stinks this semester. I'm going to ask Dr. C to do the introductions, for at this moment in time I want to attend tomorrows lecture "fashionably late".

I just realised that I have to also worry about the key to the kitchen tomorrow and the tables.

I am beginning to understand why sometimes you hear of people who do something once and then not do it again, no matter how great it was. You would think that the second time round, the contacts have been made and people know your business. That is not quite true and it is a naive assumption to make. I honestly don't understand how I am sat here calmly when my insides quiver with fury.

Fury at the central timetabling people. Fury at tomorrows lectures. Fury at everything. Once again I should remind you of a child who doesn't get the red power ranger, but instead the silly blue one. What am I expected to do? Be patient? Hope for the best?

Things might turn out nice tomorrow, but when for example you want jam on your toast but there's none left (anywhere in the world!), what do you do? You either go without, or make a big fuss. I am currently trying to control this big fuss desperate to come out from within me, but I need my jam.

Meh. I accidentally let it slip to Bella that I wrote something for something and she went and told Milo. Now I'm in trouble for not telling them in the beginning for now they can't read what I wrote. (That was the initial plan...).

What do I need to do? Well get rid of the refreshments is a start! Never in my life* have I wanted to close my eyes and then open them to find everything honky dory, as I do now. *my life is defined by intervals, let us not worry about which interval I am in now!

Anyway, you could all help and make my worries lessen by attending tomorrow. Hopefully I'll grow out of this furious equilibrium I'm in, but I'm sure the walk home will help. Just now I noticed someone notice my poster. The lectures tomorrow at 1:10pm in G.107, I shout silently. It's tomorrow.

This sense of being defeated is quite demoralising if I say so myself, even though the defeat isn't yet a physical thing.

Monday, October 13, 2008

Thinking like a proper mathematician.

Firstly I must apologise for actually posting a picture of my "rough notes" on my blog the other day. That's no way to write mathematics and I was being very rough and vague (in a manner of speaking).

Today was a Monday. The dreaded Monday. Six hours of sheer \sout{delight} torture! Why doesn't it surprise me that I can hear someone else's evil laugh on this occasion. Meh.

It was the usual 9am start but I had to be there slightly early due to my attempt at buying some refreshments and sending reminder emails to everyone about the lecture this Wednesday. (You just have to be there!) I only managed to buy the coffee for that was all I was really willing to carry on my back. (I dump everything in my back pack to avoid carrying anything in my hand...).

From today's lectures I can honestly say that I was only following what was being said in Applied Complex Analysis! Combinatorics at 9am was a blur. We have started some max-cut-min-cut thingy and network flows, but the proof was quite a horrible thing which gobbled me up straight away. I honestly was a lost sheep wondering where I had woken up on this particular Monday!

The example class was less of a blur for I was extremely delighted to see that the lecturer would not be doing examples on the board. (Well he did some things on the board but just some). There was a particular tedious question involving five unknown variables which we had to solve, and it was just the right type of question for a sheep like myself. I decided that no matter how tedious the question was, (row-reduction and what not), I would complete it. At the end of the example class I was on the last row of my "row-reduced" matrix and very frustrated. The lecturer spotted what I was doing and was not sympathetic as I yawned "tedious question - it's taking flippin' ages" and replied that "I shouldn't do it then and do an interesting question".

Well I would have probably not been able to digest anything interesting, so I will define my tedium as fascinating maths. (One has to work hard to make one feel better on odd occasions). Straight after this lecture it was Topology and a massive struggle for my poor self. I was over the moon when the lecture finally finished, even though I knew I had to return to the dreaded room again for the example class and a partial lecture. The only thing I remember from my Topology lecture is the very last thing - the words the Heine-Borrel Theorem. Not bad indeed.

Lunch was a quiet affair (if you take the philosophical discussions that two friends were having out of the equation!). I tried to rid the coffee from my very heavy bag during this time but unsuccessfully. But thankfully I remembered to see Prof. S' today and I was even lucky to remember what I had forgotten to ask him... !

After my discussion with PS' (with about 8 minutes left to my next lecture), I have decided to study Measure Theory for 15 credits and not Topology. Topology seems the easier option (namely because some of the extra material seems to have been covered in metric spaces), but it's not what I'm motivated in studying. With this decision comes my next decision to blog about my measure theory lectures. I understand that the lecturer provides notes, but I don't ever use them until exam time. Thus I will be typing my version of "my lecturers notes from the board". This decision comes with the hope that if I'm typing about Measure Theory I might be encouraged to actually make an effort to do the extra reading for the course. (I am also hopeful that readers will be able to help fill any gaps I have, although I will most likely be bugging the lecturer anyway!)

I also have, thanks to PS', another book shelf available for me to "steal" books of. Well the idea is that if any book is not available from the library and PS' doesn't need it himself, I can "steal" it. (The "not available from the library" condition is one which I have inserted, otherwise I would borrow books for the fun of it!)

Thanks to PS' watch I managed to avoid being late for my lecture (namely because my next lecture is in the AT building and I was lucky because the lecturer himself was at least one minute late himself...).

As a naive mathematician, I have learnt that one can only really comment on a module or area of mathematics when one comes across the subject a second time round. Last year my battles with "Cauchy Analysis" were partly due to the OHP being used during lectures (which was no one's fault really) and Cauchy. I have matured an epsilon amount (which if I recall correctly, Prof. S' said was a good thing!) but even last year I had not denied that Complex Analysis was an interesting subject.

Last year in many modules we didn't really get to the meat of the bone. We were learning how to add and multiply for example, without ever using them in anything else. Last year I became "mean" towards complex analysis and decided that topology was a course to look forward to, as metric spaces had me intrigued. Metric spaces was quite a "bare" course and during revision time I understood that in my third year it will get better. That sounds weird - I whinged when it was bare and now when it's getting more meatier, I'm whinging again! (I'm not complaining about the course material, but just pointing out that if I was forced to choose a PhD topic tomorrow, then Topology is definitely of that list).

Well my views keep on changing and my observations are after two weeks of lectures and I am not on top of any course at all. I need to do the reading and problem sheets, but straight away I can predict that Topology and Group Theory are going to be stinkers of modules. I guess it's partly because the lecturers (in my humble opinion!) go very fast in the lectures and there is so much previous knowledge that is required.

In the book that I have stolen from Dr. Coleman, the author has very rightly said that Topology, more than anything else, requires "mathematical maturity". I don't have that yet and I am finding it hard to keep up with things. I need to get over my "hate" for algebra because group theory gives me the shivers.

So all in all the start of this week has been blurry eyed, but I shockingly survived! I don't know how I managed to pay attention in Applied Complex Analysis right at the end of the day, and how I managed to not get a headache! Actually I should stop lying. Today we recalled Cauchy's theorem's which I remembered better than the Cauchy-Riemann equations, hence why I only ever had to stay in second gear. (I didn't bother getting into the higher gears, even when I should have at certain points of the lecture for I promised myself to read over the notes later!)

I have just spotted my title and remembered what I was meant to write! As I left the AT building to my half-way destination home, I realised that I had 14 minutes to do so. Now my bag was quite heavy today and I am still not walking at the pace I used to, so you can understand my annoyance at discovering that I would probably be late. (Last semester I would have been confident in getting from A to B in 12 minutes). Nevertheless I put up a fight and whilst walking discussed the following non-trivial question with myself: this year I can get from A to B in at least 16 or 17 minutes. How much do I have to increase my speed by to get there in 14 minutes?

Running was not option if you were thinking of suggesting that. Nor is to leave the building a few minutes earlier! So as you can imagine this conversation was very one-sided, but I felt like a "proper mathematician" thinking "proper thoughts" whilst walking half way home. That makes me sound quite sad I know. (I wouldn't usually write that word, but on Sunday I said something equally "sad" to the student I tutor and I am finding it hard to look myself in the mirror \hyperbole!) :p Well don't tell anyone this, but I deliberately say "sad" things like that to non-mathematicians. You should try it too. They look at you like you're mental. Oh the things they don't know...

OK OK - I'm going to sleep now! (Without doing the group theory or coding theory that I had very nearly promised myself to do.... . Why make such promises?!) Once again please do attend the Galois Group lecture this Wednesday, and once again I hope to make sure that the refreshments are all there.

Wow - I have just reminded myself about a grave injustice that happened to me about my posters, yet again (!), but you can be spared the details of that today, for tomorrow when blood flows (not mine of course) you'll know the full story anyway.

Sunday, October 12, 2008

If only complex logs were that simple...

Today I have woken up on the wrong side of bed.

Normally I would make a big deal about that statement for it isn't physically possible for me to do such a thing, but today you'll have to forgive me for not trying to be remotely funny.

Once again I have been a couch potatoe since I woke up, but at 2pm I forced myself off the sofa and made a cup of tea for myself. This was an achievement indeed for I then proceeded to my desk and *drum roll* some applied complex analysis.

I have to train myself to endure this subject for two hours at least, because unsurprisingly, after an hour or so of just going through the first lecture notes and recalling some information from a text book, my head is going to explode. I honestly am in need of another cup of tea now which is a bad thing! (I had reduced my tea intake to two cups a day, and now I'm heading back to three or four per day again.) But I best get used to this head exploding feeling and learn how to carry it with me without it affecting my stability, for the sake of my Topology lectures if nothing else.

We have only had four lectures on this module but we are expected to have remembered what we did in Complex Analysis last year. Now that's where the problem lies. I remember things and things about things, but nothing about the things that I need to remember! I mean Cauchy-Riemann equations are one of the things that I need to remember, but to remind myself I have to now fish my last years folders out from where ever they are. (I can remember the idea of the proof of Cauchy-Riemann equations, but strangely not much else!)

You might be happy to read, or perhaps proud (!) to see that I have matured an ickle bit from last year. Now I shan't mention what might give you such a silly idea, for if you haven't noticed it then you are not from those who I speak off. (But since I can't resist saying one thing, I will say that the above paragraph is the biggest clue in this post...).

So what about complex logs was I meant to say? Well write if you're being so and so-ish! Instead of writing anything out again, here's the beginning of what the problem is - the function ln(z):
Now my writing is awfully unlike itself there, so I am going to lie and say that I was squinting due to the pain in my head, and couldn't see much. The truth is that my time for complex analysis was nearing its end... (my tea had finished).

In applied complex analysis one idea that is quite difficult to get your head around (initially) is that of the branches and cut planes. The complex logarithm is multi-valued (the 2n\pi above) and we don't like that at all. Hence we do some cutting here and there, to find ourselves a nice range where this silly function is single-valued and "nice". (Nice could mean analytic which just means that a function is differentiable at every point inside a domain D.) Things get ugly along the branch, but we can ignore that for now and just say that our point cannot cross any cuts, for the previous "niceness" disappears. (Pictures are needed for this in my opinion, but I have a student coming soon so that's not possible now).

For ln(z), we can take the branch cut to be anywhere we want, and examples of two particular cuts are:
a) the "Principal Branch" : - \pi (arg z + 2n\pi) \leq \pi and
b) 0 \le (arg z + 2n\pi)  2\pi.

We often choose the branch in such a way that, for z real, we would have just the "normal" value of \ln z= \ln(x+iy) = \ln x.

It's when we get to functions like:

 \ln \left(\frac{z-1}{z+1}\right),
that things get more interesting. (I invite readers to guess what the branch cut would be in this instance.)

I realise that this isn't a very meaty post, and I hope to fill the details in soon (especially about the last function mentioned). It is my intention to post my lecture notes on at least one module this semester and see if it helps me in anyway. Some people go home and write their whole notes out again, (once understood), which is a very good way of keeping on top of things. Although I would dearly love to write notes on this module due to its level of difficulty, I am slightly reluctant due to having to insert images etc.

Anyway, as always please feel free to correct any nonsense that I write, but I will have to run now for I need tea before that student comes!

PS: Any faulty inequalities will be edited later - silly html won't allow the less than symbol!