Friday, September 28, 2007

In want of a peaceful title: Hi

The more provocative title has to be 'unfair lectures'. Do I proceed lightly, trying not to step on as many peoples feet as possible, or do I just jump straight in?

Ha, my original title may have raised some eyebrows, but rest assured this may be a somewhat trivial matter. *cue weird look for using the 't' word* This post is going to be messy, but it will basically be a round up of the weeks lectures. I know it has been a week (as the Tweenies constantly remind me), but I have a feeling that Friday's are not going to be enjoyed as much as they used to be, and probably Thursday's too. Thankfully Monday to Wednesday will be nicer.

Today, after Bella and myself bought the book Complex Analysis for a module, I was asked something along the lines, 'Why complex numbers, and why i?' [or something similar]. We were sat on a bus, which I was forced to take (exercise: what is wrong with that statement?) and I tried my best to keep my voice down as I constructed a reply. Ignoring the weird looks, I started with the Natural numbers or the counting numbers. This was all obvious to Bella but I couldn't resist. From the naturals I went to the integers - why because we needed negative numbers. Then in came the rationals, and finally we had the real numbers. All the time saying that we extended the sets for completeness.

The way I used to see it was there is this huge line that is infinitely long. We basically want to be able to give a 'label' to every point on that line. Thus enter the integers, rationals etc. but this doesn't correspond with imaginary numbers. As I learnt the other day, and try to recall, complex numbers are 4-dimensional? The only way I was able to introduce i, was that we wanted to know the solution to the equation x^2=-1. However, even I went onto wonder why 'i' in particular? Why not another letter. Yes, that question is quite silly compared to the 'what's so important about complex numbers?' question. I know that they are used a lot in mechanics and oscillations, but isn't it remarkable that an "imaginary thing" has such a huge role?

I obviously am not well versed in such answers, so I did point out to Bella not to take my word for anything! Nevertheless the conversation was interesting. After the free bus came to a stop, I found myself discussing lectures with Bella.

I told Bella that lecturers are story tellers - they tell us a story. The idea is to communicate this story to us. Different lecturers are different story tellers. Some talk to the audience. They ask the audience for a number. No one replies, so they ask again. Still no one replies, so again they ask until finally someone shouts the number three. These story tellers make you feel part of the story. They write on the board and you copy down what they write with them. All the time being involved with this story telling process. If they pause for a few minutes, and discuss other matters you listen carefully. If something funny is said you laugh; consider it an intermission during the tale. (I later repeated all this to Fizz as we walked to our final lecture today too).

Everyone has their own outlook on things, but I really enjoy going to lectures because of this story telling process. I love writing notes. I love writing notes with the lecturers. I love listening to what the lecturers say when they are NOT writing. I am able to listen, because if the lecturer is not writing, then that means I am not writing as well.

I think my feelings during the holidays were quite clear. I was itching to get back into the action - to get to some solid maths. I was desperate for that challenge. All my modules are challenging indeed, but the ones that tell a brilliant story are Algebraic Structures and Real Analysis. We have had two lectures for them two modules, and it feels like many more. The story has started beautifully, and I am desperate for it to continue in the same way. Where am I going with this? Where indeed.

I don't know whether to apologise for being a weird learner, but it is something that just is. I like pictures and they greatly aid my learning process. The final thing that made the epsilon definition stick last year, was the graph drawn in the example class. The graph of epsilon and any natural number depending on it. I can survive without pictures, for some things can't be viewed in such ways, but they aid me greatly.

Unfortunately, as I continue to state: I am 'poor' at multi-tasking. I believe that it is better to do one thing and do it properly, rather than do a million things, of which a few may be improper. This may be a problem for me later on, but I don't know whether it is possible train one to 'multi-task'. I don't care about the future problem, but about the current one.

If I am copying notes from a prepared acetate, then I am sorry but I am not listening to a word you are saying. Fragments of the important story you are communicating to me, are picked up, but it is infuriatingly nonsensical. As I am 'copying' parts of the story i.e. not 'writing' the story with you, I once again don't take anything that I copy in. The process of this note copying is like being asked to remove all the peas from a pea pod. You just remove them - not caring about a thing in the world and not thinking about what you are actually doing.

Sigh. This is all connected to my inability to copy and listen at the same time. A possible solution is not to copy things down, but just to listen; however that is only half a solution. When I am writing the story with the lecturers, my brain actually tries to acknowledge the story and tries to process it. That is 90% of my learning - it all happens during lectures!!! If you asked me about my lecture at 12pm-1pm I will be able to tell you that we discussed binary operations. We had three 'exotic' examples (which I found cool!) and some natural ones. Today we talked about the identity element in a non-empty set S, and some associativity properties. (a^n= a*a.......*a*a, n times). We did a neat little proof of why the identity has to be unique as well. Ah, we also drew a multiplication table for modulo 3 and noticed that a binary operation is commutative if and only if the table is symmetric about the diagonal. And no - I have not looked at my notes since the lecture.

If you ask me about the real analysis lecture I will dodgily be able to communicate the idea of a neighbourhood, and that of a deleted neighbourhood. When I saw dodgily I mean the lecture was on a Tuesday or Wednesday! However, I am sure that I could tell you about the limit of a function f, as it tends to a, being L iff.....(for all epsilon more than zero, there exists a delta such that: 0 <|x-a|< delta, implies that | f(x) - L | < epsilon). BTW - don't take my word for that since it is probably mumbo jumbo and has a mistake somewhere. I haven't defined the function properly and made other things clear.

The rather dragged out point I am trying to make is that I am really following these two stories continuing. Albeit the second one being slightly above board, I am really looking forward to it. I love these two stories already, namely because of the story tellers. Already they are slowly bringing me back into everything.

I really miss Professor Dold. He wrote a magnificent story using the OHP. Yes, you read that correctly - a story WITH the OHP. What did Prof. D do? Well he wrote on the acetates and we then copied down what he wrote with him. That's fair enough. If he had just stuck the acetate up with everything written on it beforehand then that wouldn't have been very fair in my opinion. I don't mind lecturers using the OHP, however it would be fairer if they wrote on it during lectures, rather than preparing stuff before hand and sticking them up. Maybe diagrams and other things are an exception, but is it fair that we have to try and quickly copy down everything, whilst trying to listen to what is being said and then process it all? (Yeah, I know life's not fair, but when has that stopped people from complaining?)

I know that the Roscoe theatre is awful, and we are doomed with acetates. But I just want to write the story with the lecturers - is that too much to ask? I suppose it is, since I tend to be the only one voicing these opinions. I have a certain way which works for me and I try to achieve that way. More than white boards, I hate the OHP. And I also hate notes being put up on the internet before the lectures. That kind of spoils the story if that makes sense... I know shoot me - I am a lame student who makes a big hoo haa over small things. I can't help it. The two best story tellers in the university and the two best stories that I am going to be told, are being overshadowed. And that by the OHP. Isn't that enough to make any bean angry?

Surprisingly I kept my cool today. I could really feel my blood boiling and causing me internal physical problems! The urge to exclaim loudly was too darn strong, yet I kept it bottled up. What to do beans? I suffered in a similar manner in the first six weeks of the linear algebra lectures, but I think even they were brilliant compared to now. Then the problem had been having to copy everything from the book into my notes. Now the problem is that I am copying things down but not actually taking anything in whatsoever. Please story tellers - can't you write the definitions or notes on the OHP during the lectures WITH US, rather than before hand.

I want to go to lectures and learn and be happy about it. I don't think that is going to be the case for two lectures (on Thursdays and Fridays). A lot of definitions were put on the OHP, and I honestly can't remember any of them. Only fragments like the words: open set, closed set, limit of a point... are coming to mind. And for the other lecture - I only can remember the double integral.

Maybe the OHP is used to save time? I doubt that for we did finish five minutes early, so there was time to spare. I think this is a lose lose situation for me, but I am just going to bite my tongue for another week.

Sometimes I wish I was born 20 or so years ago. All this tecnological advancement is making my hair go grey. (Well if we didn't have OHPs I wouldn't be having this problem, and if we didn't have the Internet then no notes could go online before the lectures! Ha - imagine life with no Internet. I was joking at that suggestion BTW.)

The week did end on a dull note, but it was really great to be back. I now realise why there are soooooo many people on our course this year: we have joint honour students and people re-sitting their second year too. Normally if you came late, you could find a place to sit down - now that is impossible. And for a blind bat like me, I can't really see much the further back I go. Also, before I do shut up I have a tip. I would definitely recommend that you sit near the front of the lecture room. Due to me being early 'but late' at the same time (i.e. I went after ten too but before o'clock!) I had to sit at the back in the mornings lecture. At the front you have to look straight ahead at the lecturer, and so you focus on what is being said. However, at the back the whole room is your distraction and refocusing yourself is a pain. Note to self: aim to get to lectures before ten too if possible! Do you think my story telling analogy is a fair one?

First years and third years

I was meant to post this yesterday, but unfortunately could only muster one post. Yesterday I bumped into a first year and a third year. The first year I had tried to 'scare' as I waited for someone, and the third year went to the same secondary school as me. Thankfully my 'boo' hadn't actually scared anyone, so I had tried it again yesterday. No surprises to it not working again, but it gave me a chance to talk to the first year in question.

The feelings expressed about how the first week was going, reminded me of my own struggles. I just encouraged the student to keep at it, and hopefully things will start falling into place. I reassured the student that most people will be feeling the same way, and so had I, but supervisions etc are a great help.

The student didn't look too reassured - a great burden seemed to be carried around. I was reminded of my own first year during this instance, and how life had been a struggle. The other day I had even told my PT, that I had seriously considered changing my course during the struggle, but had seen sense after some positive encouragement countered the negative. Yes, I don't think that people\{mathematicians} were 'sympathetic' to my struggles. I didn't want their sympathy, but I didn't want to constantly hear that I had chosen the wrong degree and that 'it served me right'. I also didn't want to hear people telling me that it is not too late to transfer! What made it worse sometimes was when Noddy or certain other people said these comments to me.

I got lucky though, or should I say that DC entered the picture. Why are these feelings coming back to me in a jolt? I don't know to be honest, but they were dark days indeed. I was honestly not understanding the course material - especially numbers, sets and functions. It was a completely different module and proofs had been an alien concept to me. This had all happened in the first five or six weeks.

The concept of 'giving advice' is what is possibly causing this reflection. Is it right to give advice, or is it better to share experiences? What advice would I give to the first years? I honestly can't say, since it is unlikely that there is another nutter out there like me! I would just say that if people are being negative about you doing maths, try to ignore them and remain positive. Or if it is possible, find sources of positivity, which you can always rely on when the negativity returns. Due to the initial negativity, I still don't understand most of the set theory we did in the first six weeks. However, one of my aims in life is to be able to understand the Pigeon-Hole principle properly! (It does have a cool name...)

It has been a week and I have seen a few first years carrying this weary look, like they didn't know what they let themselves in for (but thankfully only a few). I encourage them to come to PASS, and not to worry. I think encouragement is required, but we have to be careful with it. I used to know a few second year student in my first year, and only one seriously encouraged me in a positive way. The others echoed, 'chill out in your first year'. You must create a balance for yourself, and only you know what works for you.

The third year I met on Wednesday was the same second year who told me 'chill out'. I understand where this student is coming from, but I was told 'don't do Algebraic Structures II, because it is really hard, but some stats module in my second semester, due to it being easier'. This student didn't do metric spaces so I think the third year choices are quite limited! I will not mention this student again, because yesterday I bumped into the 'encouraging' second year (now third year) student mentioned above. I really like this student. Why? Because this was something that was said, 'Real and Complex analysis are fun, and so is Algebraic Structures.' The word FUN was used. FUN.

I actually consulted this student after I had chosen my second semester choices, and the feedback I was given was very reassuring. Why am I talking about third years? It's weird how I have only started my second year, and I am looking at my third! Another weird thing is how we all progress through this cycle. In out first year we are sort of timid and worried. Or is overwhelmed the right word? During my second year, I am currently feeling more at ease with myself. Then in the third, I will once again become worried and overwhelmed by things. BTW I have some good news for myself! I can take the fourth year module Galois Theory in my third year.

Something 'funny' happened yesterday, in relation to me being at ease with my maths. In our Partial Differential Equations (PDE) lecture we were given a sheet of PDE's and told to find the equations in our spare time. Later, as I attempted to painfully organise myself, the Tweenies were in conversation. Bella saw me putting away the PDE sheet and remarked, 'Who would be that sad to find the equations in their spare time?' I coughed pointedly. The message had been communicated!! I guess one reason I feel at ease is due to the fact that I am not hiding 'my maths'. We had a discussion about Alan Turing after my sadness had been exposed, since the building was named after him.

My current question has been: who is your favourite mathematician from the past. I don't mean who you think has made a massive impact on mathematics, but to put it in baby language: who did you find cool? I wrote past here, because when I asked someone I was made to clarify this and it is needed I think. If we were talking about present mathematicians, it has got to be the lecturers that I always mention! [DC and PS...].

Anyway, that is enough down memory lane. It is just that I want my years at university to represent a cycle: (1,2,3). Today on two occasions I talked about four years or more, of maths studying. The first time it was with the tweenies. Milo is lucky that he will be doing four years of maths. I just kept quite during this discussion, and mulled over things in my head. Later, I spoke to someone else about four years or more and I was positively encouraged to consider further studies in maths. I was slightly embarrassed at this suggestion, namely because although I want to do such a thing, I didn't think myself competent of doing so. I have not yet conquered the art of teaching oneself. It does sound like an extremely cool thing though: 'studying maths further'. I must confess to sometimes, in my sad little world, thinking about what I would actually research. (I apologise for the overuse of the word cool - shift f7 isn't working!)

However, with this discussion I was overcome with a brief moment of sadness. How do I explain my circumstances? How do I explain that there is something else I want to achieve, but I don't know what to prioritise? About why what I do isn't as simple as I would like it to be. One reason why I want that cycle to exist is because I don't ever want to leave studying and university. I really love it. Lectures, the struggles, and everything is just great. The one thing that I must do this year, is somehow suppress my desire to study maths beyond my degree. Well straight after I guess. I can always do it some time in the future I hope. Last year, the prospect of not doing further studies was really taxing for me, and that is the reason why I want to make them thoughts disjoint from myself. Is that a fair thing?

Yes, I am currently feeling sad at the moment. No surprises there. Nuno just saw two of my maths books and said, 'You can teach me this can't you?' I just laughed and said I will after she has finished learning fractions and everything else. I do want to be a teacher, but am I writing that just to convince myself? I do, but not now I suppose. See, this topic is very problematic for me. I would never have imagined myself capable of further studying of mathematics, but am I reminded of my friend in school who is doing medicine. I used to say to my friend that I will be a doctor one day too... but not in the same way.

Meh, that is enough depressing things for one post! The feeling of still having time reassures me, and hence I should not worry too much about the future yet. Would you believe it - it's a Friday as well! (Yes, I am finishing this post this morning). I wonder how the day is going to progress.

I wrote the above paragraph before coming into university, and now I'm finishing this whilst at university!

I did a very stupid or impulsive thing this morning, before my lectures started. I couldn't help myself. I just saw, though a little and then did! I don't know why I did what I did. I just didn't think. Meh, it's not surprises that I am an ickle freak.

This Friday has been a long day: I will be posting the first episode of 'Oscillating Fridays', when I get home. The day has yet to end you see, but I am upset that not all my lectures seem like stories. More later I hope. To complex analysis and beyond...

Wednesday, September 26, 2007

a^0=1 and negative powers.

In college I was told that a^0=, and I remember why that is the case being explained. However, the finer details escaped me and I quickly forgot 'why' or how we can show this. Today, I once again came across this fact and it is them neat little mathematical things, that make you go 'awe'. ;) [Well it came across as cool!]

We have to know about certain rules before proceeding, but I will only be stating the few used.

(a) \text{If }ab=ac, \text{where } a,b,c \in \mathbb{R} \text{ then } b=c. Also, a must not equal to zero. [Cancellation law for multiplication].

(b)\text{For } a\in \mathbb{R}, a^1=a.

(c)\text{If } a\in \mathbb{R}\text{ and } i,j \in \mathbb{N}, \text{ then } a^{i+j}=a^i \times a^j.

Now there are a few ways to go about doing this, but it depends on what you already take for granted I suppose. I will do it in the way I read it from the book first, because that is needed for negative powers.

From (b), a= a^1 = a^{1 +0} = a^1 \times a^0 = a \times a^0. Hence, (a) [the multiplication cancellation laws] then tell us that no matter what a is, a^0=.

Now for the negative powers, we use the 'infamous trick' of adding in zero. [We actually used it in a lecture today - bringing a wry smile to my face.]

We start from knowing what a^k is equal to, then: 1= a^0 = a^{k+(-k)}= a^k \times a^{-k} . (By using the rules mentioned above). So from this we can see that a^{-k} = \frac{1}{a^k}.


If we know about negative powers, we can always use that fact to show that a^0=.

Consider: \displaystyle 1= \frac{a^l}{a^l} = a^{l+ (-l)} = a^0.

It does seem circular, but I guess you don't have to be 'that' rigorous. It's quite embarrassing, the way I had the 'ah ha' moment when I recalled the above. We take a lot of things for granted in maths, and 'nice' little things like the above are just 'nice'.

Tuesday, September 25, 2007

Maths new year resolutions.

I will not write any of the hocus pocus about 'Not' tables tonight (this morning!) but just jot a few that spring to mind before I go to sleep (finally).

1) Take buses at all times - whoops I lied. I mean try not take the bus; even if it's raining. Valid excuses are when I am running late for lectures, and that is all I think.

2) Sleep properly

3) Read at least 5 general audience maths book I have. Or should it be finish reading what I start!

4) Attend as many example classes as possible. This is a clever one, because it is directly linked to the amount of time I spend on example sheets, and in understanding course material. The more time spent doing the mentioned, results in me having more problems and questions that might need answering. This should hopefully cause me to go to the example classes.

5) HATE STATS! HATE STATS! Yeah, I have switched back into the NOT thing it seems. I think that this is one of the most important ones, so I dare not edit it tomorrow. Basically I have to do the opposite of that i.e. try to at least 'like' stats. Even though it is evil and doesn't like me, I must be the more responsible person in this relationship. :( Oh sweet youth, I miss you and being irresponsible ... This is going to be really difficult, but hey, we got off to a positive start today I hope. :/

6) The obvious one 'which must not be mentioned' (It has a taboo on it like Voldemort's name.) However, I am quite happy about this after todays proceedings, and just hope that I can successfully finish my list.

Post to be updated tomorrow some time. I really need some sleep now. (Wow its been a while since I have posted two a day.)

Monday, September 24, 2007

First day of \sout{school} term

I really should stop with this '\sout{}' business, but it's the only time I ever get to use LaTeX (apart from when I post). Some may read '\sout{school}, others may see ... erm 'formula does not parse', or if you are lucky, you might see. BTW, I produced that through TeXnic centre, and then copy-pasted it to paint. If you want to use the \sout{} command, then stick, 'usepackage{ulem}' in your preamble.

That was my preamble in case you are wondering. Since I have started reading really slowly, I find the need to insert commas in inappropriate places at times. Apologies if this is irksome, for sometimes I do find myself looking to the skies and crying why! [Oh and before I forget: A BIG thank you to a once upon a time anon commenter, who told me to take it easy with the exclamation marks. I'm not sure if you are still reading this blog, but if so, I really mean it. Some of my previous posts are unreadable and make me feel ill too! I am hoping that my English writing slightly improving is another benefit of this blog.]

I have wrote about everything BUT my first day. Was it that forgettable you ask. Actually it wasn't; I am just fighting with my body, to hold on for another fifteen minutes. I have resisted the temptation to allow my painful limbs to communicate their annoyance to me. I sort of over did it with the 'walking really fast' today. Anyway, why am I causing my back more annoyance by adding to my preamble?

The stats lecture I mentioned during the day. It was nice and slow, just the way I prefer stats to be. Some bits honestly did make sense, whereas I must be careful not to zone out. Well a 5 second 'nap' is perfectly fine, but I should be awake when something is being said. Maybe it was slow because it was at 9am, and the lecturer felt sorry for us? You will be hearing more about stats in my upcoming maths new year resolution post.

Today most of the Tweenies were suffering from a lack of sleep it seems. Both Milo and Fizz went to sleep at early times, and both woke up at equally early times! They then obviously found it harder to fall asleep again. Oscillating Mondays eh, who would have imagined it? Todays oscillations were quite weird though. When I was walking and doing something, I was OK. However, the minute I sat down 'casually', my eyes started drooping and my senses dulled. I didn't fall asleep fortunately, but Mondays are potentially going to be very painful.

I saw quite a few faces from last year, and a few million more. I wasn't to know that joint honours students had joined with us, but nevertheless it was sort of daunting. I'm ashamed to admit that some names have escaped me, and I am still wondering whether the person I said hi to was a Tim, Tom, or something beginning with T. (well it's really another letter and name...) My money is on Tom, but I didn't want to embarrass myself by saying, 'Hi Tom', only to be told it was Tim. But hey - I bet you (every single penny I have, which is negative at the moment) that only one or two remember my name. So all is well I suppose. (Actually only one probably remembers my names.

You see I'm dragging this lazy (and possibly boring post) out, because I want to demonstrate what effect the Algebraic Structures lecture had on me! Although I have done 'perms' last year, and did have a quick glance over them in the holidays, it was a great lecture. That will probably be the only lecture that I ever follow, but it was an enjoyable lecture (as always). The lecture theatre was FULL. Never in my days have I seen it like that. I risk repeating myself, but it didn't feel like 4am and the end of a long day. It's just something about wanting to be there and bouncing towards the lecture, which makes such a big difference.

Now I have a question. If a maths lecturer was to wake you up at 2am, and ask you to write the composite of two permutations, would you be able to? And if again at 3am, you were once again woken up to write a composition of cycles in standard notation, would you be able to? Yes I have avoided the question about you being irked by this, but shame on you if you would be! :D If you are not asleep and are blogging, then it shouldn't be a problem. However, if in your half sleep like state you are able to murmur the correct answer, then you deserve a pat on the back. (OK, fine, maybe not everyone would be happy at this 'intrusion', but you need to sort your priorities out if you value sleep more than being able to compose permutations. ;) )

The lecture was good for many other reasons too - one which I shall semi mention, and the other I won't. Although I was in a rush at the end of the lecture (which later caused me great pain), I can now do a little song and dance about something. A better explanation has to be given to someone (probably on Thursday) but I felt overjoyed to be blunt. I have decided not to explicitly mention what I'm going on about about in this blog, but I am desperate to leave a clue. Does the word 'minority' help? Please remain calm if it doesn't. :p P.S is just great - a brilliant lecturer, and I'm quite looking forward to what is to come hopefully. [Oh, I will probably be using a lot of different code words this year, which is annoying, but I fear being 'precise'].

I had a 'James Bond' moment today, but as always the director wasn't happy with it. Filming will resume tomorrow (I hope), and please note: I do my own stunts. :8

That signals the end of the post. The day ended on a positive, and a friend of mine from college said that no one can beat me when it comes to talking. Do I act offended, or secretly be pleased? :D (Although I seriously doubt this claim, as I am sure you might agree! I really don't talk that much...) Well I can at least hopefully happily state, that I can stay quiet in lectures. *touch wood*

Did I mention that it's good to be back? (Do I hear a 'It's good to have you back too.' from somewhere? Or is that just me talking to myself again? :p )

Resolution One: Sleep properly

I'm currently at University, having painlessly survived a 9am statistics lecture. The next few weeks are going to difficult, but I am going to be aiming to get 7 hours sleep a day. This means going to sleep at a reasonable time, and waking up when I should! It also means that I must resist the temptation to press the Snooze button. (Unlike today, which resulted in me running around like a head less chicken).

I will soon explain the way in which my resolutions work, but the basic idea is to do with 'Not' truth tables (I think). I believe that resolutions are meant to be broken, so by saying that I'm going to sleep properly, I won't. Hence, I will be proposing to 'not have seven hours sleep', rather than 'to have seven hours sleep'.

Actually- forget all this. I have obviously had less than seven hours sleep today, and I honestly have lost another screw. The above paragraph isn't registering and I will deal with this tonight, or another time. Probably not tonight because I will most likely be in the same frame of mind as now. I just don't want to make the same mistakes that I did during the beginning of my
first year. I made them mistakes so that I would learn from them. Maybe I'm being too .... something about all this, but I want the year to get of to a good start. I know what I am capable of (as in laziness and what not), so self-control is required. (I can potentially vex a few people out with this attitude).

I am an 'organised mess' to put it bluntly. Oh, that reminds me- I really need to clean my room. It is normally a 'must' task before the year starts, but one which I haven't got round to yet. My computer has been off for the past two days, and that explains the blogging absence too. It's weird not being able to access my bookmarks from other computers, but hey, I haven't turned it on for a reason!

Yesterday I accomplished something quite great. Well it won't seem that way to others, but I honestly feel lighter and now hope that I can relax slightly. (Don't worry this has nothing to do with United's win last night! :D Although I do have a football post in the queue). My 'accomplishment' is the reason why I went to sleep at 1am, and then had very bad broken sleep.

Oh, and I have finally got my hands on the Fraleigh book, which is a good thing indeed. because the copy I had from the library was recalled today! I got it for a whooping... wait for it... £35.00. (In Blackwells they are ripping us off (cough), and selling it for £57.00). The internet is your friend, if you are interested (Amazon etc). However, I liked the 5th edition better - it was
more 'compact' and generally had a better feel to it. :o I have another surprise for any readers, about my maths book shelf, but I have to organise myself before I surprise you. (Trust me, to get to that update I have suffered a lot of bruises and a very sore back indeed.)

The stats lecture BTW, was ... (I think that means it wasn't bad and it wasn't awesome, but made sense and was mind boggling at the same time). This post does seem rushed, but such is my current state of mind. Got some business to attend to at 4pm, you see. ;)

Friday, September 21, 2007

Random Paragraph Generator

From Ars Mathematica I found the link to a random paragraph generator. After a (deserved) nap and some food, I think I can be excused for having this bit of fun...

"The injury calculates before a waste! Maths differentiates Beans opposite the cleared artist. How will Beans zoom? Why can't the alarm broadcast the misfortune? Maths burns in Beans. The family remembers the crystal."

"Maths boggles with a problem. Maths overwhelms a flagging ethic. The rushed official maximizes Beans. Why does Beans pretend after Maths? Beans steams after the intellect. The damp fear speaks Maths past the intended episode."

".... Beans likes Maths....." (A weird one!)

OK, I will stop there. :D Today has been a heavy, rainy day. The rain I didn't mind - it was nice and warm. The heaviness was painful, but it is over now. I shouldn't have taken the stairs that many times. I even forgot to count them in my haste. Maybe I should try to walk slightly slower, and stop when thinking. But then... I would never get anywhere!

Do I say that I won't be a good PASS leader before it actually starts, or do I say, I will try to my best to be a good PASS leader? Something tells me it should be the second option, but it is so easy to sink into negativity. However, I am actually looking forward to this, albeit nervously. Some of the first years I spoke to seem nice, so I just have to make sure that I don't scare them too much. (A difficult task indeed, as I am sure you would agree).

BTW, the Tweenies are great. I think it is nice when some understanding is apparent amongst friends. For instance, I didn't have to say that I'm tired today and my deflated balloon actions gave it away. I am even more happy, since I am no longer hiding how much I like Maths to the Tweenies. Last year I did tone it down a bit, which probably caused an 'ickle' bit of friction; but now they know and they 'bare' with me. :D I don't mind that - I can ignore body language when I have to you see... (It's all in good nature I am told).

Woohoo for the weekend, and boo hoo for the 9am Monday stats lecture. And I would say boohoo for the 4-5pm lecture on Monday (after a huge gap), but I think it's Algebraic Structures, which definitely changes the boohoo to another woohoo. So thankfully, the woohoo's > boohoos.

Thursday, September 20, 2007

Maths building: round two.

I thought it was best to reply to a comment from someone here. (Well I was going to post this anyway, so might as well try to do two things at once).

My first impression of the new building was fifty fifty, as you might all have read. However, I always like stating my first impressions and opinions, because I am glad of the fact that they are never concrete. Why does this make me happy? Well there are some types of people, who having only spoken to you for a few minutes, might form a negative opinion about you. Some then stubbornly refuse to change this impression, and sometimes this causes them to never speak to you again. Other times, they don't really 'talk' to you when talking. Or maybe these people have just come to the conclusion that they don't like you?

Why am I talking about people? Well I had a bad experience with a person recently, and it got me thinking about 'people'. About why some people find it necessary to humiliate others, and why they find it funny to insult people in a supposedly 'subtle way'. Ah well, I will bite my tongue since I have decided to remain good natured about this, and not let it bother me too much. I was really tired and may be over-reacting slightly, but at that moment in time I wasn't made to feel good.

Body language is a really handy form of communication, as is your tone of voice. If you are going to joke about, say how short a person is (and you don't want to offend them); then my advice would be to make sure your body language and tone, communicate your intentions to the person concerned. :) I know that I can't really have gotten it out of my system, but heck I am trying my hardest! [Anyway, I don't think you should be making a joke out of someones height in the first place.] I do 'joke' around a lot (maybe too much), and the first rule of thumb is: if you can't laugh at yourself, then you shouldn't be laughing at others. Admitting to have been made to feel the way I had, would have been a weakness on my part. I was unable to respond in my normal manner because all cogs hadn't been firing, and I wasn't fully awake. So guess what - I went quiet! Is that too hard to believe? Sigh, come on beans button it.

OK, on to the new building (again). The anonymous commenter made a point that I have noticed myself, and agree with. The good or brilliant thing about the new building is that everyone is in one place. I actually really like this, since memories of having to run from the mss building to the lamb building in 10 minutes (to hand in work), still prey on my mind. The one reason why I didn't attend PASS sessions was because on Mondays our lectures were in the Renold building, and then PASS was in the Newman building. This may be a small and petty excuse from my part, but after a 9am lecture PASS didn't seem as appealing as food did. However, now with everything 'centrally located', my excuse would no longer be valid.

I spoke to someone about this, and it seems that I don't like the sensation of 'people' watching' me, without me being aware (I know no one actually might be, but there seem to be eyes everywhere). Like I said, I like mooching around and talking to myself (amongst other erm.. 'normal' things) which might frighten people. If I see you in the building, 'and make eye contact', I normally will smile. It's my natural response (which I blame my flight hormone for), so if I smile at you please smile back! Otherwise, you are going to cause me to injure my neck, when I quickly look back to see who you were glaring at. :p I will try not to embarrass you though. [I have been counting the weird looks I have been getting from smiling you see, but it's not my fault that I sometimes know people without them knowing me. I'm psychic-muhahaha! ]

A second person who I discussed the new building with, said that when the undergraduates start arriving in numbers next week, it will be different. So I will be reporting what the building is like with actual students around next week sometime! And in reply to the commenter - I don't know what difference the cafe will make, but I will forward to it. It might actually feel less bare and less like a hospital then I guess.

Once again there is this inevitable divide between 'higher floors' and 'ground floor', but one can get used to that I suppose. I do like the hustle and bustle though, and I have a confession to make. Although I do like bumping into and talking to people in the new building, now they can't avoid me. :/ Well I think some people might become sick of seeing my face around, but if you see me walking in a direction towards you; walking in the opposite direction might help, or jumping into any office. (But hey- I'm not that scary I hope!) It was quite nice waiting for someone in the corridor and scaring first years whilst doing so. I'm happy to report that they are made out of strong material, and a 'boo' didn't frighten them! And worry not, I didn't say anything negative about the building to them. ;) (Most of them liked it). Gosh, I remember my first day, first year and first everything! I just hope that I can have same memories for my second year. [The first years seem like a friendly bunch.]

One thing I wouldn't mind having on the ground floor is a black board. I have yet to fully explore this building, and am making a map of it at the moment(!) for future adventures. However, if anyone knows of a blackboard for the 'undergraduates' hanging about, then I would be grateful to be pointed in the right direction. There used to be black boards in the Lamb and Newman building corridors, so it makes sense to have one in the new building I hope. (Are seven year olds known for writing on walls? :D)

I can't comment on the wi-fi since I don't really have a use for it, but round two seems to be more positive. When an airport terminal is busy, it is much easier not to be spotted. (Yes, I still have this fear that someone might shout- 'there's beans' and I will have no hiding place in this building! I could do a Jason Bourne I suppose... :D) This month is going to be a tough one indeed - being constantly tired, amongst other things is my excuse this time round! Bring on round three? (Still need to get them stairs counted you see. ;) )

Tuesday, September 18, 2007

Maths building is an airport!

I will get to the new building soon, but it is best that I leave all potentially unpleasant things till the end. Today was my first proper day back to the university, and, well it didn't feel like it. To be honest it felt like a Monday morning, straight after a lazy weekend. I don't know whether or not that's a good thing, but I saw quite a few lecturers, and it didn't feel like it had been 3.5 months! (I saw my calculus supervisor and a few other people, which was good). However, obviously I'm sure they were all looking for the nearest exits.

It was also great seeing the Tweenies again, and I used this opportunity to discuss something in detail. :( I have every reason to be negative, since being back, once again makes me feel somewhat 'lonely'. The Tweenies are with me; it's part of the 'friendship code' and I really appreciate this. However, I want them to be in for the right reasons too (but beggars can't be choosy right?) It's pointless, trying to persuade my friends, since they're already in. It's the other people that worry me.

I must confess that upon seeing all the freshers, I did wonder whether any first year students will actually care about such things. There is such a big emphasis on 'chilling out in the first year', that sometimes things get overlooked. The loneliness that I mentioned above, is that which makes blogging that much more worthwhile. It's not physical loneliness (if that makes any sense), but the mental one, which can be worse at times. I want to talk about Fermat's Last Theorem with other students. I want to talk about my stupid take on what Alan Turing said about humans as machines. But no one wants to talk to me. They dismiss me saying I'm obsessed and what not. Actually some never get a chance to dismiss me, since I try to hide this 'obsession' and just go with the flow. (Well it's not hidden in front of the tweenies, lecturers and this blog, so that's a start).

It's weird, but having just wrote about the loneliness thing, I feel sad. I know that I end up bugging people like my lecturers and some post graduate students, but it's only them who I can bug. The reason for this is, that I don't hide my obsession in front of them, and sometimes actually have a proper discussion about maths with them. The question of hiding my obsession never arises when I'm talking to my lecturers - I am beans then!! I honestly can't wait to see my personal tutor soon, and talk 'shop' with him. He's great. I was really hoping to see him today, but I hadn't sent him an email before hand and didn't know where his office was. I don't think I'll be seeing him a lot in the new building though. :( Last year, his office was near mine(!), so we always saw each other.

I know that I'm to one extreme of the scale, which is why I have been trying to gather thoughts and opinions from people on the other side. Maybe second year students might have settled after their first year, and might like it? Actually, term hasn't even officially started yet and I'm the voice of doom. Well I did say that it feels like the holiday didn't even exist... The funny thing is that in all conversations today, I kept on saying, 'Next year it's going to be tough'. I was talking about my second year when I said next year i.e. this year. I guess the whole seeing everyone again thing made me forget myself today.

If this post is long and nonsensical, then I must warn you that I only had approximately 3.5 hours sleep last night. I woke up at some early hour (read the sun had risen!) and thought that I might as well try to get into the habit of waking up early, so didn't go back to sleep. Shock horror. Hence, this is my PUBLIC apology to all the people who saw me or who I talked to today. (Especially the man near the elevator, and some other students and a few lecturers). I guess I was over joyed at being back, and my bounciness went into fifth gear!! It felt amazing.

I'm slowly going to park up for the night, but it really does feel great to be back. I know that I have been having doubts about my venture, but this will always happen until we move from A to B. I just wish that more students actually liked talking about maths. I did wonder a minute ago, about what I would have done, without this blog? I honestly can't imagine what kind of beans I would have been without it. I think the wheels had been set in motion before the blog was created, but this blog (and Blogistan) definitely helped moved things along.

I am pretty exhausted at the moment, but really wanted to dig this post out. I have also been slowly thinking about my 'New Maths Year Resolutions'; but the trick is to think in opposites. Resolutions are meant to be broken, so I have to write the resolutions such that there 'broken form' is what I intend to do. Confused? Yes, it is slightly, but hopefully they should be up on Sunday (before lectures officially start). Onto to maths building now I suppose (grudgingly!)

I speak no lies when I say airport; well that is my first impression of it anyway. The Alan Turing building, renamed the AT building is open for business. You may have noticed, that this building has yet to acquire the privilege of being written in small fonts (as the mss building), but first impressions can always change. Actually no building will get that privilege - ever. It was specially made for the mss one.

I must drift into the clouds, and speak of some sad news though. The mss building was actually open today. :( I do have an 'attachment' with that building it seems, but I resisted the temptation to pop in. I walked passed it and kept my eyes straight ahead; looking back would have been too painful. Although I was pleased to see my home, it naturally caused me to compare it with the AT building. AT vs mss, who wins you decide? Actually I will tell you anyway - the mss building (from my first impressions that is!) will wipe the floor with the
AT building. (I'm not biased about this you know!)

Hyperbole and me, is like milk is to tea. Well something like that anyway. The new building is quite good actually; I never said it was bad! Its just not my type of building if you follow me. It honestly felt like an airport terminal - now Manchester can boast two airports. I asked the Tweenies for their first impressions and 'cold, grey and stark', were their words. (I'm going to see how they will change). I can't but help go back to the airport comparison. You walk in and above, you notice 'the waiting lounge'. This I gather is the common room. You do a 360 degrees slow turn, whilst looking up and see eyes gazing back at you. Some familiar and others not so familiar. (It's good in the sense that you do get a chance to speak to more of your course mates (outside lectures), and people from the maths department. A bit like an open-plan office, where you might spot people from the top and hurry down to bug them.)

I could see my face on the floor, which gave me the heebedy jeebies indeed! Gah- I'm not saying that the building is 'bad', since it does look cool and it is impressive. Normally when you walk on your own and what not, you are in your own zone. I unfortunately do various other things without thinking (i.e. talking to myself) when in this zone. In the mss building, I could do these normally and never felt weird (because no eyes were on me). I don't think that might be the case with the AT building - I can no longer mooch around the building which is a pain! That's what I don't like. (Bearing that in mind, nothing stopped me today... )

When I get the time, I will be linking Professor's Borovik's post about the new building, since I liked the pictures of this other building that he had posted. The words hospital and plastic also bounced about today, but I think this building needs 'living in'. Tomorrow I am going to (try) and examine all the stair cases, and count how many stairs there are to the top. There is no point in jumping into a lift; the stairs are quicker. Don't worry, I know my attitude towards this building might change, but the amount of stairs might help! At the moment I am fifty fifty about it, which is quite good considering the fact that I didn't even go to the top most floor, and everywhere else. It's a new taste that I have to get used to; but once again: BEANS IT HAS ONLY BEEN A DAY! (Just reminding myself).

PS: I had my first 'formal' driving lesson yesterday (Monday), and I survived (duh). My instructor is cool, but not one who is friendly with maths! The problem: I can't multi task. Everything feels mechanical and not fluid - I didn't like that. I know I can't expect it to click straight away, but this is my theory: in computer games you play a tutorial level, or something which helps you to become fluent with the controls and the game. Then you start the game and get into the advanced stuff. With driving, why don't they take you to a large field or area of land first, and do the 'tutorial' sessions there? With no cars, it will make you more comfortable and you can mess up as long as you like. I like the idea of that, since once you have your clutch control sorted out, you can move onto the advanced stuff. I don't think I'll be liking this driving thing too much!

My instructor told me to read books about it. The reply in my head was: Sorry preoccupied trying to read maths books! I'm not really learning to pass if that makes any sense. It is just another skill that I would like to acquire, and I don't really care about 'having my own car and driving it everywhere'. (I understand that that feeling might change too - as other drivers have been telling me! ;) )

Friday, September 14, 2007

Brakes please

All throughout these holidays, you have probably grown sick and tired of me whinging about the holidays being too long. I have technically speaking been on holiday from 29th May, so I did have some reason to complain (in my defence). However, I find myself in a weird position now. Today is officially my last holiday, and I don't want it to be. Have I got used to the holidays? Have they drained all the life out of me?

I doubt it, but this week has honestly been very busy and a lot has been going on. I just want it all to stop. Stop so that I can somehow mentally deal with it all. The week has gone too fast for my liking, and next week is kinda full for me too. Do I need to bang my head against the wall again? This feeling of wanting Monday not to come is quite new. I spoke to Milo and Fizz today, and during that time I was excited about the prospect of getting together again. (I had made a timetable interpretation error, and now my timetable officially stinks. On Monday I have a 9-10am lecture and then I have nothing until 3pm-5pm! I would very much like to utilise them free hours, but I don't know if that is possible. I could always plan my driving lessons then?)

Seriously, my 'emotions' are new and awkward. I don't want Monday to come. For the past few days I have thankfully been falling asleep at 1am, which is a drastic improvement from 4am; but it is not the waking up which is making me hesitant. The weird thing is, that just as I want to apply the brakes, I don't as well. Confused? Yeah, me too. I think I'm not ready for the year to start just yet, because I haven't completed what I was meant to by then. Week 0 is not a big deal, and lectures officially start on Monday 24th September, so I guess I still have some time. I hope that I'm able to remember everything that I have forgotten. :( Meh.

I bet you were all waiting for my 'Woohoo last holiday' post! I have probably mentioned this before, but during the first month back I can't see myself visiting Blogistan as much. I really should be doing something else at this moment, and am going to rush away now, but I'll be posting occasional updates, eg: 'first day back'. ;)

My student loan is still playing up, and having rang both the university and the SLC I am still waiting. If the on-line system doesn't register my financial registration, then next week I will have to wait in this long queue for quite sometime , with my payment schedule (which I have yet to receive). What joy. Maybe if that all was sorted out, I would be much calmer? I'm sure it's swings and roundabouts, and I will be blowing a different trumpet tomorrow..

Wednesday, September 12, 2007

Bad Beans

Initially I was going to use a different title, but obviously it wasn't chosen. Surprisingly for me, these past few days have been quite busy. More importantly, not busy in the way I would have liked to be. This post is just a slab of all happenings in the past few days.

Funnily enough, my mind just went blank. I know there wasn't much there to begin with, but my short term memory is too^{\infty} short. Actually I don't have a brilliant memory, full stop. I was nearly involved in a car accident today, which might explain this weird post. Relax, I wasn't driving but I had been sat in the front passenger seat. This silly silly driver, driving a silly silly BMW, had seen our car but still decided to pull out. If the driver hadn't stopped suddenly, I would indeed be a squashed bean. A few well chosen adjectives escaped me at that moment, (nothing to fancy, a child was in the back!) but there are some really stupid drivers out there. I think I was more in shock than anything else, at the drivers nerve to pull out on a busy road (read: really busy). But thankfully nothing happened, apart from me being on edge for the rest of the journey. :o

On the topic of driving; I will hopefully be having my first official driving lesson next Monday. You have been warned- it may be better if you stay indoors from 5pm! (Well it depends where you are from). Hmm, maybe you don't have to be over cautious... I won't exactly be driving you see. My driving instructor seems nice, and after our phone conversation it has been noted that I talk really fast! Shock horror. (Actually it doesn't come as a surprise). So what do I do about this? A teacher in college had said to me that I'm already thinking/saying the next sentence whilst I am talking. (Can't remember what his exact words were you see.) In my defence, when I am nervous or excited I can't help but speak slightly faster. Thankfully though, it was negotiated that if I was to ever speak too fast, then my instructor will ask me to repeat what I said. The key thing is that I will have to keep on repeating what I'm saying, until it has been understood. Just the way I like it, if I'm being honest!

So I guess that's a message to everyone out there. If you ever do happen to meet me(!), then PLEASE PLEASE ask me to repeat myself if you didn't catch what I said. I honestly don't mind repeating what I say a million times if I have to! Hopefully it won't get to a million times, and I have been 'training hard' at slowing down (pft), but even 10 times is ok. ;) OK, I jest, but supposedly once you get used to my 'presence' then it won't be so much of a problem. Maybe I should invent some brakes for my mouth? It's just that when I do s p e a k s l o w l y it feels r e a l l y s l o w! (Just like them words).

Whoops I was talking about my driving lesson wasn't I? I think that if you know how certain things work, then that aids your learning process. I'm still taking this driving thing the way I take playing a 'new game'. (I know it's a NOT a game, and I can't drive on pavements or through lamp posts; but new game as in adjusting to the controls). Do you think if I knew more about the engine, and what happens when you press the clutch etc. it would be better for me? Since I am more of a visual person, I think it will. I guess we'll just have to wait and see. (My instructor isn't brave enough to let me drive on the first lesson. ;) Wise choice I believe.)

Moving on (yes there is loads more) I have finally registered academically for the second year. BUT (you knew that was coming I hope), as always nothing is without problems when it comes to registration. On my self service screen I am only enrolled on two modules. That isn't such a problem but my financial registration is full of mumbo jumbo. I have decided to phone the university tomorrow and do the financial registration over the phone. Since the loan company are paying for me it should have been simple. (Damn that is a lot of money- £3070!) I think if I were paying that money out of my own pocket (i.e. on cloud nine), it may have been a different matter. If all students were paying out of there own pocket, would there be any resists etc? (I mean, how dedicated would students be?)

I really need to get out of the habit of sleeping at 4am since it isn't very productive. I'm weird in the sense that I am an owl at times, and other times an early riser. For instance, I can never do a revision all-nighter but have to wake up at 4am to revise! But when it comes to coursework or homeworks, I most likely do all nighters... Can it be put down as a skill, or is it just madness?

If you have suffered through this post, you might be scratching your heads and wondering when the 'bad beans' is going to surface. Or maybe, you're hoping it won't surface! I haven't been 'bad', but I have been foolish. I know for a fact that it's bye-bye games console when university starts (at least during the beginning) so I have been scheming. During term time, I might play on weekends but I gradually lose interest (and the time).

Recently, I have added a few members to my clan on Resistance Fall of Man. NOTE: If you're a mathematician and you play the game, then send me a buddy* invite and you can join without fulfilling any requirements! Normally, I initially consider players who beat me in a round, or who came in the top four. Then I look at how many games they've played and how many people they've killed. For every one game 10kills should be registered, so if a person has played 573 games and only killed 3789 people I no longer consider them. (I don't really care about much else i.e. how many deaths etc). I have a nice sized clan, but I don't know how many actually know about 'Galois the mathematician'! So any mathematician members are most welcome, (but please don't be too bad though).

You could say that I sometimes become competitive in situations such as these. As always this is friendly competition, but the thing is that I want to become a Supreme Commander before the year officially starts. I'm currently a General (1pip) I think, so need two more promotions (which takes forever). I didn't start this competition, but silly microphone head (MH), who is ranked higher than me, has started it. I just play for the fun of it; especially when I'm a Chimera with a Rossmore in Grimsby, or anyone in Nottingham! My competition tends to be with people who are currently playing the same round as me. However, MH has now pushed me too far. I can now longer resist the urge to zip his mouth you see, and although I have been feigning disinterest in the game, I badly want to become Supreme Commander as soon as possible.

It doesn't look possible, but hey 'Impossible is Nothing' right? (I know I should grow up and what not, and maybe concentrate my efforts on maths to prepare myself for the year, but that has been covered or so I hope). BTW, I don't play all day!! I have a certain time limit in which I have to play as much as possible.

Now that's over with, shall I talk business? I mean maths? But alas, apart from trying to teach a 9/10 year old maths I haven't done much. (I've been busy... erm playing RFOM.) This kid doesn't know how to read numbers properly and doesn't know how to order them. I dedicate about an hour everyday to help the child with maths. I don't know if negative numbers are known, but I'm assuming they're not. (I did a 'bank borrowing money' example and no indication of negative numbers was made). I have been asking the student to write numbers in words. Hopefully this will help aid the kid in being able to read numbers properly. (Hmm, what shall I refer to this child by? Misty (from Pokemon) it is.)

I think some people wanted to say 'not nice' things to me today, because I sort of got over excited. Well it has been a while since I played football, and that was one of my reasons; but I have kept these not nice comments in peoples heads for now! It has been a great day today, and hopefully this week is going to get better. I'm already feeling quite excited.

As I bang my head against the wall, and try to remember what has been forgotten, I will leave you with some pictures. EDIT: There are too many of them, and I am tired, so will post them some other time. So what 'bang' can I end this post with? How many hours do you think I can go for, without talking? (That's a random question I just asked myself.) I'm sure that with a hopeful look, people will be saying, 'FOREVER', but come let us be realistic now! (Erm... is there anything that I haven't mentioned?) I have be awake at 9:30 am \sout{tomorrow} today. Humbug.

Saturday, September 08, 2007

Still alive.

(This is yesterday's quick post.)

Last night I choked on an orange piece. I could leave it at that, but as someone said to me, I like making a mountain out of a mole hill! (Pfft- I don't think I even remembered that correctly).

It was actually quite horrific. That is the second time in my life that I have choked; the first being in year 9 when I was in secondary school. (Annie had stood laughing, whilst AM had sorted me out!) The year 9 incident had been erm... trivial compared to yesterdays since it had been drink.

The orange had partially gone down but got stuck. Eugh. I spluttered, coughed my guts out but it stayed stuck. Everyone froze. You see, my tonsils play up a lot and I always lose my voice or get a nasty cough, so initially my tonsils were suspected. However, as the darn orange piece remained stuck the situation became serious. It was actually quite freaky! The orange was stuck between my oesophagus (gullet) and wind pipe (my epiglotis wasn't doing its job properly). Thankfully, although it wasn't AM sorting me out this time, someone did. After that I couldn't finish my meal - I could feel the orange piece still stuck there. I was reduced to breathing heavily and drinking lots of water, but one thing that taught me was that one second you're here and the next you're not. Oh, and I realised that there is a reason why I prefer apples, pears and bananas rather than oranges!! But yeah, a I'm still alive (thankfully).

Thursday, September 06, 2007

Periodic Table of Mathematicians

The Chemist in me (2/7 parts according to my A Levels), was overjoyed to find a 'Periodic Table of Mathematicians'. (Thanks to Vlorbik).

It also reminded me of the time when I was actually considering a 'Maths and Chemistry' degree! Boy am I glad that I stuck with the maths. I love Chemistry experiments and the organic side of things, but thanks to A2 chemistry, I realised that I wouldn't be able to do chemistry at degree level. I didn't have the same motivation for it, as I did for maths. Nevertheless, the pear drop smelling chemicals have reminded me of how great Chemistry is. (My chemistry teacher was super duper.)

That periodic table is fantastic. You all must have a favourite element, so which mathematician corresponds to it? Does that tell you something about you?* ;) I had initially gone for Hydrogen (H), then Sodium (Na) and Argon (Ar). (Hydrogen probably because of the squeaky pop experiment; sodium because that was always used with water, hydrogen etc. and it grew on me; and I have always liked the sound of 'Argon'- my favourite noble gas.) I think I'm going to make my own little version of it because Fe should have been Fermat. I will also probably, most likely, definitely be putting some of the maths teachers that I have had on it as well!! (Sm seems to be just right for Steve too. :D)

(I am too tired to go through all the names, but if you find Galois, please do let me know.)
*Not in my case, no.

The Jumping Frog

A frog has fallen into a pit that is 30m deep. (As shown in the colourful illustration by me. X marks the frog!)

Each day the frog climbs 3m, but falls 2m at night. How many days does it take for him to escape?

I invite your answers to this 'problem', if you want to call it that. It was given to me by MH, and once again I was mocked. :( They expect too much of me, people do. I mean just because I like maths, doesn't mean that I should be able to answer problems like the one above, straight away! The fact that MH and another person had solved it put the pressure on me. I bought some time by claiming to be busy, and it worked.

I don't know if the answer I have is right, but I'm sure if someone posts their solution I can always confirm if I got the same! (For those who want proof that I have some answer, I have taken a picture of it. Once I get confirmation in the morning, I will let you know. :D)

Oh, and no guessing random numbers; a small explanation would be nice (if indeed you do bother having a go)! My first 'guess' had been: 'All the numbers from 1 to n, where n=30'. This took a while to register (haha), but I was given a stern look in return. Have fun.


PS: I did some maths toady! It's true; I looked over permutations because we had done quite a few proofs by 'strong induction' in the notes, and I had found it fuzzy. It still does seem like mumbo jumbo, what with this max(s,t) business. It know it's (sort of) obvious, but is there a way of getting from max(s-1, t-1) to max(s, t)-1? If s does not equal t, then max(s-1, t-1) is defined to be either s-1 or t-1, whichever is greater (not taking into consideration that s might equal t). In the same way, max(s, t) can either be s or t (whichever is greatest). Subtracting one from max(s,t) gives me what I want, but it all seems rather 'dodgy'. Hmm, I better dig up the book I have on reasoning...

Another 'oh', but when doing proofs I would first advise(?) you to plug some numbers in, to see what is happening. Well, it's not necessary and not possible for some proofs, but give it a try when trying to prove that there are infinitely many primes (and other such proofs). It might aid you in remembering proofs, or remembering how to go about proving them.

Tuesday, September 04, 2007

Multiplication and addition in different bases (plus binary)

As promised(!) I will draw up some multiplication and addition tables, but for base 12! (Why not 13? Well an exercise in the book was to draw up base 12, and ... you'll soon find out why).

I have previously mentioned calculations in base 10 and base 13, and now have gone for something in between i.e. base 12. A quick recap (otherwise known as a 'copy and paste job' and it's allowed because this is a new post! :p) If we let k denote the integer we have, then k can be written in base 12 by the following formula,

k = (a_n \times 12^n) + (a_{n-1} \times 12^{n-1}) + ... + (a_1 \times 12) + a_0

where a_n, a_{n-1},... a_1,a_0 are integers from zero to 11 and n is any positive integer. It must be noted that we require digit symbols for '10' and '11', so we'll write A for ten and B for eleven.

Multiplication in my opinion, is much simpler than addition; but that is only initially as you will soon see. Since I'm in a slow mood today, I will be taking things slowly! Below is a blank table for addition in base 12. Guess what you're meant to do next? Well if you're not familiar with basis, have a bash at the table below and see how you do:

\begin{array}{c|ccccccccccc}+_{12} &1 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp; 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B   \\\cline{1-12} 1 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;    &  & & & &  \\ 2 &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;  &  & & & &   \\ 3 &amp;amp;amp;amp;amp;amp;amp;amp;amp;  & & & &\\ 4 \\ 5 & & \\  6 & \\ 7\\ 8 &amp;amp;amp;amp;amp;amp;amp;amp; & & & &  & & \\  9 & &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp; & & & & \\ A \\ B\\ \end{array}

I'll get you started... 1+1= , actually wait 1+2=3 should get you started! (I couldn't lie about 1+1 you see.) Now I'll ramble for a bit whilst you're filling the table in. I had initially tried completing an addition table for base 7, and is it necessary to state that I failed miserably at the addition one? I had naively, or stupidly gone into modulo arithmetic mode so using the table above, 9+4=1 in base 12, or so I had claimed. It doesn't if you've done the same as me, which I doubt since only I seem capable of bringing congruences into everything! (We got of on a rocky start you see...)

Rambling over, the completed table should look like:*

\begin{array}{c|ccccccccccc} +_{12} &1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B\\\cline{1-12} 1 &amp;2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B & 10   \\ 2 &3 &amp;4 & 5 & 6 & 7 & 8 & 9 & A & B & 10 & 11    \\  3 &4 & 5 & 6 & 7 & 8 & 9 & A & B & 10 & 11 & 12 \\  4 &5 & 6 & 7 & 8 & 9 & A & B & 10 & 11 & 12 & 13 \\ 5 &amp;6 & 7 & 8 & 9 & A & B & 10 & 11 &12 & 13 & 14  \\  6 &7&amp; 8 & 9 & A & B & 10 & 11 & 12 &13& 14 &15  \\  7 &8 & 9 & A & B & 10 & 11 & 12 & 13 & 14 &15 &16 \\ 8 &amp;9 & A & B & 10 &11 &12 &13 &14 &15 & 16 & 17  \\ 9 &A &amp; B & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 &18 \\  A &B & 10 & 11 & 12 & 13 & 14 & 15& 16& 17 & 18 & 19 \\  B &10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 1A \\  \end{array}

And yes, I have asked myself WHY BASE 12! Some of you may have spotted the pattern and completed it by that (I did), but if you haven't gone (mod12) then you should all be OK. I'll do an example: 9+3 = 12 (in base 10) but 10 in base 12. I believe its pronounced one-two? (but don't quote me on that!). We get from 12 to 10 by using the formula above as follows:

k=12= 1 \times 12 + 0

In this case a_1= 1 and a_0= 0, hence because k=a_0a_1; 12 = 10 in base 12. (If you look at the previous post, in base 10 we actually have 1 \times 10 +2, which is were we get the 12 from). If you have any problems with that or if I've written anything incorrectly, please do let me know. The key to this is that the meanings of the digits depends on their position.

Addition and multiplication both become *coughs* trivial, once you've got the hang of things. You'll notice this if when doing the sum 12+3, you think to yourself what 15 is in terms of base 12. (You'll get the spidey feeling!) If you think addition and multiplication in base 12 is tedious, then I would recommend trying a smaller base to get to grips with things. I didn't manage to complete the multiplication table for base 12, and so the reader may wish to complete it as an exercise(!). Well I have filled in the 'boring' and easy answers so you should have less reason to be bored.

\begin{array}{c|ccccccccccc} \times_{12} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B\\\cline{1-12} 1 & 1 &amp;amp;amp;amp;amp;amp;amp; 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B\\ 2 &amp;amp;amp;amp;amp;amp;amp; 2 & 4 & 6 & 8 & A & 10 & 12 & 14 & 16 & 18 & 1A\\  3 & 3 &amp;amp;amp;amp;amp;amp;amp; 6 & 9 & 10 & 13 & 16 & 19 & 20 &  &  &  \\  4 &amp;amp;amp;amp;amp;amp; 4 & 8 & 10 & 14 & 18 &20 &  \\  5 & 5 & A & 13 & 18 & 21  \\  6 & 6 & 10 & 16 & 20 &  & 30 & & & & 50 &   \\  7 & 7& 12 & 19 &  &  &  & 41 & \\ 8 &amp;amp;amp;amp;amp; 8 & 14 & 20 &  &  & 40 &  & 54 &  \\ 9 &amp;amp; 9 & 16 &  &  &  &  & &  & 69 & \\ A &amp;amp;amp;amp;amp; A & 18 &  &  &  & 50 &  &  &  & 84 \\ B &amp;amp;amp;amp; B & 1A & &  & && && & 92 &A1 \\ \end{array}

If you're feeling up to it, you could always check my answers!! (My advice is to not linger too much on addition and multiplication, once you've got that 'spidey feeling'.)

I have previously talked about multiplication in different bases, so won't dwell on this for long. I will just do a quick example for one of the numbers that haven't been done in the table, and 7 x 8 it is. In base 10, (7 x 8=56). We know that 5 x 12 =60, so we must have that 56= 4 x12 + a_0. A simple subtraction then tells us that we must have a_0=8, hence in base 12, 56 is equal to 48. (56= 4x12 + 8) If that doesn't register, have a read through my previous post here.

Woo, thankfully that is all I am going to say on multiplication and addition in different bases. Well now quite all, but I most definitely will never choose a base bigger than nine.

The second part of this post is to do with binary. What kind of a mathematician is one who is clueless of binary? Or should mathematicians know what binary is? Once upon a time in Blogistan the following image surfaced:

I knew that the other two boxes were, but the joke was lost on me. Binary numbers, for those who might be as ignorant as I was (which I doubt), are numbers in base 2. I understood that you could only use 0 or 1, since in one supervision, my PT had done something with binary numbers in connection with the Chinese triangle. (I had only copied it down but not understood it). The following 'joke' also used to go whoosh over my head:

"There are 10 kinds of people in the world, those who understand binary math, and those who don't."

I hope that having read my posts about different bases, you are now 'in on the joke'. Yes, you deserve a good old chuckle at that and at the people who think that says 10! (Oops, was I not meant to write that?) I am still chuckling at how stupid (in want of a better word) this all seems; and at my own stupidity too. I feel like I'm part of some 'cool club' now - those who know what the heck binary and different bases are. The question now being asked again is, should mathematics student know about all this before starting their degree?

What I find good about other bases, is that I have more freedom of some sort. Previously I had only ever worked in base 10 you see, but now there is no restriction. I can even dilebrately annoy people who ask me what 7x8 is by saying it's 48, or by asking what base they're working in! :D. Another question that I will look into is whether different bases are actually used in maths, and what they're used for. (Apart from binary maybe). So this concludes the base posts I think.

*If you must know I had made a mistake when typing the second addition table. Upon correcting it, the formula wouldn't work. I changed and triple checked everything, but still it was being a nuisance. In frustration, I opened up TeXnic centre and tested it there. It still didn't work. If previously I was frustrated, I was now on the verge of turning the computer off! I had written, 'begin{array}' instead of '\begin{array}'. :o

Monday, September 03, 2007

Second year timetable!

Ladies and gentlemen, children of all ages I give you...the one, the only, the damnest (provisional) timetable ever seen by mankind:

Well you might be happy to hear, that 'Oscillating Fridays' are going to be showing again! I know I don't sound too happy, but hey, it's only 5 hours every Friday and three lectures in a row! What joy. Let us get all the gloom and doom about the timetable out of they way, before we progress. Two 9am starts isn't a good thing, and one of them is on a Monday - the worst day of the week. Humbug. How awful does it sound when saying, 'I have 9am lecture on a Monday; a 9am stats lecture!' Ouch - that was a low blow to the stomach. Come now, let's be positive beans! We don't want to mess up stats like the first semester right? Yeah, you're right. It doesn't matter that I will properly wake up at 10am on Mondays!

By the way, that was me talking to myself and trying to be positive. I failed miserably! I am already dreading statistics in the worst way possible. I didn't absorb any stats from the first semester and learnt it parrot fashion. Conditional probability is my nemesis, as it the rest of it. Why must we suffer... why?

Hmmm, I think that is as far as the negativity goes! Today I was ahem... overjoyed when I found that timetable sitting in my inbox. I did a little 'two weeks left' dance, much to the displeasure of others. I'll do it again now, 'only two weeks left doo daa doo day!' It was much less embarrassing this time round as well. The timetable is going to fill up with the example classes and my PASS commitment (and maybe one other hopeful commitment!) I honestly can't wait and have been excited all morning.

We know I'm dreading stats, but what am I looking forward to? Definitely Real Analysis and Algebraic Structures; need I explain why? They're going to be a challenge, but one which I hope to enjoy. I don't know which module I'll find the hardest, but my bet is on Real and Complex Analysis (discounting stats). I haven't given a second thought to PDE's and Vector Calculus, but it's one of them modules that you have to get on with. Actually wait a minute! It says Partial differential equations and I'd been thinking it was partial differentiation (which I can do). Ah well, I will soon find out what it is about. I think that's all of them covered.

A second ago a small panic took over me. This is the normal feeling that I seem to get, before the start of any year and which comes with questions: 'What if I don't understand anything that is taught?' etc. These past insecurities tend to push me at times, but on this occasion my panic brought a startling fact to my attention. I haven't exactly done any maths in the holidays, so how am I supposed to get into the swing of things and be a good PASS person if I have no idea what I'm talking about?

Them thoughts surprisingly calmed me down, which isn't what normally tends to happen. The other day when I was in conversation with an old friend, we discussed what we hadn't done in the holidays. My friend said, ''if you don't plan, then things don't go wrong!" but still I wasn't convinced that I had utilised my holidays properly. However, then my friend said something along the lines that maybe I needed to do nothing; that I had to laze around and recharge my batteries. I think I did work during the year - more than I normally would, since apart from having to I had wanted to. This is some sort of consolation, but I will grab it with both hands!

During the year what tends to happen is that I won't play on the PS3 anymore, and other 'luxuries' like that will become limited. I'll try to watch as much football as possible, but I don't mind not doing them things. I know a healthy balance is important, but during the year when I study maths, I'm not actually studying if that makes any sense. Maths is one of the luxuries that I focus my attention on during the year! Deadlines and exams do stress me out, but I guess that's what people don't understand about me. I enjoy learning maths and before the year has started I'm already scared! (This year is going to count towards my overall degree, so no mucking around in stats you see.) I think enjoying studying and learning maths, makes the whole 'learning and education' experience less stressful and more fun. Damn, I just said the fun word again!

I am also betting that the timetable is going to change, because we don't seem to have any example classes for Algebraic Structures. (Maybe it's meant to be that way since we're going to have three lectures for it). "Only two weeks left, doo daa doo day... !" :D

PS: For the first time in AGES I managed to get through 'microphone head' as he now calls himself, about maths. On Resistance Fall of Man my clan is called 'The Galois Group' *cough*, and microphone head became bemused as I tried inviting someone (mathematical) to my clan. I got excited and spoke too fast, so was told to start again but slowly. I did that and wow, I was even asked which mathematician I found to be the greatest! My favorite has to be Galois but I have a buddy on my buddy list called 'Euler', so he had to have a mention. I even talked about Fermat's last theorem and about Fermat as a cool dude. :D Wow- I did get slightly too excited and stopped playing for a while as well. I think microphone head is having the problem of not being 'pushed' in maths. He's cleverer in maths than I was at that age, but doesn't like it anymore because of his teacher. However, every second that my heart beats, hope still remains. *cue dramatic music* hehe. Damn, I've just spoiled that scene. I actually enjoyed talking to microphone head about maths properly, rather than being called nerd, geek , freak etc etc every other second when I spoke of maths (and when I didn't on occasions). [MH can call me them names since it's a two way thing!]