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.

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