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... .]


Anonymous said...

i have missed out in a lot od maths work and find it very difficult to understand how to do it as it has all changed scince i have moved to high school now iam moving into 3rd year i still cant do it . can anyone help or give me advice ???

Beans said...

3rd year of what?

Have you tried hiring a tutor? You could also hit the library and get a good book to work through. There are also online forums, some of which are quite good in helping out when stuck.