Wednesday, October 03, 2007

Which Springer GTM would you be?

I finally found my result from when I first took this test, and I got the same again. Does it matter that I am only an undergraduate? Maybe it would help if I knew what manifold theory and Lie Groups are! That being said, I do like the word 'Lie Groups' - unless someone is going to tell me that it is not pronounced 'lie'. Does anyone find me extremely useful...

...I thought not. ;)

If I were a Springer-Verlag Graduate Text in Mathematics, I would be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups.

I give a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. I include differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provide a proof of the de Rham theorem via sheaf cohomology theory, and develop the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find me extremely useful.

Which Springer GTM would you be? The Springer GTM Test

I have resisted the temptation to do a long and troublesome post, namely because I have become overwhelmed with work at the moment. I am simply not doing all of my work, but only doing the parts that I like (if that makes sense). But a quick summary: Bella told me to NOT talk about maths after a long day today. It seems that unknowingly, I do talk 'a lot' about maths in conversations (not restricted to my course). I do talk about football, driving and other things, but depending on present company, I can't not talk about maths...

I was told that I make a big 'hoo haa' about my lectures, because I really do love going to them and enjoy doing so. Even if the lecture was on some obtuse subject like... English(?) I would still enjoy it and try to listen. I told a few people about this today, and most people were shocked. They didn't exactly enjoy lectures (in the way I do) and just copied things down. I have to bear in mind that 300ish students are being lectured - not just me. It also seems that many of the first year students who 'chilled out' are really putting their heads down this year, 'This year actually counts towards something'. I did wonder why our first year was worth zilch. Is that what it is like in other universities too?

I had a good discussion with Fizz and Bella about a group *cough*, and I got slightly depressed about this for a while. Thankfully we ended with some positive thoughts as Fizz and Bella volunteered themselves, which was encouraging to see. (Tweenies are cool). Whenever I think about this I see it all beautifully falling into place in my head. That is my mistake in life, for with every situation I always see this image in my head. I need to exercise control over my eagerness, for images in my head cannot easily be transferred into real things. (Sadly). Not knowing what to do is something which is also contributing to this restlessness.

Real anlysis is really hard, but fun in a challenging way. I feel as if this is going to be a tactical match - I have to rely on the inspirational players to take their chances, and get me through! I slightly understand the definitions, but the proofs are mind boggling. I need to organise myself properly - I can't fall behind already. I think I am also going to struggle in Vector Calculus too, because the lectures are just not registering. I spotted one of the sums that I wrote on 'My Maths Wall', and internally got excited. Sad I know. But what was even more sad was that we were left to check that it was the case ourselves. (Amongst five other things too! I have checked a few, but with trouble).

I now have more than 50 maths books, thanks to getting about 2o odd free. (My PT is awesome!) I report about them now, because I have only just shelved them. There are some classics included one by Horace Lamb! [Most are really old; but as my PT said, 'of course maths is never out of date, just out of fashion.'] The pain was well worth it, and my shelf is slowly looking less naive I hope. (My book shelf post will not be updated for a while yet). Please don't throw away any old maths books you have!

And this was meant to be a summary. Now you know why people tend to run in the other direction when they see me. (However that being said, I do ask people to tell me if they are busy and have to go. And is not all times that I talk to people - unless you classify smiling as communicating?) I think the problem is that I don't want to read the Complex Analysis story before the lectures. Humbug.

PS: Thanks to Craig for the reminder about this post.


steve said...

That being said, I do like the word 'Lie Groups' - unless someone is going to tell me that it is not pronounced 'lie'.

Lie groups are named after the Norwegian mathematician Sophus Lie and I'm afraid his name is pronounced as in the word lea.

You are very unlikely to meet Lie Groups until you are on a graduate course.
You may have already come across (or soon will) abelian groups named after the most famous Norwegian mathematican Abel. If you carry on studying group theory then you will meet another compatriot of theirs Sylow (pronounced seeloff).

Anonymous said...

pronounced as "lee" and not lie as in
"I lied to you"

beans said...

Hi Steve,

I knew it was too good to be true! Imagine telling a non-mathematician that I study 'lie' groups.

Yes, I came across Abel at the end of my first semester last year, and somehow I rememeber that the abelian group is written with a lowercase a!

So I have Sylow('s groups) to look forward too, and probably not Lie groups. Thanks for the heads up.

Thanks to the anonymous commenter too.

Craig said...

There is a course on Lie algebras at Manchester, for fourth year students.

The course will provide basic knowledge of finite-dimensional Lie algebras for those students interested in Lie groups and representation theory.


So if you're on a four year course, maybe you'll encounter them eventually...

beans said...

Hi Craig,

Thanks for the link - there are quite a few interesting courses on offer their too! I probably won't be doing four years, but I think there are some modules which I can do in my third year. (I will keep a look out for them).