Hell week has begun. A final burst of nerdism before the exams. Possibly my last exam; but probably not. 4 modules, and I've set aside 4 days this week, one day for each module. Decided to blog a bit each day, to really bore you peeps with a series of completely nerd posts.
Mathematicians solve problems, if there are no problems, we'll create one
I guess this module really epitomizes that statement. Shaun, if you think integration at secondary school level is fun, well, like I said, you are just scratching the surface.
I guess the name of this module is a little deceiving, it's not completely about integration as some people think, but its more on the Theory of Lebesgue Measure and it's applications to integration, differentiation and the Banach Space, Lp.
It's an interesting module, not as dry as some other analysis modules I've taken. But it's super crazy man... understanding the proofs take a monster effort. But I guess the approach Lebesgue took to integration is a very interesting one, and the Lebesgue integral is certainly a lot more powerful than the standard Riemann Integral. Unfortuantely, it's notoriously difficult to define. And there is a more powerful integral available now, the Henstock Integral. Maybe I should try do an honours project on it. Sounds like fun!!!
I guess, the approach I took to studying this module was a little flawed in the first few weeks of studying it, I thought it was a "soft-analysis" module, so I could avoid the tedious epsilon-delta type proofs and look for nice elegant proofs. I am so wrong.
The whole module is about convergence and approximation theorems. And once that comes into play, well, say hello to epsilon, delta, and sometimes even eta.
Looking at life, maybe there is a parallel. We always try take short cuts don't we? Instead of taking the long tedious way, we look for the path of least resistance. Sometimes it works, but sometimes, we end up backtracking and having take an even longer route.
Convergence to God. Wrote about that once. Life should like a convergent series, converging to God. Initially, hardly anyone starts out being or wanting to be close to God. Time is like n as it tends to infinity, as time goes on, our life, our patterns should follow that of Christ. Convergence.
