## Continuity

I finally finished Analysis Block A today, and oddly enough I’m a bit sad to see it go. Unit AA4: Continuity was a lot more fun that I expected, and I particularly enjoyed the section about the Intermediate Value Theorem. The bit in the DVD programme about antipodal points blew my mind – I was convinced that it was impossible to prove that you can always find two antipodal points on the Earth’s equator that have the same temperature, right up until they explained why it must be true. I even made Alex come over and watch that section, it impressed me that much! (The similar examples involving balancing a table on bumpy ground, and equally distributing sugar on pancakes, were lots of fun too.)

TMA04 is wrapped up now, and I’m proud to say that this will be my first ever LaTex-produced assignment! Well, I should say Lyx-produced, because no matter how much I tried to get to grips with LaTex editors like TeXnicCenter, I just couldn’t get the hang of it, so I ended up resorting to a more WYSIWYG-style program instead.

I really enjoyed using Lyx to type up this assignment, so I reckon I’ll be sticking with this approach in future (though I wouldn’t rule out going back to TeXnicCenter or a similar editor – perhaps when I’ve gotten thoroughly used to Lyx itself). And I’d definitely recommend Lyx for anyone who’s interested in moving away from word-processing assignments; I think Lyx has just enough WYSIWYG elements to make it a relatively easy program to learn to use.

So now, at last, I can finally get on with Group Theory Block B – it’s been a long time, so let’s hope I haven’t forgotten everything from Block A!

Unit AA3 was much more satisfying, and in a way it felt like AA2 was really just an introduction to the ideas we needed for AA3. For me, working with limits feels a lot more rewarding when it’s part of an attempt to prove that an infinite series converges/diverges. And the behaviour of infinite series is quite an interesting topic in itself – especially counter-intuitive results like the fact that $\sum_{n=0}^{\infty } 1/n^2$ is convergent but $\sum_{n=0}^{\infty } 1/n$ is divergent. I really do love results that make me go “but.. but how??” like that.