I found myself a bit underwhelmed by Unit AA2, to be honest. It was interesting, and I really enjoyed the part of the associated DVD program about approximating pi by taking exterior and interior polygons around a circle, but overall the unit didn’t quite grab me in the same way as the chapter in MS221 about sequences.

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.

Still, even though AA3 was more enjoyable than AA2, I think the Analysis Block A has been a bit of a let-down compared to the first half of the course. I’m quite looking forward to unit AA4, as it’s about continuity, and I’m quite eager to find out how on earth continuity can be formally defined (since the only definition I’ve ever come across is the informal “you can draw the graph without picking your pen up” one), but my main aim at the moment is to make it through Analysis Block A so that I can enjoy the sweet, sweet goodness of Group Theory Block B. There are only three units of it, but I’m going to savour every page!