Turns out I’m rather busy this (academic) year which probably explains my lack of posts so far. So to break the silence let’s review the courses I took last term.

Elementary Number Theory

The title of this course is misleading in two ways. Elementary certainly doesn’t mean easy, it supposedly refers to number theory using only elementary methods and let’s face it this is sometimes harder than using more advanced techniques. This incidentally is the other misleading aspect of its title. There’s a great deal of group theory and bits and pieces about rings and fields to be found in the course. Nonetheless this was actually my easiest course last term (simultaneously I know people who called this their hardest course). Overall I enjoyed this course. The lecturer was fairly entertaining and the material covered is pretty neat too.

Metric and Topological Spaces

Of all the courses I took last term this course has the best set of lecture notes. You can easily read through them and most of the course makes perfect sense. Furthermore most proofs are rather short and appear straightforward. On the other hand this course had quite likely some of the hardest exercises. There were a few questions on the problem sheets (assessed ones) that took me several hours to figure out. I don’t know if this is a general characteristic of analysis courses or whether I simply have more of a knack for algebraic courses, but I really have the impression that if you really understand everything in the lecture notes then questions in algebra are often really straightforward whereas questions in analysis can still take ages. Nonetheless, I thought this was a pretty good course, much better than expected (especially considering that the same lecturer gave the worst lecture of my second year when substituting for another lecturer).

Group Theory

This was a much anticipated course as we finally covered things such as conjugation which I had already seen in my first year project. The lecture notes were slightly disorganised, but overall I’m satisfied with the course. Though I still have to get the hang of semi-direct products.

Measure and Integration

This was by far the hardest course I took, not just last term but in my entire academic career. I still don’t fully get all the material in the course, but while revising over the holidays I started to understand a great deal of the material. Now I still have several exercise sheets to go over and see whether this new found understanding can be applied to the exercises.

Hopefully I’ll be able to find some time this term to ensure that I don’t forget everything that was covered in the last term. After all it’s always better to polish material over Easter rather than having to relearn everything. Though I already know that I’ll have to do a lot of work for Galois Theory this term as the lectures were pretty awful so far. Then again I’ve had so many ridiculously bad lecturers over the last few years that I got really good at teaching myself the relevant material.