Martin Orr's Blog


Posted by Martin Orr on Tuesday, 30 June 2009 at 22:42

I got my BA last week, and suddenly my time in Cambridge is at an end. The best bit of the graduation was when all the graduands process in academical dress (including hoods) from the college to the Senate House where the ceremony takes place. Many people, including all the bedders and no doubt a lot of unsuspecting tourists, came out to watch. I don't know if colleges which are not as central as Trinity have such a procession; and while we got lovely weather, it wouldn't be so fun in the rain (e.g. Magdalene got rained on).

A week before that, the Part II and Part III Maths results were read out in the Senate House (as last year - the results and graduation make the only three times I have been in the building). It is likely that this will be the last year that this is the first place where people hear their results. CUSU has been campaigning for them to be sent out by email before publication, on the grounds that getting your results in public is distressing for people who did badly. This has some truth, but I think that there is a significant advantage in learning your results along with your friends, as they will be in a better position to offer support than if you learned them privately (and maybe were then embarrassed about sharing them). This advantage applies to a much greater extent to the reading out of the Maths results, which everyone really does hear simultaneously, than to publication on the Senate House noticeboards as happens for other subjects.

1 comment Tags cambridge, exams, partiii, tripos

Proof of the Nullstellensatz

Posted by Martin Orr on Friday, 19 June 2009 at 11:49

Hilbert's Nullstellensatz is an algebraic result fundamental to algebraic geometry. There are many different proofs of the Nullstellensatz. In this post I will consider the proof given in this year's Part III Commutative Algebra course, and in particular one section of the proof that seems to contain lots of magic. When I was revising for the exams, I realised that part of the mystery came from the fact that the particular theorem proved in Commutative Algebra does not require an algebraically closed field, unlike the standard statement of Hilbert's Nullstellensatz.

Thanks are due to Lloyd West for starting me thinking about this, and to Jon Nelson for giving me the courage to believe that it might be true and for supplying the proof of Lemma 4.

no comments Tags alg-geom, maths, nullstellensatz, partiii

Part III exams

Posted by Martin Orr on Monday, 08 June 2009 at 13:32

The Part III exams took place in the last couple of weeks. It was quite strange for me to do exams where you are expected to answer all or most of the questions - the undergraduate maths exams have several times more questions to choose from than anyone could possibly do and in olympiad exams completing each question is an achievement.

The most common form of a Part III exam is questions which simply ask you to write out proofs from the course. Three of my five exams took this form, and it's quite boring - except one of those, where the content was very hard so just recalling bits of the lectures is a challenge. Elliptic Curves livened things up a bit with some computation, although that is rather tedious in a different way. And my last exam, in Modular Forms, had a much better balance of bookwork and problems, although it was the hardest exam I did.

no comments Tags exams, partiii, tripos