February 19, 2008 – 11:20 am
The great arithmetician Kazuya Kato visited twice over the last few weeks, so I thought I’d use the occasion to recommend some writings. An undergraduate level textbook on number theory is Number Theory I: Fermat’s Dream published by the American Mathematical Society. It is short and covers fairly standard material, but contains many unusual insights. [...]
February 11, 2008 – 4:13 pm
Hi sir, I was practicing on the 2006 paper and I was wondering what the “rank” meant for Jordan canonical forms. I’d appreciate your help. Cheers Xiao Reply: Rank is a notion that we use for any linear map, and is defined as the dimension of its image. If the map is given by a [...]
February 11, 2008 – 12:22 pm
A few weeks ago, I gave a colloquium lecture at Leeds university and subsequently wrote up an exposition based on it. It’s still not entirely `popular,’ but may give a somewhat better sense than my previous remarks of at least a few ideas. Let me know if there are some points on which you would [...]
February 8, 2008 – 11:15 am
On the course web page for algebraic number theory, I have now added a (*) next to each item directly relevant to the exams. Make sure you are familiar with the material therein. In particular, there is a new note on some elementary irrationality and a revised practical summary. The problems that have been recently [...]
February 7, 2008 – 11:35 am
dear Professor, I have a few questions regarding jordan canonical form, id be grateful if you could point me in the right direction…..im struggling to understand how you can work out Jordan form from the jordan basis…..e.g. if i have Cha(X)= (x-2)^3 Ma(X)=(x-2)^2 and a Jordan basis of B1={[1,0,3],[2,-3,0]} B2={(1,0,0]} how do i no what [...]
