This post is aimed at secondary-school students pitched roughly at the level of the British Mathematical Olympiad. It is ostensibly about a certain class of number theory problems, but the main underlying mathematical principle is broader than this. The post ..read more

The first round of the British Mathematical Olympiad was marked in early December. Belatedly, here are some thoughts of the problems. These aren’t supposed to be official solutions, and some of them are not in fact solutions at all. Students ..read more

The first round of the British Mathematical Olympiad was sat yesterday. The paper can be found here, and video solutions here. Copyright for the questions is held by BMOS. They are reproduced here with permission. I hope any students who ..read more

I’m currently lecturing the course Fundamentals of Probability at KCL, where we cover some of the measure theory required to set up probability with a higher level of formality than students have seen in their introductory courses. By this point ..read more

The second and final round of this year’s British Mathematical Olympiad took place on Thursday. Here are some thoughts on the problems. I wasn’t involved in choosing the problems, although I did write Q4. I’ll say a bit more about ..read more

The first round of the British Mathematical Olympiad was sat on Thursday by roughly 2000 pupils in the UK, and a significant number overseas on Friday. For obvious reasons, much of the past 18 months has been dominated by logistical ..read more

For a Galton-Watson tree, can one obtain upper bounds in probability on the height of the tree, uniformly across all offspring distributions with mean $latex \mu ..read more

[Ho63] addresses the alternative model where the increments of a random walk are chosen uniformly without replacement from a particular set. The potted summary is that the sum of random increments chosen without replacement has the same mean, but is more concentrated that the corresponding sum of random increments chosen with replacement. This means that any of the concentration results proved in the earlier sections of [Ho63] for the latter situation apply equally to the setting without replacement ..read more

Last week, we held our annual IMO training and selection camp in the lovely surroundings of Trinity College, Cambridge. Four of our students have subsequently spent this week in Kiev, for the ninth edition of the prestigious European Girls’ Mathematical ..read more

I am aiming to write a short post about each lecture in my ongoing course on Random Graphs. Details and logistics for the course can be found here. Preliminary – positive correlation, Harris inequality I wrote about independence, association, and the ..read more