Maths stuff

This is a collection of some maths stuff I've done:

UK University integration bee

This was a team competition I've run since 2020 and in person since 2021. From 2021 to 2024, Round 2 of the competition took place in Cambridge but for 2025 onwards, it will be in Oxford. Information about it along with many resources to learn about definite integration can be found on the website.
The competition started online in Summer 2020 on Discord, the invite to the server is here which still remains active with problems posted and an online edition of the integration bee usually taking place in December after Round 1 has taken place in person. This is to honour the original integral bee which was virtual due to COVID but also as there are students keen to take part not at participating universities. The format was teams of up to three try to solve as many of the problems as possible in two hours. I decided to do it like this as I don't like really fast paced maths - you can lose in a matter of seconds due to mistakes! Also, I think there's a really rich array of techniques used to solve definite integrals which are fun.

Over the summer after my first year I did a project on Legendre Polynomials with Dr. Joao Rodrigues. It didn't involve any original research but an exposition on their properties, giving me a chance to explore what research is like by independently exploring a new topic. This involved both their mathematical properties and applying them to physics problems such as the quantum mechanical model of the hydrogen atom.
My Part III Essay on the Skolem Problemm an unsolved problem concerning the decidability of whether linear recurrence contains a zero or not. I covered Hansel's proof of the Skolem Mahler Lech theorem and special cases of LRS where the Skolem Problem is decidable. Lastly, I covered modern results in two directions: the first concerning the relations with the Skolem Conjecture and the p-adic Schanuel conjecture and the second concerning universal Skolem sets - sets where the Skolem problem is decidable.
Here are some talks I've given on the Gamma function, divergent series and the Riemann zeta function as an undergraduate.
I've made some handouts as part of outreach activities with Cambridge University and the maths department, on integration without A level techniques, basic analytic number theory and Fibonacci numbers, along with exercises.
I wrote an article on the Frobenius coin problem for Eureka, the mathematical magazine for the Archimedeans.