# Archive

• ## Measuring Angles within Arbitrary Metric Spaces

We will generalise the concept of angles in Euclidean space to any arbitrary metric space, via Alexandrov (upper) angles.

• ## Hilbert's Hotel, but the Guests are Mere Mortals

We will consider a variation of Hilbert’s hotel, within which guests may not be relocated too far from their current room.

• ## My Oxford Postgrad Interview: Applying for the MFoCS MSc

Here I will summarise my experiences in applying for the Oxford MFoCS, including some tips on how I made my application as competitive as possible.

• ## A Powerful and Minimalist Annual Budget Template for Google Sheets

I am making publically available a template of my own annual budget spreadsheet, which tracks one’s spending on a weekly basis.

• ## A Finitely-Generated Group that is not Finitely Presentable

In this post we will work towards an example of a finitely generated group that cannot be expressed by any finite presentation.

• ## Quantum Search for the Everyday Linear Algebraist

I present a brief introduction to quantum computation, and particularly Grover’s search algorithm, written for the average linear algebraist.

• ## Modular Machines and their equivalence to Turing Machines

Modular machines are a lesser-known class of automata, which act upon $$\mathbb{N}^2$$ and are actually capable of simulating any Turing Machine - a fact which we will prove here.

• ## An Upper Bound on Ramsey Numbers (Revision Season)

I will present a short argument on an upper bound for $$r(s)$$, the Ramsey Number associated with the natural number $$s$$.

• ## Counting Derangements

I present an inefficient yet novel way of recursively counting derangements of a set, and generalise this to counting permutations without short cycles.

• ## Building this website

To kick off this blog I figured it would be fitting to write about the creation of this website, and talk about the process as well as some of the design choices I made.