Archive

• Tips for preparing for an Oxbridge undergraduate maths interview

  First published September 12, 2024
  

  From my experience as an interviewer, some advice for students preparing for an undergraduate admissions interview in maths at Oxford or Cambridge.

• A brief history of three-dimensional manifolds

  First published November 24, 2022
  

  We give a broad-brush account of some milestones in the theory of 3-dimensional manifolds, particularly the Poincaré Conjecture and its proof. We also discuss Thurston’s Geometrisation Programme.

• Measuring angles within arbitrary metric spaces

  First published October 02, 2020
  

  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

  First published July 26, 2020
  

  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

  First published June 21, 2020
  

  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 simple annual budget template for Google sheets

  First published June 06, 2020
  

  A template for an annual budget spreadsheet, which tracks one’s spending on a weekly basis.

• A finitely-generated group that is not finitely presentable

  First published November 06, 2019
  

  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

  First published August 11, 2019
  

  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

  First published June 18, 2019
  

  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)

  First published May 02, 2019
  

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

• Counting derangements

  First published April 21, 2019
  

  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

  First published April 19, 2019
  

  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.