Archive

A Brief History of ThreeDimensional Manifolds
First published November 24, 2022
We give a broadbrush account of some milestones in the theory of 3dimensional 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 FinitelyGenerated 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 lesserknown 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.
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