Archive
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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 \(s\).
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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.
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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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maths
combinatorics
recursion
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web-design
turing-machines
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spreadsheets
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ramsey-theory
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modular-machines
linear-algebra
jekyll
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