Tag: topology

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.

Latest Posts

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.

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maths combinatorics recursion metric-geometry web-design turing-machines topology spreadsheets revision ramsey-theory ramsey-numbers quantum-computation modular-machines linear-algebra jekyll group-theory formula finances education design derangements computability automata algorithm-theory algebra admissions