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

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.

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