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Mathematics

Quasiregular dynamics

With Alastair Fletcher, I wrote some code for producing images of Mandelbrot and Julia sets for quasiregular mappings.

Quasi-empirical formalism and rationality

Note: I wrote this in May 2003. It's unfinished but still of some interest I think. 


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Countdown numbers game solver

While learning Python, I wrote the program attached below to solve the Countdown numbers game.

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Philosophy of Maths seminar

I've been interested in the philosophy of maths for quite a long time. In the last year of my PhD I started writing a pair of seminars on the subject to be given at the Maths department at the University of Warwick. Unfortunately, writing up my thesis got in the way and I never got round to writing the second part.


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The twisting boundary of the Maskit slice

This is an unfinished paper, based on chapter 5 of my thesis.

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The use of mathematics in computer games

This article for NRICH is an introduction (suitable for ages 14+) at the mathematics used in programming computer games. It covers some aspects of geometry and vectors, 3d graphics, graphs and path finding, and some physics.

Published on NRICH (May 2000)


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Solving Impuzzable

This article for NRICH describes how I used QBASIC to solve a particularly difficult jigsaw puzzle called Impuzzable. Suitable for ages 14 and up.

Published on NRICH (February 2001)

 


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An introduction to complex numbers

This is an article for NRICH. It introduces the topic of complex numbers for mathematically inclined school children of ages 15 or 16 and up, in a way which resembles the way university maths is taught rather than the way school maths is taught, with less emphasis on rote learning and calculation and more emphasis on the intuition, abstraction and creativity required for higher maths. For this reason, it may be more difficult than a school level introduction, but I think that those interested in studying maths at university would benefit from the change in style.


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An introduction to Galois theory

This is an article for NRICH. It introduces the topic of Galois theory at the level of a good 17 or 18 year old school student student. The two primary motivations for studying it that are given are solving equations by radicals and geometric constructibility proofs.

Published on NRICH (February 2002)


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Articles

I have written several articles on mathematics for the website NRICH. The full list is below.

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