Articles

2007

Programs from Proofs via the Curry-Howard Correspondence

Given a (polymorphic) type, we can automatically find a function having that type, if one exists.

A Theorem Prover for Intuitionistic Propositional Logic

2006

Sums of Squares and Additive Number Theory

A maths investigation for the kids leads to some nice code for looking at additive number theory.

Symmetric Polynomials and the Characters of Sn

The easy way to work out the character table of Sn, using combinatorics of symmetric polynomials.

The Outer Automorphism of S6

The number 6 has a property shared by no other natural number.

Polya Counting, part 2

How many non-isomorphic graphs are there on n vertices?

Polya Counting

How many ways are there to colour the faces of a dodecahedron with three colours, up to rotation? Questions of this type can be answered using Polya counting - which looks like magic the first time you see it.

Dirichlet Series

Series of the form a1/1z + a2/2z + ... + an/nz + ... have deep connections to number theory.

Umbral Calculus

Why do some sequences of polynomials, such as the Bernoulli polynomials, appear to obey analogues of the binomial theorem?

p-adic Numbers

Can 1/7 be expressed as a whole number?