Here's a paper I've written showing why mathematical economics should be built around the mathematics of the digital computer, building on Prof K.V. Velupillai's work in actually showing economists how to do this. Comments are most welcome.

Abstract: Algoritmic economics helps us stipulate, formulate, and resolve economic problems in a more precise manner than mainstream mathematical economics. It does so by aligning theorising about an economic problem with both the data generated by the real world and the computers used to manipulate that data. Theoretically coherent, numerically meaningful, and therefore policy relevant, answers to economic problems can be extrapolated more readily using algorithmic economics than present day mathematical economics. An algorithmic economics would allow mathematical economics to prove theorems relating to \emph{economic} problems, such as the existence of equilibria defined on some metric space, with embedded mechanisms for getting to the equilibria of these problems. A blueprint for such an economics is given and discussed with an example.

Right Click this link to download the paper.