Paul Taylor - Foundations of Mathematics and Computation

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May 2013: I am sorry for the lack of activity here over the past three years. I am now getting back to work after the death of my parents; my mother had Alzheimer's Disease and my father had Lewy Body Dementia.

Abstract Stone Duality is a revolutionary direct axiomatisation of general topology and constructive real analysis that is inherently computable. May 2013: A new draft paper that gives A Concise Presentation for Locally Compact Spaces.

Practical Foundations of Mathematics relates category theory and type theory to the idioms of mathematics (Cambridge University Press, 1999, ISBN 0-521-63107-6).

Induction, recursion, replacement and the ordinals are studied categorically using well founded coalgebras.

Introduction to Algorithms and Reasonned Programming: a first year computer science course.

Commutative diagrams, proof trees and boxes and other TeX macros. My right-justified end-of-proof square is the only one that works.

Classical (Scott) and stable domain theory, also called analytic or polynomial functors, shapes, containers, or multiadjoints.

Proofs and Types by Jean-Yves Girard, which I translated, is out of print but downloadable.

Gauss's second proof of the fundamental theorem of algebra, which I translated from Latin.

Undergraduate algebra and other course notes that I wrote when I was a graduate student.