Paul Taylor - Foundations of Mathematics and Computation

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I am sorry for the lack of activity here over the past four 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. July 2014: New draft papers about Local Compactness and Bases in various formulations of Topology and Overt Subspaces of Rn.

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.