Paul Taylor - Foundations of Mathematics and Computation

photo of Paul Taylor
www. Paul Taylor. EU
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Conferences and Seminars
Links to Related Work
About these Web pages
 

I am sorry for the continued lack of mathematical activity here, even though I am now an Honorary Research Fellow in Achim Jung's Theory Group in the Computer Science Department at the University of Birmingham.

Both of my parents became ill in 2010: my Dad had Lewy Body Dementia and died in February 2012 and my Mum had Alzhemeimer's and died in January 2013. After their house was sold I bought one in Birmingham and then spent much too long renovating my house in London, which now has tenants.

During that period there was the National Suicide Vote in Britain, on 23 June 2016, and I have since spent my time campaigning against that, in particular with EU in Brum locally and my own website IStopBrexit.info from which you can find your local grass roots campaign group.

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.