Nicholas J. Peatfield- Doctor of Philosophy
- Senior Lecturer at Bath Spa University
Nicholas J. Peatfield
- Doctor of Philosophy
- Senior Lecturer at Bath Spa University
About
12
Publications
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Introduction
I am interested in encouraging mathematical resilience, including a growth mindset around mathematics, and how teaching in secondary schools, and the changing UK mathematics curriculum, might support this.
I am also interested in how an enactivist standpoint might effect mathematics teaching in schools.
I use largely qualitative methods to investigate these issues, including interviews, surveys with open questions, and direct action research methods, as well as more theoretical investigations.
Current institution
Publications
Publications (12)
E-Article on the BSRLM Website (from Masters Thesis)
We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined
in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups
defined in o-minimal expansions of the ordered set of real numbers.
We prove the existence of a Čech cohomology theory in arbitrary o-minimal structures with definable Skolem functions satisfying
the Eilenberg–Steenrod axioms.
Here we prove the existence of sheaf cohomology theory in arbi- trary o-minimal structures.
Here we prove the proper base change theorem and the projec- tion formula for sheaf cohomology theory in o-minimal expansions of groups. As a consequence of this we prove in this setting the Kunneth formula. These results when applied to denable groups give a uni- form bound on the size of the torsion subgroups. We also prove these results in arbit...
Here we prove the existence of sheaf cohomology theory with sup- ports in arbitrary o-minimal structures.
Here we prove an analogue of the Hurewicz theorem for denable groups in an arbitrary o-minimal context, and as an application prove a conjecture of Berarducci on the cohomology of denable groups and Lie groups.
We show that any model of the theory of a generic function with deriv- atives from (Zil02b) is an analytic Zariski structure, as described in (PZ05), and that this abstract topological structure is compatible with a genuine analytic structure.
Here we prove the analogue of the Hurewicz theorem for definable groups in an arbitrary o-minimal context.
We use o-minimal topological methods to prove very good reduction results for denable covering homomorphisms in arbitrary o-minimal structures.
BLDSC reference no.: D225263. Supervisor: Prof. Boris Zilber. Thesis (D. Phil.)--University of Oxford, 2003. Includes bibliographical references.
