## Projects

- Non-classical foundations of analysis (funded by the Royal Society of New Zealand)
- Correctness by Construction (funded by RSNZ counterpart funding to the European Commission FP7 IRSES framework)
- Mathematical Maturity: How can it inform teaching and learning of mathematics? (Funded by Ako Aotearoa and the University of Canterbury)

## Publications

### Articles in Refereed Journals

- Z-stability in constructive analysis.
*Logical Methods in Computer Science*, 12(3:10)2016:1-13. (With D.S. Bridges & J. Dent.)

(arxiv) - Constructive connections between anti-Specker, positivity, and fan-theoretic properties.
*New Zealand Journal of Mathematics*44:21--33. (With D.S. Bridges & J. Dent.)

(Journal) - Uniformly convex Banach spaces are reflexive - constructively.
*Mathematical Logic Quarterly*59(4-5):352-356. (With D.S. Bridges & H. Ishihara.)

(DOI) - Solving the Dirichlet Problem Constructively.
*Journal of Logic & Analysis*5(3):1-22. (With D.S. Bridges.)

(DOI) - Setting Water Quality Objectives for the Health of Freshwater Fish.
*ANZIAM Journal*53:M62-M103. (With J.M. Dunn, J. Rong, B. Henderson, R. Goudey & R.S. Anderssen.)

(DOI) - Two direct proofs that $\mathrm{LLPO}$ implies the detachable fan theorem.
*Logic Journal of the IGPL*March 2013. (With D.S. Bridges.)

(DOI) - Real Analysis in Paraconsistent Logic.
*Journal of Philosophical Logic*41(5):901--922. (With Z. Weber.)

(DOI) - Deformations with smallest weighted $L^p$ average distortion and Nitsche type phenomena.
*Journal of the London Mathematical Society*85(2):282--300. (With G. Martin.)

(DOI)

### Book Chapters

- This is not a carrot: Paraconsistent mathematics. In S. Parc (Ed.),
*50 Visions of Mathematics*, Oxford University Press, ISBN: 978-0-19-870181-1.

(OUP) - New approaches to modeling elastic media. In Y. Mastai (Ed.),
*Materials Science - Advanced Topics*, InTech Publishers. ISBN 980-953-307-918-4. (With G. Martin & J. Hussan)

(DOI) - Constructive Mathematics. In B. Dowden and J. Fiesen (eds.),
The Internet Encyclopedia of Philosophy , ISSN 2161-0002. Originally published: 7 December 2012.

(webpage)

### Theses & Dissertations

*Minimising Weighted Mean Distortion*. Ph.D., Massey University. Supervisor: Gaven J. Martin.

(PDF)*Minimising $L^p$ Distortion for Mappings Between Annuli*. M.Sc., Massey University. Supervisor: Gaven J. Martin.

(PDF)*A constructive approach to continuity in uniform and apartness spaces*. Honours dissertation, University of Canterbury. Supervisor: Douglas S. Bridges.

(PDF)

### Other Publications

- Invited review of Feng Ye,
*Strict Finitism and the Logic of Mathematical Applications*. In*Philosophy in Review*34(5):278--281.

(Journal) - This is not a carrot: Paraconsistent mathematics.
*+Plus*Magazine. First published in August 2011.

(Magazine) - Towards a constructive Vitali covering theorem. Unpublished manuscript, University of Canterbury, 2006. (With D. Bridges; not intended for publication)

(PDF preprint)

### In Progress / Under Review

- Theorem and counterexample in non-classical theories.
- Paraconsistent notions of convergence.
- Classifying material implications over minimal logic. (with H. Diener) (arXiv preprint)
- A paraconsistent type theory. (with P. Lumsdaine and H. Gylterud)
- Paraconsistent Measurement of the Circle. (with Z. Weber)
- Normalizing Naive Set Theory. (with E. Istre)
- Basing holomorphy on power series in constructive analysis. (with D.S. Bridges & J. Dent)