Articles in Refereed Journals

  1. Z-stability in constructive analysis. Logical Methods in Computer Science, 12(3:10)2016:1-13. (With D.S. Bridges & J. Dent.)
  2. Constructive connections between anti-Specker, positivity, and fan-theoretic properties. New Zealand Journal of Mathematics 44:21--33. (With D.S. Bridges & J. Dent.)
  3. Uniformly convex Banach spaces are reflexive - constructively. Mathematical Logic Quarterly 59(4-5):352-356. (With D.S. Bridges & H. Ishihara.)
  4. Solving the Dirichlet Problem Constructively. Journal of Logic & Analysis 5(3):1-22. (With D.S. Bridges.)
  5. 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.)
  6. Two direct proofs that $\mathrm{LLPO}$ implies the detachable fan theorem. Logic Journal of the IGPL March 2013. (With D.S. Bridges.)
  7. Real Analysis in Paraconsistent Logic. Journal of Philosophical Logic 41(5):901--922. (With Z. Weber.)
  8. 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.)

Book Chapters

  1. This is not a carrot: Paraconsistent mathematics. In S. Parc (Ed.), 50 Visions of Mathematics, Oxford University Press, ISBN: 978-0-19-870181-1.
  2. 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)
  3. Constructive Mathematics. In B. Dowden and J. Fiesen (eds.), The Internet Encyclopedia of Philosophy, ISSN 2161-0002. Originally published: 7 December 2012.

Theses & Dissertations

  1. Minimising Weighted Mean Distortion. Ph.D., Massey University. Supervisor: Gaven J. Martin.
  2. Minimising $L^p$ Distortion for Mappings Between Annuli. M.Sc., Massey University. Supervisor: Gaven J. Martin.
  3. A constructive approach to continuity in uniform and apartness spaces. Honours dissertation, University of Canterbury. Supervisor: Douglas S. Bridges.

Other Publications

  1. Invited review of Feng Ye, Strict Finitism and the Logic of Mathematical Applications. In Philosophy in Review 34(5):278--281.
  2. This is not a carrot: Paraconsistent mathematics. +Plus Magazine. First published in August 2011.
  3. 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 Unpublished manuscript, University of Canterbury, 2006.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