The Turing Guide

NOTES TO PAGES 380–408 | 523

18. A. Nakamasu, G. Takahashi, A. Kanbe, and S. Kondo, ‘Interactions between zebrafish pigment cells
    responsible for the generation of Turing patterns’, Proceedings of the National Academy of Sciences of
    the United States of America, 106 (2009), 8429–34.


19. T. E. Woolley, R. E. Baker, E. A. Gaffney, and P. K. Maini, ‘Stochastic reaction and diffusion on growing
    domains: Understanding the breakdown of robust pattern formation’, Physical Review E, 84 (2011),
    046216.


20. G. E. P. Box and N. R. Draper, Empirical Model-building and Response Surfaces, Wiley (1987).


21. Turing (1952).

CHAPTER 35 RADIOlARIA: VAlIDATING THE TURING THEORy (RICHARDS)

1. D. W. Thompson, On Growth and Form, Cambridge University Press (1917) (expanded 2nd. edn
   published 1942).


2. Turing (1952).


3. B. Richards, ‘The morphogenesis of Radiolaria’, MSc Thesis, University of Manchester (1954).


4. P. T. Saunders, Morphogenesis, North-Holland (1992).

CHAPTER 36 INTRODUCING TURING’S mATHEmATICS (wHITTy AND wIlSON)

1. J. L. Britton (ed.), The Collected Works of A. M. Turing: Pure Mathematics, North-Holland (1992).


2. I. J. Good, ‘Studies in the history of probability and statistics, XXXVII: A. M. Turing’s statistical work
   in World War II’, Biometrika, 66(2) (1979), 393–6.


3. A. M. Turing, ‘On the Gaussian error function’, King’s College Fellowship Dissertation (1935).


4. S. L. Zabell, ‘Alan Turing and the central limit theorem’, American Mathematical Monthly, (June–July
   1995), 483–94.


5. W. Burnside, The Theory of Groups of Finite Order, 2nd edn, Cambridge University Press (1911).


6. Britton (Note 1).


7. P. S. Novikov, ‘On the algorithmic unsolvability of the word problem in group theory’, Tr u dy
   Matematicheskogo Instituta imeni V. A. Steklova, 44, Academy of Sciences of the USSR (1955), 3–143.


8. J. Stillwell, ‘The word problem and the isomorphism problem for groups’, Bulletin of the American
   Mathematical Society, 6(1) (1982), 33–56.


9. Britton (Note 1).


10. A. E. Ingham, The Distribution of Prime Numbers, Cambridge Mathematical Tracts 30, Cambridge
    University Press (1932).


11. D. Zagier, ‘The first 50 million prime numbers’, Mathematical Intelligencer, (1997), 221–4.


12. B. Riemann, ‘Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse’ [On the number of
    primes less than a given magnitude], Monatsberichte der Berliner Akademie, (November 1859), 671–80.


13. E. C. Titchmarsh, ‘The zeros of the Riemann zeta-function’, Proceedings of the Royal Society of London.
    Series A, Mathematical and Physical Sciences, 157 (1936), 261–3.


14. Turing (1943).


15. Turing (1953a).


16. A. R. Booker, ‘Turing and the Riemann hypothesis’, Notices of the American Mathematical Society,
    53(10) (2006), 1208–11.


17. D. A. Hejhal and A. M. Odlyzko, ‘Alan Turing and the Riemann zeta function’, in S. B. Cooper and
    J. van Leeuwen (eds), Alan Turing—His Work and Impact, Elsevier (2013), 265–79.

CHAPTER 37 DECIDABIlITy AND THE ENTSCHEIDUNGSPROBlEm (wHITTy)

1. Turing (1936).


2. J. J. Gray, The Hilbert Challenge, Oxford University Press (2000).


3. P. Smith, An Introduction to Gödel’s Theorems, Cambridge University Press (2007).