Mathematics and Chess

John MacQuarrie

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References (show)

  1. Aumann, R.J. (1989) Lectures on Game Theory. Boulder, Westview Press.
  2. Ball, W.W.R. (1939) Mathematical Recreations & Essays, Eleventh Edition, Revised by H.S.M. Coxeter. London, Macmillan and Co.
  3. Binmore, K. (1992) Fun and Games: A Text on Game Theory. Lexington, Mass., D.C. Heath.
  4. Cull, P. and De Curtins, J. (1978) Knight's tour revisited. Fibonacci Quarterly, 16(3), 276-286.
  5. Dimand, M.A. and Dimand, R.W. (1996) A History of Game Theory, Volume 1: From the Beginnings to 1945. London, Routledge. Quoted in Schwalbe and Walker (1997), 124
  6. Eales, R. (1985) Chess: The History of a Game. London, B.T. Batsford.
  7. FIDE (2001) Laws of Chess. [Accessed 12/12/04].
  8. König, D. (1927) Über Eine Schlussweise aus dem Endlichen ins Unendliche. Acta Scientiarum Mathematicarum (Szeged) 3, 121-130. Quoted in Schwalbe and Walker (1997), 128
  9. Kuhn, H (2004) Introduction. In: von Neumann, J. and Morgenstern, O. (2004) Theory of Games and Economic Behaviour (Commemorative Edition). Princeton, Princeton University Press.
  10. Löbbing, M. and Wegener, I. (1996) The Number of Knight's Tours Equals 33,439,123,484,294-Counting with Binary Decision Diagrams. The Electronic Journal of Combinatorics 3(5), [Accessed 8/12/04].
  11. Morse, M. and Hedlund, G.A. (1944) Unending Chess, Symbolic Dynamics and a Problem in Semigroups. Duke Mathematical Journal, 11, 1-7.
  12. Murray, H.J.R. (1913) A History of Chess. Oxford, Clarendon Press.
  13. Reider, N. (1959) Chess, Oedipus, and the Mater Dolorosa. International Journal of Psychoanalysis, 40, 320-333. Reprinted in Avedon, E.M. and Sutton-Smith, B. (1971) The Study of Games. New York, John Wiley & Sons.
  14. Roth, A. (n.d.) The Problem of the Knight: A Fast and Simple Algorithm. Quoted in: Weisstein, nd [Accessed 5/12/04].
  15. Schnoebelen, P. (n.d.) The Retrograde Analysis Corner: A Collection of Coloring Problems. [Accessed 2/12/04].
  16. Schwalbe, U. and Walker, P. (1997) Zermelo and the Early History of Game Theory. Games and Economic Behaviour 34, 123-137.
  17. Schwenk, A. J. (1991). Which rectangular chessboards have a knight's tour? Mathematics Magazine, 64(5) (December), 325-332.
  18. Wegener, I. (2000) Branching Programs and Binary Decision Diagrams. Philadelphia, Society for Industrial and Applied Mathematics (SIAM). Quoted in: Weisstein, n.d. [Accessed 5/12/04].
  19. Weisstein, E.W. (nd) Knight's Tour. From MathWorld--A Wolfram Web Resource. [Accessed 5/12/04].
  20. White, A.C. (1911) First Steps in the Classification of Two-Movers. Leeds, Whitehead and Miller.
  21. Zermelo, E. (1913) On an Application of Set Theory to the Theory of the Game of Chess, Translated in Schwalbe and Walker (1997), 133-136.