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References
Sutherland, S., Finding roots of complex polynomials with Newton’s method, Preprint, Institute for Math. Sciences, SUNY, Stony Brook, 1989.
Blum, L., Shub, M. and Smale, S., On a theory of computation and complexity over the real numbers: NP-completeness, Recursive functions and Universal Machines,Bull. Amer. Math. Soc. (New Series). Also abstracted in theIEEE 1988 FOCS 21 (1989), 1–46.
Cook, S. A., The complexity of theorem-proving procedures, Proceedings 3rd ACM STOC, 1989, 151–158.
Karp, R. M.,Reducibility among combinatorial problems, inComplexity of Computer Computations, (R. E. Miller, and J. W. Thatcher, eds.), Plenum, New York, 1972, 85–104.
Garey, M. and Johnson D.,Computers and Intractability, Freeman, San Francisco, 1979.
Shub, M. and Smale, S., Complexity of Bezout’s Theorem I: Geometrical aspects,J. Amer. Math. Soc. 6 (1993), 459–501.
Shub, M. and Smale, S., Complexity of Bezout’s Theorem II: Volumes and probabilities,Computational Algebraic Geometry (F. Eysette & A. Galliger, eds.) Progress in Mathematics, Vol. 109, Birkhäuser Boston, (1993), 267–285.
Shub, M. and Smale, S., Complexity of Bezout’s Theorem III: Condition number and packing,J. Complexity 9, (1993), 4–14.
Kostlan, E., Random polynomials and the statistical fundamental theorem of algebra. Preprint, University of Hawaii, 1987.
Shub, M., Some remarks on Bezout’s Theorem and complexity theory, inFrom Topology to Computation, Proceedings of the Smalefest (M. Hirsch, J. Marsden and M. Shub, eds.)Springer, 1993, 443–455.
Demmel, J., On condition numbers and the distance to the nearest ill-posed problem,Numer. Math.51 (1987), 251–289.
Demmel, J., The probability that a numerical analysis problem is difficult,Math. Comp.50 (1988), 449–480.
Kostlan, E., On the distribution of the roots of random polynomials, inFrom Topology to Computation, Proceedings of the Smalefest, (M. Hirsch, J. Marsden and M. Shub, eds.) Springer, 1993, 419–432.
Kac, M., On the average number of real roots of a random algebraic equation,Bull. Amer. Math. Soc. 49 (1943), 314–320.
Shurkin, J.,Engines of the Mind, W. W. Norton, New York, 1984.
McCulloch, W. S. and Pitts, W., A logical calculus of the ideas imminent in nervous activity,Bull. Math. Biophys.5 (1943), 115–133. Reprinted in McCulloch, W. S.,Embodiments of Mind, MIT Press, 1988.
Goldstine, H. H.,The Computer from Pascal to von Neumann Princeton University Press, Princeton, NJ, 1972.
Hodges, A.,Alan Turing: The Enigma, Simon & Schuster, New York, 1983.
Davis, M., Logic and the Origin of Modern Computers, inThe Universal Turing Machine. A Half Century Survey (Rolf Hecken, eds.), Verlag Kammerer & Unverzagt, Hamburg- Berlin; Oxford University Press, Oxford, 1988.
Shub, M., Book review ofElements of differentiable dynamics and bifurcation theory by David Ruelle,Bull. Amer. Math. Soc. (New Series)24 (1991), 199–211.
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Shub, M. Mysteries of mathematics and computation. The Mathematical Intelligencer 16, 10–15 (1994). https://doi.org/10.1007/BF03026609
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DOI: https://doi.org/10.1007/BF03026609