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== 1940s ==
* Monte Carlo simulation (voted one of the top 10 [[algorithm]]s of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.<ref>{{cite journal|last=Metropolis|first=N.|title=The Beginning of the Monte Carlo method|journal=Los Alamos Science|year=1987|volume=No. 15, Page 125|url=http://library.lanl.gov/cgi-bin/getfile?15-12.pdf}}. Accessed 5 may 2012.</ref><ref>S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). [http://library.lanl.gov/cgi-bin/getfile?00329286.pdf Statistical methods in neutron diffusion]. Los Alamos Scientific Laboratory report LAMS–551.</ref><ref>N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335–341.</ref>
* Dantzig introduces the [[simplex method|simplex
* First [[Computational Fluid Dynamics|hydro simulations]] at Los Alamos occurred.<ref>Richtmyer, R. D. (1948). Proposed Numerical Method for Calculation of Shocks. Los Alamos, NM: Los Alamos Scientific Laboratory LA-671.</ref><ref>A Method for the Numerical Calculation of Hydrodynamic Shocks.
Von Neumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, pp. 232–237</ref>
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* Molecular dynamics invented by Alder and Wainwright<ref>Alder, B. J.; T. E. Wainwright (1959). "Studies in Molecular Dynamics. I. General Method". J. Chem. Phys. 31 (2): 459. Bibcode 1959JChPh..31..459A. doi:10.1063/1.1730376</ref>
* [[John G.F. Francis]]<ref>
J. G. F. Francis, "The QR Transformation, I", ''The Computer Journal'', vol. 4, no. 3, pages 265–271 (1961, received Oct 1959) [http://comjnl.oxfordjournals.org/cgi/content/abstract/4/3/265 online at oxfordjournals.org];<br />
J. G. F. Francis, "The QR Transformation, II" ''The Computer Journal'', vol. 4, no. 4, pages 332–345 (1962) [http://comjnl.oxfordjournals.org/cgi/content/abstract/4/4/332 online at oxfordjournals.org].<br /></ref> and [[Vera Kublanovskaya]]<ref>Vera N. Kublanovskaya (1961), "On some algorithms for the solution of the complete eigenvalue problem," USSR Computational Mathematics and Mathematical Physics, 1(3), pages 637–657 (1963, received Feb 1961). Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).</ref> invent [[QR factorization]] (voted one of the top 10 algorithms of the 20th century).
== 1960s ==
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== 1970s ==
*Computer algebra replicates and extends the work of Delaunay in lunar theory.<ref>http://www.umiacs.umd.edu/~helalfy/pub/mscthesis01.pdf {{Bare URL PDF|date=March 2022}}</ref>
* Mandelbrot, from studies of the [[Fatou set|Fatou]], [[Julia set|Julia]] and [[Mandelbrot set]]s, coined and popularized the term 'fractal' to describe these structures' [[self-similarity]].<ref>B. Mandelbrot; ''Les objets fractals, forme, hasard et dimension '' (in French). Publisher: Flammarion (1975), {{ISBN|9782082106474}}; English translation ''Fractals: Form, Chance and Dimension.'' Publisher: Freeman, W. H & Company. (1977). {{ISBN|9780716704737}}.</ref><ref>Mandelbrot, Benoît B.; (1983). The Fractal Geometry of Nature. San Francisco: W.H. Freeman. {{ISBN|0-7167-1186-9}}.</ref>
*Kenneth Appel and Wolfgang Haken prove the [[four colour theorem]], the [[Computer-assisted proof#Theorems proved with the help of computer programs|first theorem to be proved by computer]].<ref>Kenneth Appel and Wolfgang Haken, "Every planar map is four colorable, Part I: Discharging," Illinois Journal of Mathematics 21: 429–490, 1977.</ref><ref>Appel, K. and Haken, W. "Every Planar Map is Four-Colorable, II: Reducibility." Illinois J. Math. 21, 491–567, 1977.
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