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Monte Carlo methods are algorithms for solving various kinds of computational problems by using random numbers (or more often pseudo-random numbers), as opposed to deterministic algorithms. Monte Carlo methods are extremely important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms. These methods have proven efficient in solving the integro-differential equations defining the radiance field, and thus these methods have been used in global illumination computations which produce photo-realistic images of virtual 3d models, with applications in video games, architecture, design, computer generated films and special effects in cinema, and other fields.Interestingly, the Monte Carlo method does not require truly random numbers to be useful. Much of the most useful techniques use deterministic, pseudo-random sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense. That is that they must either be uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered.
Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computertower of a personal computer. A computer is a device for making calculations or controlling operations that are expressible in numerical or logical terms. While factually accurate, this definition and those found in other dictionaries are so broad that th, utilizing many techniques of computer simulationA computer simulation or a computer model is a computer program which attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of modeling many natural systems in physics, chemistry and biology, human s.
A Monte Carlo algorithm is a numerical Monte Carlo method used to find solutions to mathematical problems (which may have many variables) that cannot easily be solved, for example, by integral calculus, or other numerical methods. Its efficiency relative to other numerical methods increases when the dimensionAbstract algebra Algebra Linear algebra Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space. In common usage, the dimensions of an object are the measurements that define its shape and s of the problem increases.
1 History
Monte Carlo methods were originally practiced under more generic names such as "statistical sampling". The " Monte CarloMonte Carlo is a very wealthy section of the city-state of Monaco known for its gambling, beaches, casino, glamour, and sightings of famous people. Monte Carlo is home to most of the Circuit de Monaco, on which takes place the Formula One Monaco Grand Pri" designation, popularized by early pioneers in the field (including Stanislaw Marcin UlamStanislaw Marcin Ulam ( April 13, 1909- May 13, 1984) was a Polish- American mathematician who helped develop the key theory behind the hydrogen bomb. Biography Ulam was born in Lwow, Poland (then also called Lemberg and part of Galicja, an autonomous pro, Enrico FermiEnrico Fermi ( September 29, 1901 29 November 1954) was an Italian- American physicist most noted for his work on beta decay, the development of the first nuclear reactor and for the development of quantum theory. Fermi won the 1938 Nobel Prize in Physics, John von NeumannA separate article covers Saint John Neumann, the American priest. John von Neumann (Neumann Janos) ( December 28, 1903 February 8, 1957) was a Hungarian- American mathematician who made important contributions in quantum physics, set theory, computer sci and Nicholas Metropolis), is a reference to the famous casino in that area, under the belief that Monte Carlo lends its name to this method because of the use of randomness and the repetitive nature employed to find an approximation to the solution. Stanislaw Marcin Ulam tells in his autobiography "Adventures of a Mathematician" that the method was named in honor of his uncle, who was a gambler at the mentioned casino.
Random methods of computation have their roots in the pre-electronic computing era. Perhaps the most famous early use was by Fermi in 1930, when he used a random method to calculate the properties of the newly-discovered neutron (see also Buffon's needle). Monte Carlo methods were central to the simulations required for the Manhattan Project. (An alternate explanation of the Monte Carlo name is that the Manhattan Project team met in Monte Carlo to create their methods.) However, it was only after electronic computers were first built (from 1945 on) that Monte Carlo methods began to be studied in depth.
