About the book
In applied mathematics, the name Monte Carlo is given to the method of solving problems by means of experiments with random numbers. This name, after the casino at Monaco, was first applied around 1944 to the method of solving deterministic problems by reformulating them in terms of a problem with random elements which could then be solved by large-scale sampling. But, by extension, the term has come to mean any simulation that uses random numbers.
The development and proliferation of computers have led to the widespread use of Monte Carlo methods in virtually all branches of science, ranging from nuclear physics (where computer-aided Monte Carlo was first applied) to astrophysics, biology, engineering, medicine, operations research, and the social sciences.
The Monte Carlo Method of solving problems by using random numbers in a computer – either by direct stimulation of physical or statistical problems or by reformulating deterministic problems in terms of one incorporating randomness – has become one of the most important tools of applied mathematics and computer science. A significant proportion of articles in technical journals in such fields as physics, chemistry, and statistics contain articles reporting results of Monte Carlo simulations or suggestions on how they might be applied. Some journals are devoted almost entirely to Monte Carlo problems in their fields. Studies in the formation of the universe or of stars and their planetary systems use Monte Carlo techniques. Studies in genetics, the biochemistry of DNA, and the random configuration and knotting of biological molecules are studied by Monte Carlo methods. In number theory, Monte Carlo methods play an important role in determining primality or factoring of very large integers far beyond the range of deterministic methods. Several important new statistical techniques such as “bootstrapping” and “jackknifing” are based on Monte Carlo methods.
Hence, the role of Monte Carlo methods and simulation in all of the sciences has increased in importance during the past several years. These methods play a central role in the rapidly developing subdisciplines of the computational physical sciences, the computational life sciences, and the other computational sciences. Therefore, the growing power of computers and the evolving simulation methodology have led to the recognition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Additionally, at the kernel of Monte Carlo simulation is random number generation.
Finally, the aims of the current book are to discuss the Monte Carlo methods and techniques applied in mathematics in particular and in various and diverse scientific problems in general.