Monte Carlo theory and practice

The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The author tries to lay a theoretical basis for both the 'traditional' Monte Carlo and quasi-Monte Carlo methods, and, to present some practical aspects of when and how to use them. An important theme is the comparison of Monte Carlo, quasi-Monte Carlo and numerical quadrature for the integration of functions, especially in many dimensions.