Based on numerous courses held at the Universities of Erlangen, Jena, Madgeburg, and Darmstadt we develop an introductory textbook on Monte Carlo Algorithms (in German). We aim at readers with a basic knowledge in probability and numerical analysis, which is typically provided in second year university courses on these topics.
First we study direct simulation, i.e., the classical Monte Carlo algorithm, as well as simulation of distributions and variance reduction techniques together with applications in, e.g., particle physics, computational finance, and insurance risk modeling. In a second part, we investigate Markov chain Monte Carlo methods and high-dimensional numerical integration. For the latter problem we also address the issue of optimal randomized or deterministic algorithms within the framework of information-based complexity. A third part is devoted to random numbers, covering the practical issue of random number generation as well as the question of how to define randomness of sequences of bits or real numbers.
Several optional parts of the text provide outlooks to related but mathematically more advanced topics like quasi Monte Carlo methods, Monte Carlo methods for integral equations, approximation of stochastic differential equations, and quantum computing.

T. Müller-Gronbach (Universität Passau), E. Novak (Universität Jena), K. Ritter

Please contact one of the authors if you would like to receive a copy of a preliminary version.

Springer-Verlag, to appear 2009.