Chapter I describes concepts such as systems, models, and the ideas of Monte Carlo and simulation. A discussion of these concepts seems necessary as there is no uniform terminology in the literature. Instead of giving rigid definitions, I try to make clear what I mean when I use these terms. In addition to the terminology, some examples and ideas of simulation and Monte Carlo methods are given. Chapter 2 deals with several alternative methods for generating random and pseudorandom numbers on a computer, as well as several statistical methods for testing the "randomness" of pseudorandom numbers. Chapter 3 describes methods for generating random variables and random vectors from different probability distributions. Chapter 4 provides a basic treatment of Monte Carlo integration, and Chapter 5 provides a solution of linear, integral, and differential equations by Monte Carlo methods. It is shown that, in order to find a solution by Monte Carlo methods, we must choose a proper distribution and present the problem in terms of its expected value. Then, taking a sample from this distribution, we can estimate the expected value. In addition, variance reduction techniques (importance sampling, control variates, stratified sampling antithetic variates, etc.) are discussed. Chapter 6 deals with simulating regenerative processes and in particular with estimating some output parameters of the steady-state distribution associated with these processes. Simulation results for several practical problems are presented, and variance reduction techniques are given as well. Chapter 7 discusses random search methods, which are also related to Monte Carlo methods. In this chapter I describe how random search methods can be successfully applied for solving complex optimization problems.
