Computer simulation and related Monte Carlo methods are widely used in engineering and scientific work. Simulation provides a powerful tool for the analysis of real-world systems when the system is not amenable to traditional analytical approaches. This course is intended to introduce upper-level undergraduates and early-to-mid-level graduate students to fundamental tools in designing, conducting, and interpreting Monte Carlo studies. As an applied math course, the emphasis is on generic principles and algorithms that are widely applicable in simulation, as opposed to detailed discussion of specific applications and/or software packages. At the completion of this course, it is expected that students will have the insight and understanding to critically evaluate or use many state-of-the-art methods in simulation. Topics covered include random number generation, simulation of Brownian motion and stochastic differential equations, output analysis for Monte Carlo simulations, variance reduction, Markov chain Monte Carlo, simulation-based estimation for dynamical (state-space) models, and, time permitting, sensitivity analysis and simulation-based optimization.
• Review and discuss some of the most important principles and algorithms for simulation and Monte Carlo methods.
• Develop a rigorous basis for understanding and analyzing relevant algorithms in a stochastic sense.
• Recognize key limitations and assumptions associated with popular methods in simulation and Monte Carlo.
• Become aware of some of the important literature in simulation and Monte Carlo.
• Provide the background to implement the algorithms and/or critically evaluate the implementations of others in a wide variety of practical problems.
• Recognize that most significant real-world simulation problems will require additional application-specific knowledge not covered in this course (important!).