Explores realistic applications from a variety of disciplines, including biological, chemical, physical, engineering, and financial examples Presents a completely new treatment of modeling with stochastic differential equations, and expanded coverage of Brownian motion and martingale processes New applications of Markov chains to the simulation of chemical reactions via the Gillespie algorithm and to Bayesian inference via the Metropolis-Hastings algorithm Provides extensive end-of-section exercises sets with answers, as well as numerical illustrations Each chapter concludes with a section focusing on computational examples, code, and exercises that will empower students to explore concepts in a practical way Offers online support, sample code and solutions to coding problems for instructors, and electronic access to sample Python code for students.