Ökten G. Probability and Simulation

Springer, 2020. — 157 p. — (Springer Undergraduate Texts in Mathematics and Technology). — ISBN: 3030560694.This undergraduate textbook presents an inquiry-based learning course in stochastic models and computing designed to serve as a first course in probability. Its modular structure complements a traditional lecture format, introducing new topics chapter by chapter with accompanying projects for group collaboration. The text addresses probability axioms leading to Bayes’ theorem, discrete and continuous random variables, Markov chains, and Brownian motion, as well as applications including randomized algorithms, randomized surveys, Benford’s law, and Monte Carlo methods. Adopting a unique application-driven approach to better study probability in action, the book emphasizes data, simulation, and games to strengthen reader insight and intuition while proving theorems. Additionally, the text incorporates codes and exercises in the Julia programming language to further promote a hands-on focus in modelling. Students should have prior knowledge of single variable calculus.Note from the Preface:The book uses the Julia programming language (version 1.1.0). The Julia software is free on a license from MIT. The simplicity of Julia allows incorporating the computer code within the main narrative, without a significant distraction to the main flow of the narrative. A tutorial on Julia can be found in Chapter 1 of "First Semester in Numerical Analysis with Julia", an open-access textbook I wrote on numerical analysis, published by Florida State University Libraries. For readers who might prefer the Python programming language, a companion book "Probability and Simulation: A Python Companion" cowritten with Yaning Liu is available on the Springer web page for the book. The companion book has the Python translations of the Julia codes presented here.True PDF