Probability and Simulation

ISBN-13: 9783030560690 / Angielski / Miękka / 2020 / 152 str.

Opis

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.

Giray Ökten received his PhD from Claremont Graduate University. He has held academic positions at University of Alaska Fairbanks, Ball State University, and Florida State University. He received a Fulbright U.S. Scholar award in 2015. He is the author of an open access textbook in numerical analysis, First Semester in Numerical Analysis with Julia, published by Florida State University Libraries, and a co-author of a children’s math book, The Mathematical Investigations of Dr. O and Arya, published by Tumblehome. His research interests include Monte Carlo methods and computational finance.

 

Spis treści

Probability.- Discrete Random Variables.- Continuous Random Variables.- Markov Chains.- Brownian Motion.- Benford's Law.- Data for Project 12.- Partial Solutions to Projects.- References.

O autorze

Giray Ökten received his PhD in 1997 from Claremont Graduate University. He has held academic positions at Ball State University and Florida State University. He received a Fulbright US Scholar award in 2015, and a graduate faculty mentor award from Florida State University in 2019. He is the author of an open access textbook in numerical analysis, First Semester in Numerical Analysis with Julia, and a co-author of a children's math book under contract with Tumblehome. He has published over 40 research papers mostly in the field of Monte Carlo methods and computational finance. He has advised or co-advised fourteen PhD students.

Blurb

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.

Giray Ökten received his PhD from Claremont Graduate University. He has held academic positions at University of Alaska Fairbanks, Ball State University, and Florida State University. He received a Fulbright U.S. Scholar award in 2015. His research interests include Monte Carlo methods and computational finance.