- Presents an inquiry-based learning approach
- Aims to teach probability through games, data, and simulations
- Integrates the Julia programming language in-text to write codes for simulation and data analysis
- Includes significant projects at the end of each section for student collaboration and further study
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- About this Textbook
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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.
- About the authors
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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.
- Table of contents (5 chapters)
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Probability
Pages 1-20
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Discrete Random Variables
Pages 21-46
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Continuous Random Variables
Pages 47-80
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Markov Chains
Pages 81-98
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Brownian Motion
Pages 99-113
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Probability and Simulation
- Authors
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- Giray Ökten
- Series Title
- Springer Undergraduate Texts in Mathematics and Technology
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-56070-6
- DOI
- 10.1007/978-3-030-56070-6
- Softcover ISBN
- 978-3-030-56069-0
- Series ISSN
- 1867-5506
- Edition Number
- 1
- Number of Pages
- X, 152
- Number of Illustrations
- 11 b/w illustrations, 39 illustrations in colour
- Topics
