Date of Award
Spring 2025
Degree Name
Bachelor of Science
Department
Computer Science & Mathematics; College of Arts & Sciences
First Advisor
Weihong Ni
Abstract
This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.
Recommended Citation
Quisito, Joseph J. Jr.; Brown, Gallean; and Yoder, Elijah, "Theory and Applications Surrounding Markov Chains" (2025). Capstone Showcase. 1.
https://scholarworks.arcadia.edu/showcase/2025/comp_sci_math/1
Theory and Applications Surrounding Markov Chains
This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.