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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Transition Matrix and Markov Chains

Now, we will be looking at one of the applications of matrices, which is a field of study all by itself. Markov chains make use of transition matrices, probability, and limits to solve real-world problems. The real world is rarely as perfect as the mathematical models we create to solve them. A car may want to travel from point A to B, but distance and speed prove insufficient parameters in reality. A cat crossing the street may completely alter all the calculations that were made to calculate the time traveled by the car. A stock market may seem to be following a predictable pattern for a few days, but overnight, an event occurs that completely crashes it. That event may be some global event, a political statement, or the release of company reports. Of course, our development in mathematical and computational models has still not reached the place where we can predict the outcome of each of these events, but we can try and determine the probability...