#### Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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Working with Randomness and Probability

In this chapter, we will discuss randomness and probability. We will start by briefly exploring the fundamentals of probability by selecting elements from a set of data. Then, we will learn how to generate (pseudo) random numbers using Python and NumPy, and how to generate samples according to a specific probability distribution. We will conclude the chapter by looking at a number of advanced topics covering random processes and Bayesian techniques, and using Markov chain Monte Carlo methods to estimate parameters on a simple model.

Probability is a quantification of the likelihood of a specific event occurring. We use probabilities intuitively all of the time, although sometimes the formal theory can be quite counterintuitive. Probability theory aims to describe the behavior of random variables, whose value is not known, but where the probabilities of the value of this random variable...