#### 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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Geometric Problems

This chapter describes solutions to several problems concerning two-dimensional geometry. Geometry is a branch of mathematics concerned with the characteristics of points, lines, and other figures (shapes), the interaction between such figures, and the transformation of such figures. In this chapter, we'll focus on the characteristics of two-dimensional figures and the interactions between these objects.

There are several problems we must overcome when working with geometric objects in Python. The biggest hurdle is the problem of representation. Most geometric objects occupy a region in the two-dimensional plane, and as such, it is impossible to store every point that lies within the region. Instead, we have to find a more compact way to represent the region that can be stored as a relatively small number of points. For example, we might store a selection of points along the boundary of an object...