#### 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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# Selecting items at random

At the core of probability and randomness is the idea of selecting an item from some kind of collection. As we know, the probability of selecting an item from a collection quantifies the likelihood of that item being selected. Randomness describes the selection of items from a collection according to the probabilities without any additional bias. The opposite of a random selection might be described as a deterministic selection. In general, it is very difficult to replicate a purely random process using a computer, because computers and their processing are inherently deterministic. However, we can generate sequences of pseudo-random numbers that, when properly constructed, demonstrate a reasonable approximation of randomness.

In this recipe, we will select items from a collection and learn some of the key terminology associated with probability and randomness that we will need throughout this chapter.