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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Accounting for uncertainty in calculations

Most measuring devices are not 100% accurate and instead are accurate up to a certain amount, usually somewhere between 0 and 10%. For instance, a thermometer might be accurate to 1%, while a pair of digital calipers might be accurate up to 0.1%. The true value in both of these cases is unlikely to be exactly the reported value, although it will be fairly close. Keeping track of the uncertainty in a value is difficult, especially when you have multiple different uncertainties combined in different ways. Rather than keeping track of this by hand, it is much better to use a consistent library to do this for you. This is what the uncertainties package does.

In this recipe, we will learn how to quantify the uncertainty of variables and see how these uncertainties propagate through a calculation.