#### 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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# How it works...

The schema that we created is a technical description of all the criteria that we need to check against our data. This will usually be defined as a dictionary with the name of the item as the key and a dictionary of properties, such as the type or bounds on the value in a dictionary, as the value. For example, in step 1, we defined a schema for floating-point numbers that limits the numbers so that they're between the values of -1 and 1. Note that we include the coerce key, which specifies the type that the value should be converted into during the validation. This allows us to pass in data that's been loaded from a CSV document, which contains only strings, without having to worry about its type.

The Validator object takes care of parsing documents so that they're validated and checking the data they contain against all the criteria described by the schema. In this recipe, we provided the schema to the Validator object when it was created...