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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Finding Optimal Solutions

In this chapter, we'll address various methods for finding the best outcome in a given situation. This is calledoptimizationand usually involves either minimizing or maximizing an objective function. An objective function is a function that takes a number of parameters as arguments and returns a single scalar value that represents the cost or payoff for a given choice of parameters. The problems regarding minimizing and maximizing functions are actually equivalent to one another, so we'll only discuss minimizing object functions in this chapter. Minimizing a function, f(x), is equivalent to maximizing the function -f(x). More details on this will be provided when we discuss the first recipe.

The algorithms available to us for minimizing a given function depend on the nature of the function. For instance, a simple linear function containing one or more variables has different algorithms...