Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore 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.
Table of Contents (13 chapters)

Minimizing a simple linear function

The most basic type of problem we face in optimization is finding the parameters where a function takes its minimum value. Usually, this problem is constrained by some bounds on the possible values of the parameters, which increases the complexity of the problem. Obviously, the complexity of this problem increases further if the function that we are minimizing is also complex. For this reason, we must first consider linear functions, which are in the following form:

To solve this kind of problem, we need to convert the constraints into a form that can be used by a computer. In this case, we usually convert them into a linear algebra problem (matrices and vectors). Once this is done, we can use the tools from the linear algebra packages in NumPy and SciPy to find the parameters we seek. Fortunately, since this kind of problem occur quite frequently, SciPy has routines that handle this conversion and subsequent solving.

In this recipe, we...