Preface

Python is a powerful and flexible programming language that is fun and easy to learn. It is the programming language of choice for many professionals, hobbyists, and scientists. The power of Python comes from its large ecosystem of packages and a friendly community, and its ability to communicate seamlessly with compiled extension modules. This means that Python is ideal for solving problems of all kinds, especially mathematical problems.

Mathematics is usually associated with calculations and equations but, in reality, these are very small parts of a much larger subject. At its core, mathematics is about solving problems, and the logically structured approach to solutions. Once you explore past the equations, calculations, derivatives, and integrals, you discover a vast world of beautiful, elegant structures.

This book is an introduction to solving mathematical problems using Python. It introduces some of the basic concepts of mathematics and how to use Python to work with these concepts. It also introduces some basic templates for solving a variety of mathematical problems across a large number of topics within mathematics. The first few chapters focus on core skills such as working with NumPy arrays, plotting, calculus, and probability. These topics are very important throughout mathematics and act as a foundation for the rest of the book. In the remaining chapters, we discuss more practical problems, covering topics such as data analysis and statistics, networks, regression and forecasting, optimization, and game theory. We hope that this book provides a basis for solving mathematical problems and the tools for you to further explore the world of mathematics.

Who this book is for

This book is primarily aimed at people who have some experience with Python and have projects (for work or just for fun) that involve solving some kind of mathematical problem. In the first few chapters we aim to give a small taste of the mathematical background for those who are not familiar with the basics, but we are rather limited by space. I’ve provided some suggestions for further reading at the end of each chapter to point you to resources where you can learn more. I hope that this book gets you started on your mathematical problems, and sparks your curiosity to learn more about the mathematics behind these subjects.

What this book covers

Chapter 1, An Introduction to Basic Packages, Functions, and Concepts, introduces some of the basic tools and concepts that will be needed in the rest of the book, including the main Python packages for mathematical programming, NumPy and SciPy.

Chapter 2, Mathematical Plotting with Matplotlib, covers the basics of plotting with Matplotlib, which is useful when solving almost all mathematical problems.

Chapter 3, Calculus and Differential Equations, introduces topics from calculus such as differentiation and integration, and some more advanced topics such as ordinary and partial differential equations.

Chapter 4, Working with Randomness and Probability, introduces the fundamentals of randomness and probability, and how to use Python to explore these ideas.

Chapter 5, Working with Trees and Networks, covers working with trees and networks (graphs) in Python using the NetworkX package.

Chapter 6, Working with Data and Statistics, gives various techniques for handling, manipulating, and analyzing data using Python.

Chapter 7, Using Regression and Forecasting, describes various techniques for modeling data and predicting future values using the Statsmodels package and scikit-learn.

Chapter 8, Geometric Problems, demonstrates various techniques for working with geometric objects in Python using the Shapely package.

Chapter 9, Finding Optimal solutions, introduces optimization and game theory, which uses mathematical methods to find the best solutions to problems.

Chapter 10, Increasing your Productivity, covers an assortment of situations you might encounter while solving mathematical problems using Python.

To get the most out of this book

You will need to have a basic knowledge of Python. We don’t assume any knowledge of mathematics, although if you are familiar with some basic mathematical concepts, you will better understand the context and details of the techniques we discuss.

The only requirement throughout this book is a recent version of Python – at least Python 3.6, but higher versions are preferable. (The code for this edition has been tested on Python 3.10, but should work on earlier versions too.) You might prefer to use the Anaconda distribution of Python, which comes with many of the packages and tools required in this book. If this is the case, you should use the conda package manager to install the packages. Python is supported on all major operating systems – Windows, macOS, and Linux – and on many platforms.

The packages that are used in this book and their versions at the time of writing: NumPy 1.23.3, SciPy 1.9.1 Matplotlib 3.6.0, Jax 0.3.13 (and jaxlib 0.3.10), Diffrax 0.1.2, PyMC 4.2.2, pandas 1.4.3 Bokeh 2.4.3, NetworkX 3.5.3, Scikit-learn 1.1.2, StatsModels 0.13.2, Shapely 1.8.4, NashPy 0.0.35, Pint 0.20.1, Uncertainties 3.1.7, Xarray 2022.11.0, NetCDF4 1.6.1, Geopandas 0.12.1, CartoPy 0.21.0, Cerberus 1.3.4, Cython 0.29.32, Dask 2022.10.2.

Software/hardware covered in the book	Operating system requirements
Python 3.10	Windows, macOS, or Linux

If you are using the digital version of this book, we advise you to type the code yourself or access the code from the book’s GitHub repository (a link is available in the next section). Doing so will help you avoid any potential errors related to the copying and pasting of code.

You may prefer to work through the code samples in this book in a Jupyter notebook rather than in a simple Python file. There are one or two places in this book where you might need to repeat plotting commands, as plots cannot be updated in later cells in the way that is shown here.

Download the example code files

You can download the example code files for this book from GitHub at https://github.com/PacktPublishing/Applying-Math-with-Python-2nd-Edition. If there’s an update to the code, it will be updated in the GitHub repository.

We also have other code bundles from our rich catalog of books and videos available at https://github.com/PacktPublishing/. Check them out!

Download the color images

We also provide a PDF file that has color images of the screenshots and diagrams used in this book. You can download it here: http://packt.link/OxkXD.

Conventions used

There are a number of text conventions used throughout this book.

Code in text: Indicates code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input, and Twitter handles. Here is an example: “The Decimal package also provides the Context object, which allows for fine-grained control over the precision, display, and attributes of Decimal objects.”

A block of code is set as follows:

from decimal import getcontext
ctx = getcontext()
num = Decimal('1.1')
num**4  # Decimal('1.4641')
ctx.prec=4  # set the new precision
num**4  # Decimal('1.464')

When we wish to draw your attention to a particular part of a code block, the relevant lines or items are set in bold:

from numpy import linalg
A = np.array([[3, -2, 1], [1, 1, -2], [-3, -2, 1]])
b = np.array([7, -4, 1])

Any command-line input or output is written as follows:

$ python3.10 -m pip install numpy scipy

Bold: Indicates a new term, an important word, or words that you see onscreen. For instance, words in menus or dialog boxes appear in bold. Here is an example: “Select System info from the Administration panel.”

Tips or important notes

Appear like this.

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