I will make the argument that the disciplines of math and statistics have captured mainstream interest because of the growing availability of data, and we need math, statistics, and machine learning to make sense of it. Yes, we do have scientific tools, machine learning, and other automations that call to us like sirens. We blindly trust these “black boxes,” devices, and softwares; we do not understand them but we use them anyway.

While it is easy to believe computers are smarter than we are (and this idea is frequently marketed), the reality cannot be more the opposite. This disconnect can be precarious on so many levels. Do you really want an algorithm or AI performing criminal sentencing or driving a vehicle, but nobody including the developer can explain why it came to a specific decision? Explainability is the next frontier of statistical computing and AI. This can begin only when we open up the black box and uncover the math.

You may also ask how can a developer not know how their own algorithm works? We will talk about that in the second half of the book when we discuss machine learning techniques and emphasize why we need to understand the math behind the black boxes we build.

To another point, the reason data is being collected on a massive scale is largely due to connected devices and their presence in our everyday lives. We no longer solely use the internet on a desktop or laptop computer. We now take it with us in our smartphones, cars, and household devices. This has subtly enabled a transition over the past two decades. Data has now evolved from an operational tool to something that is collected and analyzed for less-defined objectives. A smartwatch is constantly collecting data on our heart rate, breathing, walking distance, and other markers. Then it uploads that data to a cloud to be analyzed alongside other users. Our driving habits are being collected by computerized cars and being used by manufacturers to collect data and enable self-driving vehicles. Even “smart toothbrushes” are finding their way into drugstores, which track brushing habits and store that data in a cloud. Whether smart toothbrush data is useful and essential is another discussion!

All of this data collection is permeating every corner of our lives. It can be overwhelming, and a whole book can be written on privacy concerns and ethics. But this availability of data also creates opportunities to leverage math and statistics in new ways and create more exposure outside academic environments. We can learn more about the human experience, improve product design and application, and optimize commercial strategies. If you understand the ideas presented in this book, you will be able to unlock the value held in our data-hoarding infrastructure. This does not imply that data and statistical tools are a silver bullet to solve all the world’s problems, but they have given us new tools that we can use. Sometimes it is just as valuable to recognize certain data projects as rabbit holes and realize efforts are better spent elsewhere.

This growing availability of data has made way for data science and machine learning to become in-demand professions. We define essential math as an exposure to probability, linear algebra, statistics, and machine learning. If you are seeking a career in data science, machine learning, or engineering, these topics are necessary. I will throw in just enough college math, calculus, and statistics necessary to better understand what goes in the black box libraries you will encounter.

With this book, I aim to expose readers to different mathematical, statistical, and machine learning areas that will be applicable to real-world problems. The first four chapters cover foundational math concepts including practical calculus, probability, linear algebra, and statistics. The last three chapters will segue into machine learning. The ultimate purpose of teaching machine learning is to integrate everything we learn and demonstrate practical insights in using machine learning and statistical libraries beyond a black box understanding.

The only tool needed to follow examples is a Windows/Mac/Linux computer and a Python 3 environment of your choice. The primary Python libraries we will need are numpy, scipy, sympy, and sklearn. This book will not make you an expert or give you PhD knowledge. I do my best to avoid mathematical expressions full of Greek symbols and instead strive to use plain English in its place. But what this book will do is make you more comfortable talking about math and statistics, giving you essential knowledge to navigate these areas successfully. I believe the widest path to success is not having deep, specialized knowledge in one topic, but instead having exposure and practical knowledge across several topics. That is the goal of this book, and you will learn just enough to be dangerous and ask those once-elusive critical questions.