Introduction

While mathematics can be pided into multiple subfields, such as calculus, number theory, and geometry, there are certain fundamental concepts that every mathematics student must be familiar with. Two of these concepts are functions and algebra, which are the main topics of this chapter.

A function is a general mathematical process that describes a certain mapping from one object to another. A function can take in one number and produce another number. It can also take in an array or vector of numbers and return a single output, or even multiple outputs. Functions are so important that they are also widely used in other scientific fields, including physics, economics, and, as we have seen throughout this book, programming.

Our goal in this chapter is to establish a concrete foundational discussion on the concept of functions in a mathematical context. This discussion will be coupled with other related topics, such as the domain, the range, and the plot of a function. A solid understanding of these topics will allow you to explore more complex mathematical analyses in later chapters.

In addition to functions, we will also consider algebra, one of the most important parts of mathematics. While the term generally denotes the analysis and manipulation of mathematical objects in the broadest sense, we will consider it in the context of algebraic equations and systems of equations. This will allow us to study its important role in mathematics while learning how to apply that knowledge to practical problems.