Depending on whether one is a student or a professional mathematician, the word can mean either of the following (both of which are further described elsewhere in this chapter). School algebra is what mathematicians refer to as the algebra we learn in middle and high school and call “arithmetic.” But for most of people, algebra means solving polynomial equations with one or more variables; the solutions to such equations are often obtained by the operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. (For more information about all these operations, see “Math Basics.”). This also includes determining the properties of functions and graphs.

But mathematicians use the word “algebra” most often in reference to the abstract study of number systems and operations within them, such as groups, rings, and invariant theory. This is called abstract algebra.