Algebra is a branch of mathematics, which studies the general solutions and properties of numbers, quantities, relationships, structures and algebraic equations (groups). Elementary algebra is generally taught in middle schools, introducing the basic ideas of algebra: studying what happens when we add or multiply numbers, understanding the concept of variables and how to establish polynomials and find their roots. The research object of algebra is not only numbers, but various abstract structures.

Definition of function: Given a number set A, let the element in it be X, and now apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B. Assuming that the element in B is Y, the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function includes three elements: definition field A, value field C and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

Second, the inclusion relationship is different:

Algebra contains functions, and functions are only a small part of algebra.

Extended data:

The origin of algebra can be traced back to the Babylonian era, when people developed a more advanced arithmetic system, which enabled them to calculate by algebraic methods. Through the use of this system, they can list equations with unknowns and solve them. Nowadays these problems are generally solved by linear equations, quadratic equations and indefinite linear equations.

In contrast, most Egyptians in this period and most Indian, Greek and China mathematicians in the 1 century BC generally used geometric methods to answer such questions, such as those described in Rand's mathematical cursive book Rope Sutra, Geometry Elements and Nine Chapters of Arithmetic.

Greece's work in geometry, taking geometry as a classic, provides a framework and generalizes the formulas for solving specific problems into a more general system for describing and solving algebraic equations.

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