algebra

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time.

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Algebra is a part of mathematics (frequently just called math or maths). It is used to find values and variables that make equations and inequalities true. It often needs knowledge of the rules of numbers and mathematics operations used on numbers (adding, subtracting, multiplying, dividing, and other operations). Algebra uses letters (a,b,c,...) and other symbols to represent numbers. The letters and symbols in algebra are called variables. We use variables because the numbers are unknown or can change.Algebra was first used to solve equations. Two examples are linear equations and quadratic equations.The ways developed to solve equations frequently made use of the facts of the parts of an equation. For example, how to factorize polynomials, or how to use a matrix to solve many linear equations at once. Abstract algebra is the study of things that are found in equations. For example, polynomials and matrices. These things are known as algebraic structures. Understanding the properties of more complex algebraic structures can help us solve more complex equations.Of particular importance to the study of algebra is the study of functions, since functions often appear in equations that we are trying to solve. A function is like a box you can put a number or numbers into and get a certain number out. When a function takes one variable in, like f(x), it is called a univariate function. When a function takes many variables in, like Q(x,y,z), it is called a multivariate function.In some math problems one variable is changed. The variable that is changed is called the "independent" variable. After the variable is changed the math operations in the equation are performed to make a number. The number that is made is called the "dependent" variable. Most of the time the independent variable is written as x and the dependent variable is written as y, for example, in y = 3x + 1. This is because we do not know what number they are until we are told.