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Algebra is the branch of mathematics that studies algebraic operations [a] and algebraic structures. [2] An algebraic structure is a non-empty set of mathematical objects, such as the real numbers, together with algebraic operations defined on that set, such as addition and multiplication. [3] Algebra explores the laws, general characteristics ...
Two-dimensional plot (red curve) of the algebraic equation . Elementary algebra, also known as college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, [2] whilst algebra introduces variables (quantities without fixed values). [3]
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space ...
Algebraic expression. In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations ( addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number ). [1] For example, 3x2 − 2xy + c is an algebraic expression.
In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots ( fractional power). [1] These operations may be performed on numbers, in which case they are often called arithmetic operations.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
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