Algebraic notation

Algebraic notation uses letters, numbers, and operation symbols to express quantities, relationships, and procedures. Its conventions make mathematical expressions compact and reusable.

Variable (mathematics): A symbol representing a quantity that may vary or whose value is unknown. Letters such as x stand for quantities within algebraic expressions.
Function notation: A notation, commonly f(x), that names a function and indicates its input. It makes input-output relationships concise within algebraic expressions.
Diophantus: An ancient Greek mathematician known for influential work on algebra and equations. His syncopated algebra used abbreviations between rhetorical and fully symbolic writing.
Rhetorical algebra: A form of algebra that expresses problems and solutions entirely in ordinary words. It states mathematical procedures verbally rather than through compact symbols.
Algebra: A branch of mathematics that studies operations, structures, equations, and relationships among quantities. Symbolic notation made algebraic methods easier to state and generalize.
Mathematical constant: A quantity with a fixed value, often represented by a numeral or a named symbol. Constants such as π can appear alongside variables in expressions.
Summation notation: A compact notation using Σ to specify the sum of a sequence of terms. It replaces long repeated additions with a symbolic instruction.
Al-Khwarizmi: A ninth-century Persian mathematician whose writings helped establish algebra as a discipline. His rhetorical methods preceded the symbolic conventions used in later algebra.
Geometric algebra: A tradition of expressing algebraic relationships through geometric figures and constructions. Geometric representations communicate relationships that symbolic formulas encode differently.
Analytic geometry: The study of geometric objects using coordinates and algebraic equations. Descartes-style notation helped connect equations with geometric curves.

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