Algebra

Algebra is a branch of mathematics that uses symbols and rules to represent quantities and relationships, and to solve equations. It ranges from elementary equation-solving to abstract structures such as groups and rings.

Variable: A symbol representing a quantity that may vary or have an unknown value. Variables let algebra express unknown quantities and general relationships.
Equality: A relation asserting that two mathematical expressions have the same value. Valid equation-solving steps preserve equality on both sides.
Algebraic modeling: The use of algebraic expressions and equations to represent real-world relationships. Models translate quantities and constraints into equations that can be analyzed.
Babylonian mathematics: The mathematical tradition of ancient Mesopotamia, preserved largely on cuneiform tablets. Babylonian scribes solved problems equivalent to quadratic equations without modern symbolism.
Geometry: The branch of mathematics concerned with shapes, sizes, positions, and spatial relationships. Geometry emphasizes spatial objects, while algebra represents relationships through symbols and equations.
Algebraic expression: A combination of numbers, variables, and operations that represents a quantity. Expressions are the basic symbolic objects manipulated in algebra.
Inverse operation: An operation that reverses the effect of another operation. Inverse operations isolate an unknown while preserving an equation's solutions.
Analytic geometry: The study of geometric objects using coordinates and algebraic equations. Algebra makes curves and geometric relationships calculable through equations.
Diophantus: An ancient Greek mathematician known for works on equations and integer solutions. His Arithmetica used abbreviated symbols in problems now associated with algebra.
Number theory: The study of integers and their properties, including divisibility and prime numbers. Algebraic methods often expose structure in integer equations and divisibility problems.

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