Examples of algebra on a chalkboard.
Graphing, absolute value equations and scientific notation are each an example of a topic in algebra.
- a mathematical system using symbols, esp. letters, to generalize certain arithmetic operations and relationships (Ex.: x + y = x represents a unique relationship between x and y, and has an infinite number of examples, as 3 + 6 = 9)
- any of various symbolic mathematical systems having formal rules of operation, defined relationships, finite processes, etc.: Boolean algebra
- a textbook or treatise dealing with algebra
Origin of algebraMiddle English ; from Medieval Latin ; from Arabic al-jabr, the reunion of broken parts ; from al, the + jabara, to reunite
- A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
- A set together with a pair of binary operations defined on the set. Usually, the set and the operations simultaneously form both a ring and a module.
Origin of algebraMiddle English, bone-setting, and Italian, algebra, both from Medieval Latin, from Arabic al-jabr (wa-l-muqabala), the restoration (and the compensation), addition (and subtraction) : al-, the + jabr, bone-setting, restoration (from jabara, to set (bones), force, restore; see gpr in Semitic roots).
(countable and uncountable, plural algebras)
- (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- (uncountable, mathematics) A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
- (uncountable, mathematics) The study of algebraic structures.
- (countable, mathematics) A universal algebra.
- (countable, algebra) An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear.
- (countable, set theory, analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (thereby also under intersections and differences).
- (countable, mathematics) One of several other types of mathematical structure.
- (figuratively) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
From Medieval Latin, from Arabic word الجبر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الكتاب المختصر في حساب الجبر والمقابلة (al-kitāb al-muxtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).