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# algebra

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. 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.
• n. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.

### from Wiktionary, Creative Commons Attribution/Share-Alike License

• n. A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
• n. The study of algebraic structures.
• n. A universal algebra.
• n. An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear.
• n. 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 (and thereby also under intersections and differences).
• n. One of several other types of mathematical structure.

### from the GNU version of the Collaborative International Dictionary of English

• n. That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
• n. A treatise on this science.

### from The Century Dictionary and Cyclopedia

• n. Formal mathematics; the analysis of equations; the art of reasoning about relations, more especially quantitative relations, by the aid of a compact and highly systematized notation.
• n. Any special system of notation adapted to the study of a special system of relationship: as, “it is an algebra upon an algebra,” Sylvester.
• n. A treatise on algebra.
• n. Its abbreviation is algebra
• n. Algebra of multiple units.

• n. the mathematics of generalized arithmetical operations

## Etymologies

Middle English, bone-setting, and Italian, algebra, both from Medieval Latin, from Arabic al-jabr (wa-l-muqābala), 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).
(American Heritage® Dictionary of the English Language, Fourth Edition)
From Medieval Latin, from Arabic الجبر (al-jabr, "reunion, resetting of broken parts"). (Wiktionary)

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• Al-Jabr means "reunion" from the longer title of the 9th century book by al-Khw�?rizmī. The word algorithm derives from his name.

February 12, 2009

• I send you enclosed a letter from Mr Lovelace; which, though written in the cursed algebra, I know to be such a one as will show what a queer way he is in; for he read it to us with the air of a tragedian.

Mowbray to Belford, Clarissa by Samuel Richardson

January 9, 2008

• Can also mean a code.

January 9, 2008