Algebra

Definition: Algebra

Algebra

Noun

1. The mathematics of generalized arithmetical operations.

Date "algebra" was first used: 1551. (references)

Specialty Definitions: Algebra

Domain	Definitions
Computing	Algebra 1. A loose term for an algebraic structure. 2. A vector space that is also a ring, where the vector space and the ring share the same addition operation and are related in certain other ways. An example algebra is the set of 2x2 matrices with real numbers as entries, with the usual operations of addition and matrix multiplication, and the usual scalar multiplication. Another example is the set of all polynomials with real coefficients, with the usual operations. In more detail, we have: (1) an underlying set, (2) a field of scalars, (3) an operation of scalar multiplication, whose input is a scalar and a member of the underlying set and whose output is a member of the underlying set, just as in a vector space, (4) an operation of addition of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a vector space or a ring, (5) an operation of multiplication of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a ring. This whole thing constitutes an `algebra' iff: (1) it is a vector space if you discard item (5) and (2) it is a ring if you discard (2) and (3) and (3) for any scalar r and any two members A, B of the underlying set we have r(AB) = (rA)B = A(rB). In other words it doesn't matter whether you multiply members of the algebra first and then multiply by the scalar, or multiply one of them by the scalar first and then multiply the two members of the algebra. Note that the A comes before the B because the multiplication is in some cases not commutative, e.g. the matrix example. Another example (an example of a Banach algebra) is the set of all bounded linear operators on a Hilbert space, with the usual norm. The multiplication is the operation of composition of operators, and the addition and scalar multiplication are just what you would expect. Two other examples are tensor algebras and Clifford algebras. [I. N. Herstein, "Topics_in_Algebra"]. (1999-07-14). Source: The Free On-line Dictionary of Computing.
Literature	Algebra is the Arabic al gebr (the equalisation), "the supplementing and equalising (process);" so called because the problems are solved by equations, and the equations are made by supplementary terms. Fancifully identified with the Arabian chemist Gebir. Source: Brewer's Dictionary.
Space	A branch of mathematics. Originally (and still in high school context), it refers to the art of calculating with unknown quantities, represented by letters. Modern algebra has expanded this to manipulating symbols represented by letter, following certain rules which may differ from the ones applying to numbers, e.g. vector algebra, matrix algebra etc. (references)
Source: compiled by the editor from various references; see credits.

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Specialty Definition: Algebra

(From Wikipedia, the free Encyclopedia)

Algebra (from the Arabic "al-djebr" meaning "reunion", "connection" or "completion") is a branch of mathematics which may be defined as a generalization and extension of arithmetic. The field may be roughly divided in

elementary algebra, where the properties of the real number system are recorded, symbols are used as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied
abstract algebra, where algebraic structures such as fields, groups, and rings are axiomatically defined and investigated. The specific properties of vector spaces are studied in linear algebra.
universal algebra, where those properties common to all algebraic structures are studied.
computer algebra, where algorithms for the symbolic manipulation of mathematical objects are collected

The word algebra is also used for various algebraic structures:

algebra over a field
Boolean algebra
Sigma-algebra

See also:

Diophantus, "father of Algebra"
Mohammed al-Khwarizmi, who probably deserves the title more.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Algebra."

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Synonyms within Context: Algebra

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
Numeration	Arithmetic, analysis, algebra, geometry, analytical geometry, fluxions; differential calculus, integral calculus, infinitesimal calculus; calculus of differences.
Source: adapted from Roget's Thesaurus.

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Crosswords: Algebra

English words defined with "algebra": algebraic, Algebraic curve, Algebraic sum, algebraical, algebraist, Algebraize, analytic, analytic geometry, analytical geometry ♦ binary arithmetic operation, binary operation, Boole, Boolean algebra, boolean operation ♦ coordinate geometry, Cossical ♦ diagonalisation, diagonalization, Diophantine, down, down pat ♦ Exponential calculus ♦ George Boole, Graphic algebra ♦ Imaginary calculus ♦ linear algebra ♦ mastered, matrix algebra, Multiple algebra ♦ quadratics ♦ Rule of Coss ♦ Theory of equations ♦ Universal arithmetic ♦ vector algebra ♦ Zetetics. (references)

Specialty definitions using "algebra": ACP, Aldat, Algebra of Communicating Processes, algebra priority order, algebraic structure, ALPAK, ALTRAN ♦ Banach algebra, BMASF ♦ CAMAL, CIRcuit CALculus, Codd's reduction algorithm, combinatorial test ♦ equational logic ♦ FFP, Finite State Machine, FP, Franz Lisp ♦ GRG ♦ inference rule, Information Algebra, INSPECTOR, TOOL ♦ JACAL, JAffer's Canonical ALgebra ♦ LINPACK, logical complement ♦ MAS, MATHEMATICAL TECHNICIAN ♦ OR-gate ♦ pi-calculus, precision inspector, process algebra ♦ relational algebra, relational calculus, relational data model ♦ Sadlerian Lectures, Schoonschip, Science Persecuted, Scratchpad II, set difference, surface-plate inspector, Synthesizer Specification Language ♦ tool-and-die inspector, tool-and-gauge inspector, tooling inspector, two-valued logic ♦ Universal algebra ♦ Views ♦ Whetstone of Witte, Wrath ♦ Xfun, Xy-pic. (references)

Non-English Usage: "Algebra" is also a word in the following languages with English translations in parentheses.

Afrikaan (algebra), Czech (algebra), Dutch (algebra), Esperanto (algebraic), German (algebra), Hungarian (algebra), Italian (algebra), Serbo-Croatian (algebra), Spanish (algebra), Swedish (algebra), Welsh (algebra).

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Modern Usage: Algebra

Domain	Usage
Screenplays	I mean that's what high school was about, algebra, bad lunch, and infidelity. (Clerks.; writing credit: Kevin Smith) Look at your algebra book, it looks like it's never even been opened! (Rock 'n' Roll High School; writing credit: Richard Whitley; Russ Dvonch) 5am to 7am, algebra with the mathematical Sister. (Black Narcissus; writing credit: Rumer Godden; Michael Powell)
Lyrics	Don't know much about algebra (Wonderful World; performing artist: Herman's Hermits)
Source: compiled by the editor from various references; see credits.

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Commercial Usage: Algebra

Domain	Title
Books	Algebra for Dummies (For Dummies) (reference) Algebra to Go: A Mathematics Handbook (reference) Beginning Algebra (5th Edition) (reference) How to Solve Word Problems in Algebra, 2nd Edition (reference) Schaum's Outline of Elementary Algebra (reference) (more book examples)

Periodicals	Algebra And Logic (reference) Algebra Colloquium (reference) Algebra I Analiz (reference) Algebra I Logika (reference) Beitraege Zur Algebra Und Geometrie (reference) (more periodical examples)

Theater & Movies	The Standard Deviants - Algebra Intro DVD 2-pack (Pre-Algebra 1, Algebra 1) (reference) (more DVD examples; more video examples)

Music	Abstrakt Algebra [IMPORT] (reference) Fanbelt Algebra (reference) If Arsenic Fails, Try Algebra (reference) (more classical music examples; more popular music examples)

High Tech	Casio Algebra FX 2.0 Graphing Calculator (reference) Algebra Adventure (Jewel Case) (reference) Standard Deviants Action Learning CD-ROM: Algebra (reference) (more camera examples; more video game examples; more computer examples; more electronic examples; more software examples)
Source: compiled by the editor from various references; see credits.

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Image Slideshow: Algebra

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Photo Album: Algebra

Thumbnail	Description & Credit	Thumbnail	Description & Credit
	A new rule in algebra. Five from three and one remains!! or "The three Mexican prisoners, having but one leg between them all!".Credit: Library of Congress.		Invitation to reunion of Mr. Topping's algebra class.Credit: Library of Congress.
Source: compiled by the editor from various references; see credits.

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Use in Literature: Algebra

Title	Author	Quote
Les Miserables	Hugo, Victor	Algebra, medicine, botany, have their argot.
Source: compiled by the editor from various references.

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Non-Fiction Usage: Algebra

Subject	Topic	Quote
Lexicography	Devil's Dictionary	WRATH, n. Anger of a superior quality and degree, appropriate to exalted characters and momentous occasions; as, "the wrath of God," "the day of wrath," etc. Amongst the ancients the wrath of kings was deemed sacred, for it could usually command the agency of some god for its fit manifestation, as could also that of a priest. The Greeks before Troy were so harried by Apollo that they jumped out of the frying-pan of the wrath of Cryses into the fire of the wrath of Achilles, though Agamemnon, the sole offender, was neither fried nor roasted. A similar noted immunity was that of David when he incurred the wrath of Yahveh by numbering his people, seventy thousand of whom paid the penalty with their lives. God is now Love, and a director of the census performs his work without apprehension of disaster. X X in our alphabet being a needless letter has an added invincibility to the attacks of the spelling reformers, and like them, will doubtless last as long as the language. X is the sacred symbol of ten dollars, and in such words as Xmas, Xn, etc., stands for Christ, not, as is popular supposed, because it represents a cross, but because the corresponding letter in the Greek alphabet is the initial of his name -- Xristos. If it represented a cross it would stand for St. Andrew, who "testified" upon one of that shape. In the algebra of psychology x stands for Woman's mind. Words beginning with X are Grecian and will not be defined in this standard English dictionary. Y
Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Usage Frequency: Algebra

"Algebra" is generally used as a noun (singular) -- approximately 97.22% of the time. "Algebra" is used about 180 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Noun (singular)	97.22%	175	23,506
Noun (proper)	2.78%	5	157,705
Total	100.00%	180	N/A

Source: compiled by the editor from several corpora; see credits.

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Expressions: Algebra

Expressions using "algebra": algebra of Communicating Processes ♦ algebra priority order ♦ Banach algebra ♦ boolean algebra ♦ Graphic algebra ♦ information Algebra ♦ JAffer's Canonical ALgebra ♦ linear algebra ♦ matrix algebra ♦ multiple algebra ♦ relational algebra ♦ universal algebra ♦ vector algebra. Additional references.
Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Algebra

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.

Expression	Frequency per Day	Expression	Frequency per Day
algebra	3,128	algebra lesson plan	74
help with algebra	595	algebra equation	60
pre algebra	310	algebra lineal	58
college algebra	265	algebra free help	56
algebra 2	163	algebra pre worksheets	55
algebra 1	145	learn algebra	55
linear algebra	143	algebra test	54
algebra worksheets	143	algebra game	54
algebra problem	137	college algebra help	54
boolean algebra	115	beginning algebra	53
basic algebra	107	algebra homework help	51
algebra tutorial	107	algebra 2 help	50
algebra calculator	95	algebra online	50
elementary algebra	88	algebra lesson	49
intermediate algebra	85	learning algebra	45
algebra history	80	algebra ii	44
algebra software	79	algebra boole de	43
algebra tutor	78	algebra for dummy	42
algebra formula	78	abstract algebra	42
algebra word problem	74	teaching algebra	41
Source: compiled by the editor from various references; see credits.

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Modern Translations: Algebra

Language		Translations for "algebra"; alternative meanings/domain in parentheses.
Afrikaan		algebra. (various references)

Albanian		algjebër. (various references)

Arabic		‏علم الجبر. (various references)

Bulgarian		алгебра. (various references)

Chinese		代数 (Algebraic, Algebraically), 代數 . (various references)

Czech		algebra. (various references)

Danish		algebra. (various references)

Dutch		algebra, stelkunde. (various references)

Esperanto		algebro. (various references)

Farsi		جبرومقابله , جبر (Force, Gouge). (various references)

Finnish		algebra. (various references)

French		algèbre. (various references)

German		Algebra. (various references)

Greek		άλγεβρα. (various references)

Hebrew		אל�'בר�". (various references)

Hungarian		algebra. (various references)

Indonesian		aljabar. (various references)

Irish		ailgéabar. (various references)

Italian		algebra. (various references)

Japanese Kanji		代数学 , 代数 . (various references)

Japanese Katakana		� いすうがく, � いすう. (various references)

Korean		대수 (logarithm, logarithmic, Logarithmical, logarithms). (various references)

Manx		algeerey. (various references)

Papiamen		álgebra. (various references)

Pig Latin		algebraay

Portuguese		álgebra. (various references)

Romanian		algebrã. (various references)

Russian		алгебра (algebras). (various references)

Serbo-Croatian		algebra. (various references)

Spanish		álgebra. (various references)

Swedish		algebra. (various references)

Turkish		cebir (algebraic, algebraical), cebír. (various references)

Ukranian		алгебра. (various references)

Vietnamese		đại số học. (various references)

Welsh		algebra. (various references)
Source: compiled by the editor from various translation references.

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Ancestral Language Translations: Algebra

Language	Period	Translations
Arabic	500-Modern	al jebr. (various references)
Source: compiled by the editor from various references.

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Derivations & Misspellings: Algebra

Derivations
	Words beginning with "algebra": algebraic, algebraically, algebraist, algebraists, algebras. (additional references)
Misspellings
	"Algebra" is suggested in spellcheckers for the following: Agbeka, Agbetra, Aldebert, alegebra, alegra, algabar, algerbra, algrebra, Almeira, Alnemri, Ogyebre. (additional references)
Source: compiled by the editor, based on several corpora (additional references).

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Rhyming with "Algebra"

# of Phoneme Matches	Pronunciation	Word(s) rhyming with "algebra" (pronounced a"ljubru)
4	-u b r u	vertebra.
3	-b r u	Abracadabra, candelabra, Cobra, hombre, Libra, macabre, Penumbra, Sabra, umbra, zebra.
Source: compiled by the editor (additional references); see credits.

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Anagrams: Algebra

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-a-b-e-g-l-r"
	-1 letter: aglare, alegar, arable, garble, laager.
	-2 letters: abler, algae, areal, argal, argle, bagel, baler, barge, belga, blare, blear, gable, galea, glare, gleba, graal, labra, lager, large, regal.
	-3 letters: able, agar, ager, alae, alar, alba, alga, area, baal, bale, bare, bear, berg, blae, brae, brag, earl, egal, gala, gale, garb, gear, grab, lear, raga, rage.
	-5 letters: aa.
	Words containing the letters "a-a-b-e-g-l-r"
	+1 letter: algebras, arguable, glabrate, gradable, grazable.
	+2 letters: agreeable, agreeably, algebraic, barrelage, cablegram, glabellar, grantable, graspable, grazeable.
	+3 letters: algebraist, barrelages, cablegrams, chargeable, degradable, greaseball, inarguable, propagable, targetable, unarguable, upgradable.
	+4 letters: algebraists, ballyragged, berascaling, elaborating, enlargeable, flabbergast, gallbladder, greaseballs, lawbreaking, organizable, rebalancing, talebearing, ungraspable, upgradeable.
	+5 letters: agreeability, blackguarded, diagrammable, disagreeable, disagreeably, flabbergasts, gallbladders, irrefragable, irrefragably, lawbreakings, marriageable, programmable, reassemblage, rechargeable, tabernacling, talebearings.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.