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algebra

From Wiktionary, the free dictionary

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See also: Appendix:Variations of "algebra"

English

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Etymology

Borrowed from Medieval Latin algebra, from the Arabic word الْجَبْر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الْكِتَاب الْمُخْتَصَر فِي حِسَاب الْجَبْر وَالْمُقَابَلَة (al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).

Pronunciation

  • (UK) IPA(key): /ˈæl.dʒɪ.bɹə/
  • (US) IPA(key): /ˈæl.d͡ʒɪ.bɹə/, /ˈæl.d͡ʒə.bɹə/
  • Audio (US):(file)
  • (Indic) IPA(key): /əlˈdʒɛbrɑ/, /-ˈdʒi-/

Noun

algebra (countable and uncountable, plural algebras)

  2. (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
  3. (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
  4. (countable, mathematics, algebra) Any of several objects of study in Algebra
    1. A universal algebra.
    2. An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
      Synonyms: algebra over a field, algebra over a ring
  5. (countable, set theory, mathematical 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 (and thereby also under intersections and differences).
    Synonyms: field of sets, algebra of sets
    Hypernym: ring
    Hyponym: σ-algebra
  6. (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
    • 1663, William Clark, edited by William Hugh Logan, Marciano; or, The discovery: A tragi-comedy‎, Edinburgh: Reprinted for Private Circulation, published 1871, →ISBN, page 13:
      Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?
  7. (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
    • a1420, The British Museum Additional MS, 12,056, “Wounds complicated by the Dislocation of a Bone”, in Robert von Fleischhacker, editor, Lanfranc's "Science of cirurgie."‎, London: K. Paul, Trench, Trübner & Co, translation of original by Lanfranc of Milan, published 1894, →ISBN, page 63:
      Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate, til viij. daies ben goon in þe wyntir, & v. in þe somer; for þanne it schal make quytture, and be sikir from swellynge; & þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be seid in þe chapitle of algebra.
    • 1987, John Newsome Crossley, “Latency”, in The emergence of number‎, Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65:
      Algebra is used today by surgeons to mean bone-setting, i.e. the restoration of bones, and the idea of restoration is present in the mathematical context, too.

Derived terms

Descendants

  • ⇒ Chinese: 代數 / 代数 (dàishù)

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