Algebra: Difference atween revisions
s robot Adding: si:වීජ ගණිතය |
Ondae reveesion 792538 bi 92.184.102.24 (Tauk) ? Tag: Ondae |
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(37 intermeediate reveesions bi 18 uisers no shawn) | |||
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== Clessification == |
== Clessification == |
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Algebra can be spleet up intae thir fields: |
Algebra can be spleet up intae thir fields: |
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*[[Basic algebra]] studies the parteiculars o an operations on [[naitural nummer]]s, [[integer]]s, [[raitional nummer|raitional]] an [[ |
* [[Basic algebra]] studies the parteiculars o an operations on [[naitural nummer]]s, [[integer]]s, [[raitional nummer|raitional]] an [[real nummer]]s, an hou a bodie can solve [[equation]]s wi [[variable]]s. |
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*[[Linear algebra]] is a theory o [[ |
* [[Linear algebra]] is a theory o [[vector space]]s, pairt o it bein the theory o [[linear equation]] an o [[Matrix (mathematics)|matrices]]. Ideas an methods frae linear algebra can be uised in monie sindrie brainches o mathematics. For exemplar, the chief ettle o the study o functional analysis is infinite vector spaces. |
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*[[Abstract algebra]] studies [[algebraic structur]]s like [[group (algebra)|groups]], [[ring (algebra)|rings]] an [[bodie (algebra)|bodies]] that generalises concepts frae basic algebra. |
* [[Abstract algebra]] studies [[algebraic structur]]s like [[group (algebra)|groups]], [[ring (algebra)|rings]] an [[bodie (algebra)|bodies]] that generalises concepts frae basic algebra. |
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== History == |
== History == |
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Algebra wis cleckit for tae help solve equations. The solutions o linear an quadratic equations wis aareadies kent lang syne. In the [[16t century]] Italian mathemateecians fund solutions tae cubic an quartic equations. In 1799 [[Gauss]] shawed that “ilka algebraic equation o degree <var>n</var>, haes <var>n</var> [[ruit]]s (solutions), rael or imaginar”. |
Algebra wis cleckit for tae help solve equations. The solutions o linear an quadratic equations wis aareadies kent lang syne. In the [[16t century]] Italian mathemateecians fund solutions tae cubic an quartic equations. In 1799 [[Gauss]] shawed that “ilka algebraic equation o degree <var>n</var>, haes <var>n</var> [[ruit]]s (solutions), rael or imaginar”. |
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At the stairt o the [[19t century]] [[Niels Abel]] an [[Evariste Galois]] pruived that the solutions o equations o degree bigger nor 4 canna be expressed uisin coeffeicients o the equation an algebraic operations |
At the stairt o the [[19t century]] [[Niels Abel]] an [[Evariste Galois]] pruived that the solutions o equations o degree bigger nor 4 canna be expressed uisin coeffeicients o the equation an algebraic operations juist—that is, the'r nae generalisation o the [[quadratic formula|quadratic]], [[cubic formula|cubic]] or [[quartic formula]]e tae heicher degrees. |
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== See forby == |
== See forby == |
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*[[Expression]] |
* [[Expression (mathematics)|Expression]] |
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*[[Equation]] |
* [[Equation]] |
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*[[Determinant]] |
* [[Determinant]] |
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*[[Group (algebra)|Group]] |
* [[Group (algebra)|Group]] |
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*[[Field (algebra)|Field]] |
* [[Field (algebra)|Field]] |
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*[[Matrix]] |
* [[Matrix (mathematics)]] |
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*[[Ring (algebra)|Ring]] |
* [[Ring (algebra)|Ring]] |
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*[[Space]] |
* [[Space (mathematics)|Space]] |
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*[[Structur (mathematics)|Structur]] |
* [[Structur (mathematics)|Structur]] |
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*[[Variable]] |
* [[Variable (mathematics)|Variable]] |
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{{Commonscat}} |
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[[Category: |
[[Category:Algebra]] |
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[[af:Algebra]] |
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[[an:Alchebra]] |
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[[ar:جبر]] |
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[[arz:جبر]] |
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[[ast:Álxebra]] |
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[[az:Cəbr]] |
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[[ba:Алгебра]] |
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[[be:Алгебра]] |
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[[be-x-old:Альгебра]] |
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[[bg:Алгебра]] |
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[[bn:বীজগণিত]] |
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[[bs:Algebra]] |
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[[ca:Àlgebra]] |
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[[co:Algebra]] |
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[[cs:Algebra]] |
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[[cy:Algebra]] |
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[[da:Algebra]] |
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[[de:Algebra]] |
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[[el:Άλγεβρα]] |
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[[eml:Algebra]] |
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[[en:Algebra]] |
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[[eo:Algebro]] |
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[[es:Álgebra]] |
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[[et:Algebra]] |
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[[eu:Aljebra]] |
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[[fa:جبر]] |
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[[fiu-vro:Algõbra]] |
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[[fr:Algèbre]] |
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[[gd:Ailseabra]] |
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[[gl:Álxebra]] |
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[[he:אלגברה]] |
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[[hi:बीजगणित]] |
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[[hr:Algebra]] |
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[[ht:Aljèb]] |
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[[id:Aljabar]] |
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[[io:Algebro]] |
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[[is:Algebra]] |
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[[it:Algebra]] |
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[[ja:代数学]] |
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[[jbo:turki'icmaci]] |
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[[jv:Aljabar]] |
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[[ka:ალგებრა]] |
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[[kn:ಬೀಜಗಣಿತ]] |
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[[ko:대수학]] |
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[[la:Algebra]] |
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[[lo:ພຶດຊະຄະນິດ]] |
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[[lt:Algebra]] |
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[[lv:Algebra]] |
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[[mk:Алгебра]] |
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[[ml:ബീജഗണിതം]] |
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[[mr:बीजगणित]] |
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[[ms:Algebra]] |
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[[mt:Alġebra]] |
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[[mwl:Álgebra]] |
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[[my:အက္ခရာသင်္ချာ]] |
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[[pms:Àlgebra]] |
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[[qu:Qillqanancha kamay]] |
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[[ro:Algebră]] |
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[[ru:Алгебра]] |
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[[sah:Алгебра]] |
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[[sh:Algebra]] |
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[[si:වීජ ගණිතය]] |
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[[simple:Algebra]] |
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[[sk:Algebra]] |
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[[sl:Algebra]] |
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[[sq:Algjebra]] |
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[[sr:Алгебра]] |
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[[sv:Algebra]] |
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[[ta:இயற்கணிதம்]] |
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[[tg:Алгебра]] |
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[[th:พีชคณิต]] |
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[[tk:Algebra]] |
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[[tl:Alhebra]] |
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[[tr:Cebir]] |
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[[uk:Алгебра]] |
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[[uz:Algebra]] |
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[[vi:Đại số]] |
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[[vls:Algebra]] |
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[[war:Alhebra]] |
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[[yi:אלגעברע]] |
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[[yo:Áljẹ́brà]] |
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[[zh:代数]] |
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[[zh-classical:代數學]] |
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[[zh-min-nan:Tāi-sò͘]] |
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[[zh-yue:代數學]] |
Latest reveesion aes o 17:53, 8 September 2020
Algebra is ane o the maist basic brainches o mathematics. Tho it isna aesie defined, it is chairacterised bi the uiss o seembols tae represent some operations, an o letters tae represent nummers or ither elements.
Clessification[eedit | eedit soorce]
Algebra can be spleet up intae thir fields:
- Basic algebra studies the parteiculars o an operations on naitural nummers, integers, raitional an real nummers, an hou a bodie can solve equations wi variables.
- Linear algebra is a theory o vector spaces, pairt o it bein the theory o linear equation an o matrices. Ideas an methods frae linear algebra can be uised in monie sindrie brainches o mathematics. For exemplar, the chief ettle o the study o functional analysis is infinite vector spaces.
- Abstract algebra studies algebraic structurs like groups, rings an bodies that generalises concepts frae basic algebra.
History[eedit | eedit soorce]
Algebra, like coontin an geometry, is ane o the auldest brainches o mathematics. The name comes frae a beuk bi the Arabian mathemateecian Al-Khwarizmi cried Kitab al-jabr wa al-muqabalah ("The beuk o summary anent calculatin bi transposeition an reduction").
Algebra wis cleckit for tae help solve equations. The solutions o linear an quadratic equations wis aareadies kent lang syne. In the 16t century Italian mathemateecians fund solutions tae cubic an quartic equations. In 1799 Gauss shawed that “ilka algebraic equation o degree n, haes n ruits (solutions), rael or imaginar”.
At the stairt o the 19t century Niels Abel an Evariste Galois pruived that the solutions o equations o degree bigger nor 4 canna be expressed uisin coeffeicients o the equation an algebraic operations juist—that is, the'r nae generalisation o the quadratic, cubic or quartic formulae tae heicher degrees.
See forby[eedit | eedit soorce]
Wikimedia Commons haes media relatit tae Algebra. |