Algebra

Algebra reshe ne na lissafin lissafi wanda ke nazarin wasu tsarukan ƙididdiga, waɗanda aka sani da tsarin algebra, da sarrafa maganganun da ke cikin waɗannan tsarin. Ƙididdigar lissafi ce ta gabaɗaya wacce ke gabatar da masu canji da ayyukan algebraic ban da daidaitattun ayyukan ƙididdiga kamar ƙari da ninkawa .

Elementary algebra shine babban nau'i na algebra da ake koyarwa a makaranta kuma yana nazarin maganganun lissafi ta amfani da masu canji don ƙimar da ba a bayyana ba. Yana neman sanin waɗanne kimomi gaskiya ne maganganun. Don yin haka, yana amfani da hanyoyi daban-daban na canza ma'auni don keɓe masu canji. Algebra na layin layi wani fili ne mai alaƙa da ke binciken sauye-sauyen da ke bayyana a cikin ma'auni masu yawa, wanda ake kira tsarin ma'auni na layi . Yana ƙoƙarin gano ƙimar da ke warware duk ma'auni a cikin tsarin a lokaci guda.

Abstract algebra yana nazarin tsarin algebra, wanda ya ƙunshi saitin abubuwa na lissafi tare da ɗaya ko wasu ayyuka na binary da aka ayyana akan wannan saitin. Gabaɗaya algebra ne na farko da na layi tunda yana ba da damar abubuwan lissafi ban da lambobi da ayyukan da ba na lissafi ba. Ya bambanta tsakanin nau'ikan tsarin algebra daban-daban, kamar ƙungiyoyi, zobe, da filayen, dangane da adadin ayyukan da suke amfani da su da dokokin da suke bi . Algebra na duniya ya ƙunshi ƙarin matakin gaba ɗaya wanda baya iyakance ga ayyukan binary kuma yana bincika ƙarin ƙirar ƙira waɗanda ke fasalta nau'ikan tsarin algebra daban-daban.

An fara nazarin hanyoyin algebraic a zamanin d ¯ a don warware takamaiman matsaloli a fannoni kamar lissafi . Masana lissafin da suka biyo baya sun yi nazarin dabaru na gaba ɗaya don warware ma'auni ba tare da takamaiman aikace-aikacen su ba. Sun bayyana ma'auni da hanyoyin magance su ta hanyar amfani da kalmomi da gajarta har zuwa ƙarni na 16 da 17, lokacin da aka ɓullo da ƙaƙƙarfan ƙa'ida ta alama. A tsakiyar karni na 19, iyakar algebra ta fadada fiye da ka'idar daidaito don rufe nau'ikan ayyuka da tsarin algebra iri-iri. Algebra ya dace da yawancin rassan lissafin lissafi, kamar geometry, topology, ka'idar lamba, da ƙididdiga, da sauran fagagen bincike, kamar dabaru da kimiyoyin haɓakawa .

 Ma'anarsa da ilimin ƙa'idar halitta 
Algebra reshe ne na lissafin lissafi wanda ke nazarin tsarin algebra da ayyukan  da suke amfani da su.  Tsarin algebra wani tsari ne mara komai na abubuwa na lissafi, kamar ainihin lambobi, tare da ayyukan algebra da aka ayyana akan wannan saitin, kamar ƙari da ninkawa .  Algebra yana bincika dokoki, halaye na gaba ɗaya, da nau'ikan tsarin algebra. A cikin wasu sifofi na algebra, yana nazarin amfani da masu canji a cikin ma'auni da yadda ake sarrafa waɗannan ma'auni.  

Yawancin lokaci ana fahimtar Algebra azaman jigon lissafi .  Ayyukan nazarin ilmin lissafi kamar ƙari, ragi, ninkawa, da rarrabawa, a cikin wani yanki na lambobi, kamar ainihin lambobi.  Algebra na farko shine matakin farko na abstraction. Kamar lissafin lissafi, yana taƙaita kansa ga takamaiman nau'ikan lambobi da ayyuka. Yana haɓaka waɗannan ayyuka ta hanyar ƙyale ƙididdiga marasa iyaka a cikin nau'in masu canji ban da lambobi.  Ana samun mafi girman matakin abstraction a cikin algebra na abstraction, wanda baya iyakance ga wani yanki na musamman kuma yana nazarin tsarin algebra kamar ƙungiyoyi da zobe . Ya wuce fiye da ayyukan ƙididdiga na yau da kullun ta hanyar rufe wasu nau'ikan aiki na binary.  Har ila yau algebra na duniya ya kasance mafi ƙanƙanta a cikin cewa ba'a iyakance shi ga ayyukan binaryar ba kuma baya sha'awar takamaiman tsarin algebra amma yana bincika halaye na tsarin algebra gaba ɗaya. 
alt=Title page of The Compendious Book on Calculation by Completion and Balancing|thumb| Kalmar algebra ta fito daga sunan littafin al-Khwarizmi  . 
Kalmar "algebra" wani lokaci ana amfani da ita a cikin ma'ana mafi ƙunci don komawa ga algebra na farko kawai ko kuma kawai ga algebra.  Idan aka yi amfani da su azaman suna mai ƙididdigewa, algebra wani takamaiman nau'in tsarin algebra ne wanda ya ƙunshi sararin samaniya sanye take da wani nau'in aiki na binary .  Dangane da mahallin, "algebra" kuma na iya komawa zuwa wasu tsarin algebra, kamar Lie algebra ko algebra mai haɗin gwiwa . 

Kalmar algebra ta fito ne daga kalmar larabci  (  ), wanda asalinsa yana magana ne akan aikin tiyatar gyaran kashi . A karni na 9, kalmar ta sami ma'anar lissafi lokacin da masanin lissafin Farisa Muhammad ibn Musa al-Khwarizmi ya yi amfani da shi don kwatanta hanyar warware daidaito kuma ya yi amfani da ita a cikin taken rubutun algebra,   . .  Kalmar ta shiga yaren Ingilishi a ƙarni na 16 daga Italiyanci, Sifen, da Latin na na da.  Da farko, an taƙaita ma'anarsa ga ka'idar equations, wato, ga fasahar sarrafa ma'auni na al'ada don magance su. Wannan ya canza a cikin karni na 19  lokacin da iyakar algebra ta faɗaɗa don rufe nazarin nau'ikan ayyuka da tsarin algebra iri-iri tare da tushen axioms ɗinsu, dokokin da suke bi. 

 Manyan rassa 

 Algebra na farko 

alt=Diagram of an algebraic expression|right|class=skin-invert-image|thumb| Bayanin magana na Algebra:</br> 1 - iko (mai magana)</br> 2 - coefficient</br> 3 - lokaci</br> 4 – mai aiki</br> 5 – Tsawon lokaci</br>  – m</br>  - masu canji
Algebra na farko, wanda kuma ake kira algebra na makaranta, algebra na kwaleji, da algebra na gargajiya,  shine mafi tsufa kuma mafi asali nau'in algebra. Ƙididdigar lissafi ne wanda ya dogara ga masu canji kuma yana nazarin yadda za a iya canza kalaman lissafi. 

Arithmetic shine nazarin ayyukan lambobi da binciken yadda ake haɗa lambobi da canza su ta amfani da ayyukan lissafi na ƙari, ragi, ninkawa, rarrabuwa, rarrabuwa, cire tushen, da logarithm . Misali, aikin tarawa yana hada lambobi biyu, wanda ake kira da addd, zuwa lamba ta uku, mai suna sum, kamar yadda a cikin       

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