Arithmetic group, Linear function, Geometric mean

Ithungiyar lissafi: A ilimin lissafi, rukunin lissafi rukuni ne wanda aka samu azaman adadin lambobi na ƙungiyar aljebra, misali Suna tasowa ne ta hanyar ɗabi'ar lissafi na nau'ikan siradi da wasu batutuwa na gargajiya a ka'idar lamba. Hakanan suna haifar da misalai masu ban sha'awa na yawaitar Riemannian kuma saboda haka abubuwa ne masu ban sha'awa a cikin yanayin ilimin lissafi da yanayi. A ƙarshe, waɗannan batutuwa guda biyu suna haɗuwa cikin ka'idar siffofin kere kere wanda ke da mahimmanci a ka'idar lambar zamani.
Arirgar aiki: A ilimin lissafi, kalmar aikin layi ɗaya tana nufin ra'ayoyi biyu mabanbanta amma masu alaƙa: A cikin lissafi da yankuna masu alaƙa, aikin layi yana aiki ne wanda jadawalinsa layi ne madaidaiciya, ma'ana, aikin polynomial na digiri sifili ko ɗaya. Don rarrabe irin wannan aikin layi da sauran ra'ayi, ana amfani da kalmar affine aiki sau da yawa. A cikin algebra mai layi, lissafin lissafi, da kuma nazarin aiki, aikin layi yana da taswirar layi.
Lissafi nufin: A ilimin lissafi, yanayin lissafin ma'ana yana nufin matsakaita ko matsakaici, wanda ke nuna halin tsakiya ko ƙimar yawan adadin lambobi ta hanyar amfani da ƙimar ƙimarsu. Ma'anar yanayin yanayi ana fassara shi azaman n asalin tushen lambobin n, ma'ana, don saitin lambobi x 1 , x 2 , ..., x n , ma'anar yanayin yanayi ana bayyana shi azaman
Tsarin lissafi: A cikin dabarun lissafi, tsarin lissafi, tsarin lissafi ko Kleene – Mostowski matsayi na tsara wasu saituna dangane da mawuyacin tsarin da ke ayyana su. Duk wani saiti da ya karɓi rarrabuwa ana kiran sa ilimin lissafi .
Ilimin lissafi hyperbolic 3-da yawa: A ilimin lissafi, mafi daidaito a ka'idar rukuni da lissafin wuce gona da iri, kungiyoyin Kleiniya na lissafi rukuni ne na musamman na kungiyoyin Kleiniya da aka gina ta amfani da umarni a algebras quaternion. Su ne lokuta na musamman na kungiyoyin lissafi. Harshen hyperbolic mai lissafi uku mai yawa shine ɓangaren sararin samaniya ta ƙungiyar Kleiniya ta lissafi Waɗannan nau'o'in sun haɗa da wasu kyawawan kyawawan misalai.
Fuungiyar Fuchsian ta lissafi: Fuungiyoyin Fuchsian na lissafi rukuni ne na musamman na kungiyoyin Fuchsian da aka gina ta amfani da umarni a cikin algebras quaternion. Su ne lokuta na musamman na kungiyoyin lissafi. Misalin samfurin ƙungiyar Fuchsian mai lissafi shine rukunin masu daidaito . Su, da farfajiyar da ke haɗuwa da aikin da suke yi a kan jirgin sama mai hauhawar jini galibi suna nuna halaye na yau da kullun tsakanin ƙungiyoyin Fuchsian da saman hyperbolic.
Ilimin lissafi IF: Bayanin lissafin IF bayani ne na ka'idoji uku na lissafin kudi, wanda aka fara gani a fitowar farko ta Fortran a shekarar 1957, kuma an samo shi a duk wasu juzu'i na gaba, da wasu wasu yarukan shirye-shirye, kamar FOCAL. Ba kamar maganganun IF mai ma'ana da aka gani a cikin wasu yarukan ba, bayanin Fortran ya bayyana rassa uku daban-daban dangane da sakamakon magana mara kyau, sifili, ko tabbatacce, a cikin tsari, an rubuta kamar haka:
Fastoci Guda Tara akan Fasahar Lissafi: Fasali tara a kan Lissafin Lissafi littafi ne na lissafi na kasar Sin, wanda yawancin ƙarni na malamai suka haɗu daga ƙarni na 10 zuwa 2 KZ, matakinsa na ƙarshe shi ne daga ƙarni na 2 A. Wannan littafin ɗayan farkon littattafan lissafi ne daga China, na farko shi ne Suan shu shu da Zhoubi Suanjing . Yana gabatar da hanya zuwa lissafin lissafi wanda ke kan gano manyan hanyoyin magance matsaloli, wanda zai iya bambanta da hanyar da ta saba da tsohuwar masanan lissafi na Girka, waɗanda ke son yanke shawara daga saitin farko na axioms.
Itearshen lissafin lissafi: A ilimin lissafi, lissafin lissafi na fannin lissafi shi ne lissafin a fagen iyaka wanda ya saba da lissafi a fagen da yake da abubuwa da ba su da iyaka, kamar fannin lambobin hankali.
Fastoci Guda Tara akan Fasahar Lissafi: Fasali tara a kan Lissafin Lissafi littafi ne na lissafi na kasar Sin, wanda yawancin ƙarni na malamai suka haɗu daga ƙarni na 10 zuwa 2 KZ, matakinsa na ƙarshe shi ne daga ƙarni na 2 A. Wannan littafin ɗayan farkon littattafan lissafi ne daga China, na farko shi ne Suan shu shu da Zhoubi Suanjing . Yana gabatar da hanya zuwa lissafin lissafi wanda ke kan gano manyan hanyoyin magance matsaloli, wanda zai iya bambanta da hanyar da ta saba da tsohuwar masanan lissafi na Girka, waɗanda ke son yanke shawara daga saitin farko na axioms.
Misalin Roofline: Samfurin Roofline shine ƙirar aikin gani na gani wanda aka yi amfani dashi don samar da ƙididdigar aikin kwatankwacin kwaya ko aikace-aikacen da ke gudana akan ɗimbin yawa, mahimmin abu, ko kuma tsarin haɓaka kayan haɓakawa, ta hanyar nuna ƙarancin kayan aikin da ke ciki, da fa'ida mai yuwuwa da fifikon abubuwan ingantawa. Ta hanyar haɗuwa da yanki, bandwidth, da abubuwa masu kamanceceniya daban-daban a cikin adadi guda na aiki, samfurin na iya zama madaidaicin madadin don kimanta ingancin nasarar da aka samu maimakon amfani da ƙididdigar kashi-na-ƙoli mai sauƙi, saboda yana ba da haske game da aiwatarwar da limituntatawar aiwatarwa ta asali.
Pari mai rikitarwa: A ilimin lissafi, yawan juzu'i ko juzu'i na lamba x , wanda aka nuna ta 1 / x ko x −1 , adadi ne wanda idan aka ninka shi x ya haifar da adadin mai yawa, 1. Thearin juzu'in juzu'i a / b shine b / a . Don kidayar lamba ta ainihi, raba 1 da lambar. Misali, rabon 5 ya zama daya bisa biyar, kuma rabon 0.25 an raba shi 1 da 0.25, ko 4. Aikin maidowa , aikin f ( x ) wanda ya zana taswirori x zuwa 1 / x , yana daya daga cikin mafi sauki misalan wani aiki wanda yake akasin sa ne.
Lattice (ƙungiya mai rarrabu): A Karyar ka'idar da related yankunan lissafi, raga a wani gida m kungiyar ne wani mai hankali subgroup tare da dukiya da cewa quotient sarari yana da iyaka maras canjawa gwargwado. A cikin yanayi na musamman na rukuni-rukuni na R n , wannan ya kasance daidai da tunanin geometric na lattice azaman rukunin mahimman bayanai na lokaci-lokaci, kuma duka tsarin aljebra na lattices da kuma lissafin sararin samaniya na dukkan latti an fahimta sosai.
Dyscalculia: Dyscalculia nakasa ce wanda ke haifar da wahalar koyo ko fahimtar lissafi, kamar wahalar fahimtar lambobi, koyon yadda ake sarrafa lambobi, aiwatar da lissafin lissafi da kuma sanin gaskiyar ilimin lissafi. Wani lokacin sananne ne ake kira "ilimin lissafi", kodayake wannan na iya zama mai ɓatarwa saboda dyslexia yanayi ne daban da dyscalculia.
Canjin lissafi: A cikin shirye-shiryen komputa, sauya lissafi mai sauyawa ne, wani lokacin ana kiran sa hannun da aka sanya hannu . Nau'in asali guda biyu sune canjin hagu na lissafi da kuma canjin dama na lissafin . Don lambobin binary aiki ne na ɗan gajeren lokaci wanda yake canza duk ragowar ayyukan operand ɗinsa; kowane bit a cikin operand ana canza shi kawai an ba shi wasu wurare kaɗan, kuma an cika wuraren bit-gurbin. Maimakon a cika su da duka 0s, kamar yadda yake a cikin sauƙin ma'ana, lokacin da aka canza zuwa dama, an mayar da mafi ƙanƙan hagu zuwa cika dukkan wuraren da ba kowa.
Ithungiyar ilimin lissafi: A cikin sarrafa kwamfuta, sashen ilimin lissafi (ALU) yanki ne na dijital mai haɗaka wanda ke aiwatar da lissafi da ƙaramin aiki akan lambobin binar lamba. Wannan ya bambanta da ɓangaren ma'amala (FPU), wanda ke aiki akan lambobin ma'amala. Babban ginshiki ne na nau'ikan da'idojin lissafi, gami da sashin sarrafawa na tsakiya (CPU) na kwmfutoci, FPUs, da kuma na'urorin sarrafa hotuna (GPUs)
Ithungiyar ilimin lissafi: A cikin sarrafa kwamfuta, sashen ilimin lissafi (ALU) yanki ne na dijital mai haɗaka wanda ke aiwatar da lissafi da ƙaramin aiki akan lambobin binar lamba. Wannan ya bambanta da ɓangaren ma'amala (FPU), wanda ke aiki akan lambobin ma'amala. Babban ginshiki ne na nau'ikan da'idojin lissafi, gami da sashin sarrafawa na tsakiya (CPU) na kwmfutoci, FPUs, da kuma na'urorin sarrafa hotuna (GPUs)
Ithungiyar ilimin lissafi: A cikin sarrafa kwamfuta, sashen ilimin lissafi (ALU) yanki ne na dijital mai haɗaka wanda ke aiwatar da lissafi da ƙaramin aiki akan lambobin binar lamba. Wannan ya bambanta da ɓangaren ma'amala (FPU), wanda ke aiki akan lambobin ma'amala. Babban ginshiki ne na nau'ikan da'idojin lissafi, gami da sashin sarrafawa na tsakiya (CPU) na kwmfutoci, FPUs, da kuma na'urorin sarrafa hotuna (GPUs)
Pascal's kalkuleta: Calcal kalkuleta ne mai ƙididdigar inji wanda Blaise Pascal ya ƙirƙira a tsakiyar karni na 17. Pascal ya jagoranci kirkirar kalkuleta ta hanyar ƙididdigar lissafi mai wahala wanda aikin mahaifinsa ya buƙata a matsayin mai kula da haraji a Rouen. Ya tsara injin din ne don karawa da ragi lambobi biyu kai tsaye da kuma yin ninki da rabewa ta hanyar kari ko ragi.
Arithmetic yana nufin: A lissafi da lissafi, lissafin ma'ana , ko kawai ma'ana ko matsakaita , shine jimlar tarin lambobi da aka rarraba ta ƙidayar lambobi a cikin tarin. Isarin tarin sau da yawa jeri ne na sakamakon gwaji ko binciken kulawa, ko akai-akai jerin sakamakon daga binciken. Kalmar "lissafin ma'anoni" an fifita a wasu wurare a cikin lissafi da lissafi, saboda yana taimakawa wajen bambance ta da wasu hanyoyi, kamar ma'anar lissafi da kuma jituwa.
Rashin daidaito na ilimin lissafi da na lissafi yana nufin: A lissafi, rashin daidaito na lissafi da tsarin lissafi , ko kuma a taƙaice rashin daidaito na AM-GM , ya bayyana cewa ma'anar lissafi na jerin lambobin lambobin da ba su da kyau sun fi girma ko daidaita da mahimmin lissafin lissafi iri ɗaya; kuma kuma, cewa hanyoyin biyu daidai suke idan kuma idan kowane lamba a cikin jerin iri daya ne.
Al'ada (lissafi): A ilimin lissafi, ƙa'ida aiki ne daga ainihin sararin samaniya ko hadadden abu zuwa lambobi marasa gaskiya waɗanda ke aiki a wasu hanyoyi kamar nesa da asalin: yana tafiya ne da sikeli, yana yin biyayya da wani nau'i na rashin daidaito, kuma ba komai bane kawai asalin. Musamman, nisan Euclidean na vector daga asalin al'ada ce, ana kiranta Euclidean norm, ko 2-norm, wanda kuma za'a iya bayyana shi azaman murabba'in asalin kayan cikin vector da kansa.
Lambar lissafi: A ka'idar lamba, lambar lissafi lamba ce wacce matsakaiciyar masu bambance-bambancen nata ke ma adadi. Misali, 6 lambar lissafi ce saboda matsakaita masu raba shi
Ilimin lissafi na kisan kai: Ilimin lissafi na kisan kai fim ne na laifukan Soviet na 1991 wanda Dmitry Svetozarov ya jagoranta.
Ilimin lissafi na nau'ikan abelian: A ilimin lissafi, ilimin lissafi na nau'ikan abelian shine nazarin ka'idar lamba na nau'ikan abelian, ko dangin nau'in abelian. Ya sake komawa ga karatun Pierre de Fermat kan abin da yanzu aka gane shi da lanƙwasa masu lanƙwasa; kuma ya zama yanki mai mahimmanci na lissafin lissafi duka dangane da sakamako da zato. Yawancin waɗannan ana iya sanya su don nau'in abelian A akan filin lamba K ; ko kuma gabaɗaya.
Ilimin lissafi na nau'ikan abelian: A ilimin lissafi, ilimin lissafi na nau'ikan abelian shine nazarin ka'idar lamba na nau'ikan abelian, ko dangin nau'in abelian. Ya sake komawa ga karatun Pierre de Fermat kan abin da yanzu aka gane shi da lanƙwasa masu lanƙwasa; kuma ya zama yanki mai mahimmanci na lissafin lissafi duka dangane da sakamako da zato. Yawancin waɗannan ana iya sanya su don nau'in abelian A akan filin lamba K ; ko kuma gabaɗaya.
Ilimin lissafi na nau'ikan abelian: A ilimin lissafi, ilimin lissafi na nau'ikan abelian shine nazarin ka'idar lamba na nau'ikan abelian, ko dangin nau'in abelian. Ya sake komawa ga karatun Pierre de Fermat kan abin da yanzu aka gane shi da lanƙwasa masu lanƙwasa; kuma ya zama yanki mai mahimmanci na lissafin lissafi duka dangane da sakamako da zato. Yawancin waɗannan ana iya sanya su don nau'in abelian A akan filin lamba K ; ko kuma gabaɗaya.
Itearshen lissafin lissafi: A ilimin lissafi, lissafin lissafi na fannin lissafi shi ne lissafin a fagen iyaka wanda ya saba da lissafi a fagen da yake da abubuwa da ba su da iyaka, kamar fannin lambobin hankali.
Ilimin lissafi na yau da kullun: A fannin ilimin lissafi na tsararrun ka'idoji, lissafin lissafi ya bayyana ayyuka guda uku da aka saba gudanarwa akan lambobin al'ada: kari, yawaita, da fadada abubuwa. Kowane ɗayan za'a iya bayyana ta ainihin hanyoyi daban-daban guda biyu: ko dai ta hanyar gina cikakken tsari mai tsari wanda ke wakiltar sakamakon aikin ko ta amfani da sake dawowa mara iyaka. Tsarin Cantor na yau da kullun yana ba da daidaitacciyar hanyar rubuta farilla. Baya ga waɗannan ayyukan ƙa'idodi na yau da kullun, akwai kuma "lissafin" ƙididdigar ƙa'idodi da ayyukan nimber.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Eraramar intanet: A cikin shirye-shiryen kwamfuta, yawan lambobi yana faruwa yayin da aikin lissafi yayi ƙoƙarin ƙirƙirar ƙimar lamba wanda ke waje da kewayon da za a iya wakilta tare da lambar da aka bayar - ko dai ya fi matsakaici ko ƙasa da mafi ƙarancin darajar wakilta.
P-adic L-aiki: A cikin ilimin lissafi, aikin p -adic zeta , ko kuma galibi aikin p -adic L , aiki ne kwatankwacin aikin Riemann zeta, ko kuma ƙarin ayyukan L , amma waɗanda yankinsu da maƙasudin su p-adic ne . Misali, yankin zai iya kasancewa adadin p -adic Z p , p -gamfaccen p -group , ko dangin p -adic na wakilcin Galois, kuma hoton na iya zama lambobin p -adic Q p ko rufe algebraic.
Figuresididdiga masu mahimmanci: Mahimman lambobi na lamba a cikin sanarwar matsayi sune lambobi a cikin lambar waɗanda suke amintattu kuma suna da matukar muhimmanci don nuna yawan wani abu. Idan lambar da ke bayyana sakamakon auna wani abu yana da lambobi fiye da lambobin da aka yarda da su a ma'aunin ma'auni, lambobi ne kawai da ma'auni ya bayar da su abin dogaro ne don haka kawai wadannan na iya zama manyan adadi. Misali, idan tsawon awo ya ba da 114.8 mm yayin da mafi karancin tazara tsakanin alamomi a kan mai mulkin da aka yi amfani da shi a ma'aunin shine mm 1, to, lambobi uku na farko amintattu ne kawai don haka zai iya zama adadi mai mahimmanci. Daga cikin waɗannan lambobin, akwai rashin tabbas a lamba ta ƙarshe amma kuma ana ɗaukarsa azaman adadi mai mahimmanci tunda lambobin da basu da tabbas amma abin dogaro ana ɗauka manyan lambobi. Wani misalin shine ma'aunin juz'i na 2.98 L tare da rashin tabbas na ± 0.05 L. Ainihin ƙarar tana wani wuri tsakanin 2.93 L da 3.03 L. Koda kuwa dukkan lambobi ukun basu da tabbas amma abin dogaro ne saboda waɗannan suna nuni zuwa ainihin ƙarar tare da rashin tabbas karɓaɓɓe . Don haka, waɗannan adadi ne mai mahimmanci.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Wasan ci gaban lissafi: Wasan ci gaban lissafi wasa ne na matsayi inda 'yan wasa biyu a madadin suka dauki lambobi, suna kokarin mallakar cikakken ci gaban lissafi na wani girman da aka bayar.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Zobe (lissafi): A cikin ilimin lissafi, zobba tsarin algebra ne wanda yake kera filayen: yawaitar abubuwa ba lallai bane ya zama na masu motsi bane kuma ba dole bane a samu sauyin juzu'i. Watau, zobe saiti ne wanda yake dauke da ayyukan binar guda biyu masu gamsarwa wanda yayi daidai da na kari da narkar da adadi. Abubuwan ringi na iya zama lambobi kamar lambobi masu rikitarwa ko lambobi masu rikitarwa, amma kuma suna iya zama abubuwa marasa adadi kamar polynomials, matric square, ayyuka, da jerin wuta.
Tsarin lissafi: A cikin dabarun lissafi, tsarin lissafi, tsarin lissafi ko Kleene – Mostowski matsayi na tsara wasu saituna dangane da mawuyacin tsarin da ke ayyana su. Duk wani saiti da ya karɓi rarrabuwa ana kiran sa ilimin lissafi .
Adadin dawowa: A cikin kuɗi, dawowa riba ce a kan saka hannun jari. Ya ƙunshi kowane canji a ƙimar saka hannun jari, da / ko kuɗin kuɗi wanda mai saka hannun jari ya karɓa daga wannan saka hannun jarin, kamar biyan kuɗin ruwa, takardun shaida, rarar kuɗi, rarar hannun jari ko biyan kuɗi daga wata ƙirar ko samfurin da aka tsara. Ana iya auna shi ko dai a cikin cikakkun sharuɗɗa ko a matsayin kashi na adadin kuɗin da aka saka. Na karshen kuma ana kiransa dawowar lokacin riƙewa.
Canjin lissafi: A cikin shirye-shiryen komputa, sauya lissafi mai sauyawa ne, wani lokacin ana kiran sa hannun da aka sanya hannu . Nau'in asali guda biyu sune canjin hagu na lissafi da kuma canjin dama na lissafin . Don lambobin binary aiki ne na ɗan gajeren lokaci wanda yake canza duk ragowar ayyukan operand ɗinsa; kowane bit a cikin operand ana canza shi kawai an ba shi wasu wurare kaɗan, kuma an cika wuraren bit-gurbin. Maimakon a cika su da duka 0s, kamar yadda yake a cikin sauƙin ma'ana, lokacin da aka canza zuwa dama, an mayar da mafi ƙanƙan hagu zuwa cika dukkan wuraren da ba kowa.
Ringididdigar lissafi: A cikin algebra, ana cewa ringin aiki na R ya zama lissafi ne idan ɗayan waɗannan daidaito masu zuwa sun riƙe: Yanayin gida na R a ringi ne mara sikila don kowane mafi girman manufa na R. Ga dukkan manufa , da , Ga dukkan manufa , da ,
Ilimin lissafi: Igiyar lissafi , ko igiya mai ɗaure , kayan aiki ne na lissafi da aka yi amfani da su sosai a Tsakiyar Zamani wanda za a iya amfani da shi don magance yawancin matsalolin lissafi da na lissafi.
Ka'idar Arakelov: A cikin ilimin lissafi, ka'idar Arakelov wata hanya ce ta geometry na Diophantine, mai suna Suren Arakelov. Ana amfani dashi don nazarin daidaiton Diophantine a cikin girma girma.
Theorya'idar lambar nazarin nazari: Ka'idar nazarin adadi mai nisa wani bangare ne na lissafi wanda yake daukar dabaru da dabarun ka'idar adadi na adadi na zamani kuma yayi amfani dasu zuwa bangarori daban daban na lissafi. Matsakaiciyar lambar farko ta ka'ida tana matsayin misali na samfuri, kuma an fi mai da hankali ne ga sakamakon rarraba asymptotic. Masana lissafi irin su John Knopfmacher da Arne Beurling ne suka kirkireshi kuma suka bunkasa shi a karni na ashirin.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Canjin lissafi: A cikin shirye-shiryen komputa, sauya lissafi mai sauyawa ne, wani lokacin ana kiran sa hannun da aka sanya hannu . Nau'in asali guda biyu sune canjin hagu na lissafi da kuma canjin dama na lissafin . Don lambobin binary aiki ne na ɗan gajeren lokaci wanda yake canza duk ragowar ayyukan operand ɗinsa; kowane bit a cikin operand ana canza shi kawai an ba shi wasu wurare kaɗan, kuma an cika wuraren bit-gurbin. Maimakon a cika su da duka 0s, kamar yadda yake a cikin sauƙin ma'ana, lokacin da aka canza zuwa dama, an mayar da mafi ƙanƙan hagu zuwa cika dukkan wuraren da ba kowa.
Ididdigar tunani: Lissafin tunani ya ƙunshi lissafin lissafi ta amfani da kwakwalwar ɗan adam kawai, ba tare da taimako daga kowane kayayyaki ko na'urori kamar kalkuleta ba. Mutane suna amfani da lissafin tunani lokacin da babu kayan aikin lissafi, lokacin da yake sauri fiye da sauran hanyoyin lissafi, ko ma a cikin yanayin gasa. Lissafin tunani sau da yawa ya ƙunshi amfani da takamaiman fasahohin da aka tsara don takamaiman nau'ikan matsaloli. Mutanen da suke da babban iko sosai na yin lissafin tunani ana kiransu masu lissafin tunani ko walƙiya kalkuleta s.
Ididdigar tunani: Lissafin tunani ya ƙunshi lissafin lissafi ta amfani da kwakwalwar ɗan adam kawai, ba tare da taimako daga kowane kayayyaki ko na'urori kamar kalkuleta ba. Mutane suna amfani da lissafin tunani lokacin da babu kayan aikin lissafi, lokacin da yake sauri fiye da sauran hanyoyin lissafi, ko ma a cikin yanayin gasa. Lissafin tunani sau da yawa ya ƙunshi amfani da takamaiman fasahohin da aka tsara don takamaiman nau'ikan matsaloli. Mutanen da suke da babban iko sosai na yin lissafin tunani ana kiransu masu lissafin tunani ko walƙiya kalkuleta s.
Sauti: A hankalce, mafi daidaito a cikin yanke hukunci, hujja tana da kyau idan tana da inganci a sifa kuma wuraren aikinta na gaskiya ne. Har ila yau, Soundness yana da mahimmancin ma'ana a cikin ilimin lissafin lissafi, inda tsarin ma'ana ke da kyau idan kuma idan kawai duk wata dabara da za'a iya tabbatar da ita a cikin tsarin tana da ma'ana ta hanyar ma'ana dangane da ilimin tsarin.
Archimedean karkace: Tsarin Archimedean karkace ne wanda aka laƙaba shi bayan karni na 3 BC BC masanin lissafi Archimedes. Wuri ne da ya dace da wurare a kan lokaci na ma'ana yana motsawa daga tsayayyen wuri tare da saurin gudu tare da layin da ke juyawa tare da saurin hanun mai kusurwa. Daidai, a cikin haɗin polar ( r , θ ) ana iya bayyana shi ta lissafin
Ithungiyar lissafi: A ilimin lissafi, rukunin lissafi rukuni ne wanda aka samu azaman adadin lambobi na ƙungiyar aljebra, misali Suna tasowa ne ta hanyar ɗabi'ar lissafi na nau'ikan siradi da wasu batutuwa na gargajiya a ka'idar lamba. Hakanan suna haifar da misalai masu ban sha'awa na yawaitar Riemannian kuma saboda haka abubuwa ne masu ban sha'awa a cikin yanayin ilimin lissafi da yanayi. A ƙarshe, waɗannan batutuwa guda biyu suna haɗuwa cikin ka'idar siffofin kere kere wanda ke da mahimmanci a ka'idar lambar zamani.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Ilimin lissafi: A cikin ilimin lissafi, farfajiyar lissafi akan yankin Dedekind R tare da filin yanki wani abu ne na yanayin yanayi wanda yake da girma guda daya, kuma wani ma'aunin ne wanda yake samarda shi ta hanyar rashin dacewar lokacin. Lokacin da R shine zoben adadi na Z , wannan fahimta yana dogara ne da firam ɗin ƙirar ƙirar Spec ( Z ) mai kama da layi. Ithididdigar lissafi suna tasowa ta ɗabi'a a cikin yanayin diophantine, lokacin da aka yi tunanin algebraic wanda aka ayyana akan K kamar samun ragi akan filayen R / P , inda P shine babban matakin R , kusan duk P ; kuma suna da taimako wajen tantance abin da ya kamata ya faru game da tsarin ragewa zuwa R / P lokacin da mafi ƙarancin wayo ya kasa ma'ana.
Ilimin lissafi: Arithmetic topology yanki ne na lissafi wanda yake hade da ka'idar lambar algebraic da topology. Yana sanya kwatankwacin tsakanin filayen lamba da rufaffiyar, mai daidaitawa 3-manifolds.
Coxeter – Dynkin zane: A cikin ilimin lissafi, zane-zane na Coxeter – Dynkin hoto ne wanda yake da gefuna masu lambar lamba wanda ke wakiltar dangantakar sararin samaniya tsakanin tarin madubai. Yana bayanin wani gini na kaleidoscopic: kowane hoto "kumburi" yana wakiltar madubi ne kuma lambar da aka makala a reshe tana sanya umarnin kusurwar kwanon tsakanin madubai biyu, ma'ana, adadin da za'a iya ninka kwana tsakanin jirage masu haske don samun 180 digiri. Wani reshe da ba a rajista ba yana wakiltar tsari-3.
Lissafi lissafi: Kalmar lissafi underflow wani yanayi ne a cikin shirin kwamfuta inda sakamakon lissafi ya kasance wani karamin karami ne kwatankwacin wanda kwamfutar zata iya wakilta a cikin ƙwaƙwalwar ajiyar a kan babban cibiyar sarrafa ta (CPU).
Ilimin lissafi iri-iri: A cikin ilimin lissafi, nau'ikan lissafin lissafi shine yanki na sararin samaniya na Hermitian ta wani rukuni na lissafi na ƙungiyar Algebraic Lie mai alaƙa.
Ilimin lissafi iri-iri: A cikin ilimin lissafi, nau'ikan lissafin lissafi shine yanki na sararin samaniya na Hermitian ta wani rukuni na lissafi na ƙungiyar Algebraic Lie mai alaƙa.
Aikin lissafi zeta aiki: A cikin ilimin lissafi, aikin zeta na lissafi aiki ne na zeta wanda ke da alaƙa da makirci na nau'ikan keɓaɓɓu akan adadin. Aikin lissafin zeta yana ƙaddamar da aikin Riemann zeta da aikin Dedekind zeta zuwa mafi girma girma. Aikin lissafin zeta shine ɗayan mahimman abubuwa na ka'idar lamba.
Arithmetica: Arithmetica rubutu ne na tsohuwar Girkanci akan ilimin lissafi wanda masanin lissafi Diophantus ya rubuta a karni na 3 Miladiyya. Tarin matsaloli ne na algebraic 130 wadanda ke ba da hanyoyin adadi na kayyade lissafin da lissafin rashin daidaito.
John Wallis: John Wallis malamin Ingilishi ne kuma masanin lissafi wanda aka ba shi daraja ta wani ɓangare don ci gaba da ƙididdigar ƙarancin lissafi. Tsakanin 1643 da 1689 ya yi aiki a matsayin babban masanin rubutun kalmomi na Majalisar kuma, daga baya, kotun masarauta. An yaba masa tare da gabatar da alamar ∞ don wakiltar manufar rashin iyaka. Hakanan yayi amfani da 1 / ∞ don mara iyaka. John Wallis ya kasance ɗan zamani na Newton kuma ɗayan manyan masanan ilimin farkawa na farkon ilimin lissafi.
Henry Briggs (lissafi): Henry Briggs wani masanin lissafin Ingilishi ne sananne don canza asalin logarithms da John Napier ya ƙirƙira zuwa logarithms gama gari, wanda wani lokaci ake kira Briggsian logarithms don girmama shi. Takamammen algorithm na dogon rabo a amfani na zamani Briggs c ne ya gabatar dashi . 1600 Miladiyya.
Arithmetica Universalis: Arithmetica Universalis rubutu ne na lissafi daga Isaac Newton. An rubuta shi a cikin Latin, William Whiston, magajin Newton ya zama edita kuma ya buga shi a matsayin Lucasian Farfesan Lissafi a Jami'ar Cambridge. Arithmetica ya dogara ne akan bayanan laccar Newton.
Goma Gwanayen Gwanaye: Gwanayen Gwanayen Goma tarin ayyuka goma ne na lissafi na kasar Sin, waɗanda tsohuwar masanin lissafi na daular Tang Li Chunfeng (602-670) suka tattara, a matsayin matanin lissafi na hukuma don gwajin sarauta a lissafi.
Tsarin lissafi na biyu: A cikin dabaru na lissafi, lissafin tsari na biyu tarin tsarikan tsarin ne wanda yake tsara lambobin halitta da abubuwanda suke tallatawa. Yana da madadin ka'idar kafaɗɗun axiomatic azaman tushe don yawancin, amma ba duka ba, na lissafi.
George Peacock: George Peacock FRS wani masanin lissafi ne dan Ingilishi kuma malamin darikar Anglican. Ya kafa abin da ake kira Ingilishi algebra na hankali.
Lissafi lissafi: A ilimin lissafi, lissafin lissafi yana amfani da dabaru daga lissafin aljebra zuwa matsaloli a ka'idar lamba. Ilimin lissafi yana tattare ne da geometry na Diophantine, nazarin mahimman dalilai na nau'ikan aljebra.
Ithungiyar ilimin lissafi: A cikin sarrafa kwamfuta, sashen ilimin lissafi (ALU) yanki ne na dijital mai haɗaka wanda ke aiwatar da lissafi da ƙaramin aiki akan lambobin binar lamba. Wannan ya bambanta da ɓangaren ma'amala (FPU), wanda ke aiki akan lambobin ma'amala. Babban ginshiki ne na nau'ikan da'idojin lissafi, gami da sashin sarrafawa na tsakiya (CPU) na kwmfutoci, FPUs, da kuma na'urorin sarrafa hotuna (GPUs)
Tsarin lissafi na biyu: A cikin dabaru na lissafi, lissafin tsari na biyu tarin tsarikan tsarin ne wanda yake tsara lambobin halitta da abubuwanda suke tallatawa. Yana da madadin ka'idar kafaɗɗun axiomatic azaman tushe don yawancin, amma ba duka ba, na lissafi.
Tsarin lissafi na biyu: A cikin dabaru na lissafi, lissafin tsari na biyu tarin tsarikan tsarin ne wanda yake tsara lambobin halitta da abubuwanda suke tallatawa. Yana da madadin ka'idar kafaɗɗun axiomatic azaman tushe don yawancin, amma ba duka ba, na lissafi.
Theorya'idar lambar nazarin nazari: Ka'idar nazarin adadi mai nisa wani bangare ne na lissafi wanda yake daukar dabaru da dabarun ka'idar adadi na adadi na zamani kuma yayi amfani dasu zuwa bangarori daban daban na lissafi. Matsakaiciyar lambar farko ta ka'ida tana matsayin misali na samfuri, kuma an fi mai da hankali ne ga sakamakon rarraba asymptotic. Masana lissafi irin su John Knopfmacher da Arne Beurling ne suka kirkireshi kuma suka bunkasa shi a karni na ashirin.
Aikin lissafi: A ka'idar lamba, lissafin lissafi , lissafi , ko aikin-ka'idar aiki ne ga mafi yawan marubuta kowane aiki f ( n ) wanda yankinsa shine ingantattun lambobi kuma wanda zangonsa ya zama gungun lambobin hadaddun. Hardy & Wright sun hada da ma'anar su cewa aikin lissafi "yana bayyana wasu kayan aikin lissafi na n ".
Aikin lissafi: A ka'idar lamba, lissafin lissafi , lissafi , ko aikin-ka'idar aiki ne ga mafi yawan marubuta kowane aiki f ( n ) wanda yankinsa shine ingantattun lambobi kuma wanda zangonsa ya zama gungun lambobin hadaddun. Hardy & Wright sun hada da ma'anar su cewa aikin lissafi "yana bayyana wasu kayan aikin lissafi na n ".
Tsarin lissafi: A cikin dabarun lissafi, tsarin lissafi, tsarin lissafi ko Kleene – Mostowski matsayi na tsara wasu saituna dangane da mawuyacin tsarin da ke ayyana su. Duk wani saiti da ya karɓi rarrabuwa ana kiran sa ilimin lissafi .
Arithmetic yana nufin: A lissafi da lissafi, lissafin ma'ana , ko kawai ma'ana ko matsakaita , shine jimlar tarin lambobi da aka rarraba ta ƙidayar lambobi a cikin tarin. Isarin tarin sau da yawa jeri ne na sakamakon gwaji ko binciken kulawa, ko akai-akai jerin sakamakon daga binciken. Kalmar "lissafin ma'anoni" an fifita a wasu wurare a cikin lissafi da lissafi, saboda yana taimakawa wajen bambance ta da wasu hanyoyi, kamar ma'anar lissafi da kuma jituwa.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Ci gaban lissafi: Ci gaban ilimin lissafi (AP) ko lissafin lissafi jerin lambobi ne domin banbanci tsakanin kalmomin da suke jeruwa mai dorewa ne. Misali, jerin 5, 7, 9, 11, 13, 15 ,. .. ci gaban lissafi ne tare da bambancin bambanci na 2.
Otonality da Utonality: Otonality da utonality kalmomi ne waɗanda Harry Partch ya gabatar don bayyana waƙoƙi waɗanda ajin karatun su ke da jituwa ko subharmonics na ingantaccen sautin (ainihi), bi da bi. Ga misali: 1/1, 2/1, 3/1, ... ko 1/1, 1/2, 1/3, .... Otonality shine saitin filayen da abubuwan lambobi suka ƙirƙira (... asalinsu ) ... sama da adadin lambobi a cikin adadi. Akasin haka, Utonality shine jujjuyawar Otonality, saitin filaye tare da adadin adadi a cikin lamba akan abubuwan lambobi ... a cikin adadi.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Tsarin lissafi: A cikin dabarun lissafi, tsarin lissafi, tsarin lissafi ko Kleene – Mostowski matsayi na tsara wasu saituna dangane da mawuyacin tsarin da ke ayyana su. Duk wani saiti da ya karɓi rarrabuwa ana kiran sa ilimin lissafi .
Ringididdigar lissafi: A cikin algebra, ana cewa ringin aiki na R ya zama lissafi ne idan ɗayan waɗannan daidaito masu zuwa sun riƙe: Yanayin gida na R a ringi ne mara sikila don kowane mafi girman manufa na R. Ga dukkan manufa , da , Ga dukkan manufa , da ,
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Koma lissafi: Karkataccen ilimin lissafi shiri ne a cikin ilimin lissafi wanda yake neman sanin wane yanki ake buƙata don tabbatar da ka'idojin ilimin lissafi. Ana iya bayyana ma'anar ma'anarta a taƙaice a matsayin "komawa baya daga ka'idoji zuwa axioms", ya bambanta da aikin lissafi na yau da kullun na samun ka'idoji daga axioms. Ana iya fahimtar dashi azaman sassaka yanayin dole daga wadatattu.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Ithididdigar lissafi: A cikin dabaru na lissafi, lissafin lissafi saiti ne na lambobin ƙasa waɗanda za a iya bayyana su ta hanyar tsarin tsari na farko na lissafin Peano. Setsididdigar lissafi ana rarraba su ta tsarin lissafi.
Dedekind zeta aiki: A cikin ilimin lissafi, aikin zed na Dedekind na lambar lambobin algebraic K , gabaɗaya ana nuna ζ K ( s ), cikakken bayani ne na aikin Riemann zeta. Ana iya bayyana shi azaman jerin Dirichlet, yana da faɗakarwar samfurin Euler, yana gamsar da daidaitaccen aiki, yana da ci gaba na nazari zuwa aikin meromorphic akan hadadden jirgin C tare da madaidaicin sanda a s = 1, kuma ƙimominsa suna ɓoyewa lissafin bayanan K. Fadada tunanin Riemann ya bayyana cewa idan ζ K ( s ) = 0 da 0 <Re ( s ) <1, to Re ( s ) = 1/2.
Ithididdigar lissafi, nova methodo exposita: Yarjejeniyar Arithmetices principia ta 1889 , nova methodo exposita ta Giuseppe Peano shine takaddar seminal a cikin ilimin lissafi da kuma ka'idar da aka kafa, gabatar da abin da yanzu shine daidaitaccen daidaitaccen lambobin halitta, wanda aka sani da Peano axioms, da kuma wasu sanannun sanarwa, kamar azaman alamomi don ayyukan saiti na asali ∈, ⊂, ∩, ∪, da A - B.
Ithididdigar lissafi, nova methodo exposita: Yarjejeniyar Arithmetices principia ta 1889 , nova methodo exposita ta Giuseppe Peano shine takaddar seminal a cikin ilimin lissafi da kuma ka'idar da aka kafa, gabatar da abin da yanzu shine daidaitaccen daidaitaccen lambobin halitta, wanda aka sani da Peano axioms, da kuma wasu sanannun sanarwa, kamar azaman alamomi don ayyukan saiti na asali ∈, ⊂, ∩, ∪, da A - B.
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Gasar Arts: Robert Recorde's Arithmetic: or, The Ground of Arts ya kasance ɗayan litattafan Turanci da aka fara bugawa akan lissafi kuma ya shahara a lokacinsa. The Ground of Arts ya bayyana a Landan a cikin 1543, kuma an sake buga shi kusa da ƙarin ƙarin 45 har zuwa 1700. Editoci da masu ba da gudummawa na sababbin sassan sun haɗa da John Dee, John Mellis, Robert Hartwell, Thomas Willsford, kuma a ƙarshe Edward Hatton.
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Arithmetico – lissafin lissafi: A lissafi, lissafin lissafin lissafin-lissafin sakamakon sakamako ne-zuwa-lokaci na ci gaban lissafi tare da daidaitattun ka'idojin ci gaban lissafi. Saka more fili, da n th lokaci na wani arithmetico-lissafi jerin ne samfurin na n th lokaci na wani ilmin lissafi sequenceand da n th lokaci na wani lissafi daya. Tsarin lissafi-geometric ya fito a aikace-aikace daban-daban, kamar ƙididdigar ƙimomin da ake tsammani a cikin ka'idar yiwuwar. Misali, jerin
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Lissafi-lissafi yana nufin: A lissafi, ma'anar lissafin-lissafin lambobi masu tabbatattun lambobi guda biyu x da y kamar haka:
Rashin daidaito na ilimin lissafi da na lissafi yana nufin: A lissafi, rashin daidaito na lissafi da tsarin lissafi , ko kuma a taƙaice rashin daidaito na AM-GM , ya bayyana cewa ma'anar lissafi na jerin lambobin lambobin da ba su da kyau sun fi girma ko daidaita da mahimmin lissafin lissafi iri ɗaya; kuma kuma, cewa hanyoyin biyu daidai suke idan kuma idan kowane lamba a cikin jerin iri daya ne.
Lissafi nufin: A ilimin lissafi, yanayin lissafin ma'ana yana nufin matsakaita ko matsakaici, wanda ke nuna halin tsakiya ko ƙimar yawan adadin lambobi ta hanyar amfani da ƙimar ƙimarsu. Ma'anar yanayin yanayi ana fassara shi azaman n asalin tushen lambobin n, ma'ana, don saitin lambobi x 1 , x 2 , ..., x n , ma'anar yanayin yanayi ana bayyana shi azaman
Ithungiyar ilimin lissafi: A cikin sarrafa kwamfuta, sashen ilimin lissafi (ALU) yanki ne na dijital mai haɗaka wanda ke aiwatar da lissafi da ƙaramin aiki akan lambobin binar lamba. Wannan ya bambanta da ɓangaren ma'amala (FPU), wanda ke aiki akan lambobin ma'amala. Babban ginshiki ne na nau'ikan da'idojin lissafi, gami da sashin sarrafawa na tsakiya (CPU) na kwmfutoci, FPUs, da kuma na'urorin sarrafa hotuna (GPUs)
Lissafi: Arithmetic wani reshe ne na lissafi wanda ya ƙunshi nazarin lambobi, musamman game da kaddarorin ayyukan gargajiya akan su - ƙari, ragi, narkarwa, rabewa, rabe-rabe da hakar asalinsu. Lissafin lissafi yanki ne na farko na ka'idar lamba, kuma ka'idar lamba ana daukarta daya daga cikin bangarorin ilimin lissafi na yau da kullun, tare da algebra, geometry, da kuma nazari. Anyi amfani da kalmomin lissafi da na lissafi mafi girma har zuwa farkon karni na 20 a matsayin masu kamanceceniya da lambar lamba , kuma wani lokacin har yanzu ana amfani dasu don koma zuwa wani bangare mafi yawa daga ka'idar lamba.
Arithmetization na bincike: Kirkirar lissafi na bincike wani shiri ne na bincike a ginshikan lissafi wanda aka gudanar a rabin rabin karni na 19.
Arithmetization na bincike: Kirkirar lissafi na bincike wani shiri ne na bincike a ginshikan lissafi wanda aka gudanar a rabin rabin karni na 19.
Arithmetization na bincike: Kirkirar lissafi na bincike wani shiri ne na bincike a ginshikan lissafi wanda aka gudanar a rabin rabin karni na 19.
Gödel's rashin cika ka'idoji: Ka'idojin rashin kammala Gödel ka'idoji ne guda biyu na dabarun lissafi wadanda suka shafi iyakantattun maganganu a ka'idoji na yau da kullun. Wadannan sakamakon, wadanda Kurt Gödel ya buga a 1931, suna da mahimmanci a dabaru na lissafi da kuma falsafar lissafi. Ka'idojin suna da yawa, amma ba ko'ina ba, fassara kamar yadda yake nuna cewa shirin Hilbert don samo cikakkun daidaitattun ka'idoji don duk ilimin lissafi bashi yiwuwa.
Arithmeum: Arithmeum gidan kayan gargajiya ne na lissafi mallakar Forschungsinstitut für Diskrete Mathematik a Jami'ar Bonn.
Arithmologia: Arithmologia, sive De Abditis Numerorum Mysteriis aiki ne na 1665 wanda masanin Jesuit Athanasius Kircher yayi. Varese ne ya buga shi, babban gidan buga takardu don tsarin Jesuit a Rome a tsakiyar karni na 17th. An sadaukar da shi ga Franz III. Nádasdy, wanda ya tuba zuwa Katolika wanda Kircher ya taɓa ba da gudummawa ga Oedipus Aegyptiacus . Arithmologia ita kaɗai ce daga cikin ayyukan Kircher wacce aka keɓe gaba ɗaya ga fannoni daban-daban na alamar lamba.
Numerology: Numerology ita ce imani da dangantaka ta allahntaka ko ta sihiri tsakanin lamba da abubuwa ɗaya ko fiye da suka dace. Hakanan karatun darajan lambobi ne na kalmomi, sunaye, da ra'ayoyi. Yana yawanci hade da paranormal, dab da astrology kuma yayi kama da zane-zane.
Rithmomachy: Rithmomachy wasa ne mai matukar rikitarwa, farkon wasan wasan lissafi na Turai. Bayanin farko da aka sani game da shi ya samo asali ne daga karni na sha ɗaya. Harshen fassarar sunan shine "Yakin Lambobi". Wasan yana da yawa kamar dara, sai dai yawancin hanyoyin kamawa sun dogara da lambobin da aka rubuta akan kowane yanki.
Arithmancy: A cikin kalmomin adadi na zamani, ilimin lissafi wani nau'i ne na duba wanda ya danganta da sanya lamba ta lamba ga wata kalma ko jumla, ta hanyar sauƙaƙan sigar isopsephy ta d ancient a ko Ibrananci / Aramaic gematria, kamar yadda ya dace da harafin Latin. Arithmancy yana da alaƙa da Kaldiyawa, Plato, Pythagoreans, da Kabbalah. Lokacin da aka yi amfani da ilimin lissafi ga sunan mutum, yana da nau'i na onomancy.
Arithmomania: Arithmomania cuta ce ta ƙwaƙwalwa wanda za'a iya gani azaman bayyanar cuta mai rikitarwa (OCD). Mutanen da ke fama da wannan cuta suna da ƙaƙƙarfan buƙata don ƙididdige ayyukansu ko abubuwa a cikin kewayen su.
Arithmomania: Arithmomania cuta ce ta ƙwaƙwalwa wanda za'a iya gani azaman bayyanar cuta mai rikitarwa (OCD). Mutanen da ke fama da wannan cuta suna da ƙaƙƙarfan buƙata don ƙididdige ayyukansu ko abubuwa a cikin kewayen su.
Lissafin mita: Arithmometer ko Arithmomètre shine farkon ƙididdigar injiniyar dijital mai ƙarfi mai ƙarfi kuma amintacce wanda za'a iya amfani dashi yau da kullun a cikin ofis. Wannan kalkuleta na iya ƙarawa da kuma cire lambobi biyu kai tsaye kuma zai iya yin ninkin baƙala da rarrabuwa yadda ya kamata ta amfani da mai tara motsi don sakamakon.