Chiwerengero cha chiwerengero: chiphunzitso ndi kuchita

Pali malingaliro angapo a lingaliro la "nthano ya chiwerengero". Mmodzi wa iwo akunena kuti ili ndi gawo lapadera la masamu (kapena apamwamba masamu), omwe amaphunzira mwatsatanetsatane zolemba ndi zinthu zofanana nawo.

Tanthauzo lina limatanthawuza kuti gawo ili la masamu limaphunzira zolemba za manambala ndi khalidwe lawo mmadera osiyanasiyana.

Asayansi ena amakhulupirira kuti chiphunzitsocho ndi chachikulu kwambiri kotero kuti n'zosatheka kupereka tanthawuzo lake lenileni, koma ndikwanira kugawanika mu ziphunzitso zochepa zochepa.

Sizingatheke kukhazikitsa molondola pamene chiphunzitso cha nambala chinabadwa. Komabe, izi zakhazikitsidwa momveka bwino: pakuti lero, chakale kwambiri, koma osati chilemba chokhacho, chosonyeza chidwi cha anthu akale mwa chiwerengero cha manambala, ndi chidutswa chadothi chadothi la 1800 panthawi yathu ino. Mmenemo - nambala yambiri yotchedwa Pythagorean triples (chiwerengero cha chirengedwe), zambiri zomwe zimakhala ndi zizindikiro zisanu. Chiwerengero chachikulu cha triplelescho sichisankhira makina awo. Izi zikusonyeza kuti chidwi cha chiphunzitso cha nambala chinayambira, mwachiwonekere, kale kwambiri kuposa momwe poyamba ankaganizira ndi asayansi.

Anthu otchuka kwambiri popanga chiphunzitsochi ndi Pythagoreans Euclid ndi Diophantus, Amwenye a Aryabhata, Brahmagupta ndi Bhaskara omwe anakhalapo zaka za m'ma Ages, ngakhale pambuyo pake Fermat, Euler, Lagrange.

Kumayambiriro kwa zaka makumi awiri ndi makumi awiri, chiwerengero cha chiwerengero chinakopa chidwi cha masamu monga a Korkin, EI Zolotarev, AA Markov, BN Delone, DK Faddeev, IM Vinogradov, G Chophimba, A. Selberg.

Kukulitsa ndi kukulitsa chiwerengero ndi maphunziro a akatswiri a masamu, iwo adabweretsa chiphunzitsochi kumalo atsopano, apamwamba kwambiri, kuphatikizapo malo ambiri. Kufufuza kwakukulu ndi kufufuza umboni watsopano kunabweretsa mavuto atsopano, omwe ena sanaphunzirepo mpaka pano. Zotsegula ndizo: Lingaliro la Artin ponena za zopanda malire za malipiro apamwamba, funso la kuperewera kwa chiwerengero cha masewera, ndi ziphunzitso zina zambiri.

Mpaka pano, zigawo zazikulu, zogawanika ndi chiwerengero cha nambala, ndizo mfundo: zoyambirira, ziwerengero zazikulu, manambala osasinthasintha, owerengeka, algebraic.

Nthano yoyamba ya chiwerengero ikugwira ntchito yophunzira za integers, popanda kuphatikizapo njira ndi malingaliro ochokera ku zigawo zina za masamu. Nambala za Fibonacci, Fermat's theorem yaing'ono , ndiwo malingaliro ambiri, odziwika kwa ophunzira, kuchokera ku chiphunzitso ichi.

Chiphunzitso cha chiwerengero chachikulu (kapena Chilamulo Chachiwerengero Chachikulu) ndilo gawo la lingaliro lomwe lingathe kuwonetsa kuti chiwerengero cha masamu chimaimira zitsanzo zazikulu (mwachitsanzo, chiwerengero chachikulu) chili pafupi ndi chiyembekezero cha masamu (chomwe chimatchedwanso kuti chiphunzitso cha masamu) cha chitsanzo ichi pokhapokha ngati pali gawo lokhazikitsidwa.

Chiphunzitso cha mawerengero osasinthasintha, kugawa zochitika zonse kukhala zosakwanira, deterministic ndi zosasintha, amayesa kudziwa mwayi wa zosavuta zochitika ndi mwayi wa zovuta. Gawoli likuphatikizapo zinthu zomwe zimakhala zovomerezeka ndi zochitika zowonjezera. Kuwonetsa kwa maganizo (zomwe nthawi zambiri zimatchedwa Bayes formula), ndi zina zotero.

Kusanthula chiwerengero cha nambala, monga momveka kuchokera ku dzina lake, amagwiritsira ntchito njira ndi njira za masamu kuunika kuti aphunzire masamu ndi ziwerengero za masamu . Chimodzi mwazimene zikuluzikulu za chiphunzitso ichi ndi umboni wa theorem (kugwiritsira ntchito zovuta zowonongeka) ponena za kufalitsa manambala akuluakulu.

Chiwerengero cha algebraic chiwerengero chimagwira ntchito mwachindunji ndi manambala, mafananidwe awo (mwachitsanzo, algebraic manambala), amaphunzira chiphunzitso cha ogawa, magulu a cohomology, Dirichlet ntchito, ndi zina zotero.

Kuwonekera ndi kukula kwa chiphunzitso ichi kunayambitsa zaka mazana ambiri kuyesa kutsimikizira Fermat's theorem.

Mpaka zaka makumi awiri, chiwerengero cha nambala chidawerengedwa ngati sayansi yeniyeni, "luso lochokera ku masamu," lomwe linalibe ntchito yeniyeni kapena yogwiritsira ntchito. Masiku ano, makompyuta ake amagwiritsidwa ntchito pazithunzithunzi za cryptographic, powerengera njira za satellites ndi mapulogalamu apakati, pulogalamu. Economics, Finance, Science, Geology - Scientific zonsezi sizitheka lero popanda chiphunzitso cha manambala.