Imibare
nigice cyubumenyi gikubiyemo ingingo zimibare, formula nuburyo bujyanye, imiterere numwanya urimo, numubare nimpinduka zabo. Izi nsanganyamatsiko zigaragara mu mibare igezweho hamwe n’ibice byingenzi by’imibare y’imibare, [1] algebra, [2] geometrie, [1] nisesengura, [3] [4]. Nta bwumvikane rusange mubibare bujyanye nibisobanuro rusange kubijyanye na disipuline yabo. Ibikorwa byinshi byimibare birimo kuvumbura imitungo yibintu bidafatika no gukoresha impamvu zifatika zo kubigaragaza. Ibi bintu bigizwe no gukuramo ibintu biva muri kamere cyangwa - mu mibare igezweho - ibice biteganijwe kugira imitungo runaka, bita axioms. Icyemezo kigizwe nuruhererekane rwo gukurikiza amategeko agabanya ibisubizo bimaze gushingwa. Ibisubizo birimo ibitekerezo byerekanwe mbere, axiom, kandi-mugihe habaye gukuramo ibidukikije - ibintu bimwe na bimwe by'ibanze bifatwa nk'intangiriro nyayo y'igitekerezo kirimo gusuzumwa. Imibare ni ngombwa muri siyansi karemano, ubwubatsi, ubuvuzi, imari, ubumenyi bwa mudasobwa n'ubumenyi mbonezamubano. Nubwo imibare ikoreshwa cyane mugushushanya ibintu, ukuri shingiro kwimibare ntigutandukanye nubushakashatsi ubwo aribwo bwose. Ibice bimwe byimibare, nkibarurishamibare hamwe nimikino yimikino, byatejwe imbere bifitanye isano rya hafi nibisabwa kandi akenshi bishyirwa hamwe mubibare byakoreshejwe. Ibindi bice byatejwe imbere byigenga bivuye mubikorwa ibyo aribyo byose (kandi byitwa imibare itanduye), ariko akenshi bigasanga mubikorwa bifatika. [6] Ikibazo cyo kwishyiriraho integer, kurugero, rusubira muri Euclid muri 300 mbere ya Yesu, ntabwo cyari gifite gahunda ifatika mbere yo gukoreshwa muri cryptosystem ya RSA, ubu ikoreshwa cyane mumutekano wurubuga rwa mudasobwa. Mu mateka, igitekerezo cyo guhamya hamwe n’imibare ifitanye isano n’imibare yagaragaye bwa mbere mu mibare y’ikigereki, cyane cyane mu bice bya Euclid. Kuva yatangira, imibare yagabanijwemo geometrie na arithmetic (manipulation yimibare isanzwe nuduce), kugeza mu kinyejana cya 16 na 17, igihe algebra [a] na calculus itagira ingano yatangijwe nkibice bishya. Kuva icyo gihe, imikoranire hagati yimibare mibare nubuvumbuzi bwa siyansi yatumye ubwiyongere bwihuse bwiterambere ryiterambere ryombi. Mu mpera z'ikinyejana cya 19, ikibazo cy'ifatizo cy'imibare cyatumye habaho uburyo bwa axiomatic, [10] bwatangaje ko ubwiyongere bukabije bw’imibare y’imibare n’imirima yabo ikoreshwa. Imibare Yibihe Byibihe Byiciro Urutonde rurenga 60 murwego rwa mbere rwimibare. Etymology Ijambo imibare rikomoka mu kigereki cya kera máthēma (μάθημα), risobanura "icyigishijwe", [11] "icyo umuntu amenya", bityo rero "kwiga" na "siyanse". Ijambo ryaje kugira ibisobanuro bigufi kandi byinshi bya tekinike y "kwiga imibare" no mubihe bya kera. Inshinga yacyo ni mathēmatikós (μαθηματικός), bisobanura "bijyanye no kwiga" cyangwa "umunyeshuri", ari nako yaje gusobanura "imibare". By'umwihariko, mathēmatikḗ tékhnē (μαθηματικὴ τέχνη; Ikilatini: ars mathica) bisobanura "ubuhanzi bw'imibare". [11] Mu buryo nk'ubwo, rimwe mu mashuri abiri y'ingenzi yatekerezaga muri Pythagoreanism yari azwi ku mibareēmatikoi (μαθηματικοί) - icyo gihe icyo gihe cyasobanuraga "abiga" aho kuba "imibare" mu buryo bwa none. Pythagoreans birashoboka ko abambere babujije gukoresha ijambo kugirango bige gusa imibare na geometrie. Mugihe cya Aristote (384–322 mbere ya Yesu) ubu busobanuro bwarashizweho neza. Mu kilatini, no mu Cyongereza kugeza ahagana mu 1700, ijambo imibare ryakunze gusobanura "inyenyeri" (cyangwa rimwe na rimwe "inyenyeri") aho kuvuga "imibare"; ibisobanuro byahindutse buhoro buhoro kugeza ubu kuva nko mu 1500 kugeza 1800. Iri hinduka ryatumye abantu benshi batavuga rumwe: Urugero, umuburo wa Mutagatifu Agusitini uvuga ko abakristo bagomba kwirinda imibare, bisobanura "abaragurisha inyenyeri", rimwe na rimwe ntibisobanurwa nabi nko kwamagana imibare. 15] Imiterere igaragara mu Cyongereza isubira mu kilatini neuter plural mathica (Cicero), ishingiye ku kigereki cyinshi ta mathēmatiká (τὰ μαθηματικά) kandi isobanura "ibintu byose imibare", nubwo bishoboka ko icyongereza cyatijwe gusa inyito y'imibare (( al) maze akora izina imibare mishya, nyuma yuburyo bwa fiziki na metafizika, twarazwe mu kigereki. Mu cyongereza, izina imibare rifata inshinga imwe. Bikunze kugabanywa kubiharuro cyangwa, muri Amerika ya ruguru, imibare. Ibice by'imibare Mbere yubuzima bushya, imibare yagabanyijwemo ibice bibiri byingenzi: imibare - yerekeranye no gukoresha imibare, na geometrie, bijyanye no kwiga imiterere. Ubwoko bumwebumwe bwa pseudoscience, nka numerologiya na astrologiya, ntabwo noneho byari bitandukanye cyane n'imibare. Mugihe cya Renaissance, hagaragaye utundi turere tubiri . Imibare yerekana imibare iganisha kuri algebra, tuvuze hafi, igizwe nubushakashatsi hamwe no gukoresha formulaire. Ibara, rigizwe nubutaka bubiri butandukanye butandukanye hamwe na calculus yuzuye, ni ubushakashatsi bwibikorwa bikomeza, byerekana ubusanzwe umubano utari umurongo hagati yubwinshi butandukanye, nkuko bigaragazwa nimpinduka. Iri gabana mu bice bine by'ingenzi - imibare, geometrie, algebra, calculus [20] - byakomeje kugeza mu mpera z'ikinyejana cya 19. Ibice nkubukanishi bwo mwijuru hamwe nubukanishi bukomeye noneho bigishijwe nabashinzwe imibare, ariko ubu bifatwa nkibya fiziki. Isomo rya combinatorics ryizwe mu mateka menshi yanditswe, nyamara ntiryabaye ishami ryihariye ry’imibare kugeza mu kinyejana cya cumi na karindwi.