Ingxaki Combinatorial. Iingxaki ezilula combinatorial. Iingxaki Combinatorial: Imizekelo

Ootitshala bemathematika balazi abafundi babo ingcamango "ingxaki combinatorial" isekhona kwibakala yesihlanu. Oku kuyimfuneko ukuqinisekisa ukuba bakwazi ukuqhubeka ukusebenza imisebenzi enzima kakhulu. Phantsi ingxaki combinatorial nga kuthakazelelwa kakhulu ithuba lokuba ukusisombulula ngokusebenzisa yokulungisa izinto iseti ezisikelwe.

Uphawu engundoqo iingxaki yalo myalelo umbuzo kubo, nto leyo iyalila "Cebo liphi na endingalikhetha?" Okanye "Zingaphi iindlela?" Iingxaki Combinatorial kuxhomekeke ukuba okanye hayi uzisombulule intsingiselo kakuhle, ukuba wakwazi ukumela ngokuchanekileyo intshukumo okanye inkqubo iye yachazwa lo msebenzi.

Indlela yokusombulula ingxaki combinatorial?

Kubalulekile ukuchonga ngokuchanekileyo uhlobo zonke unxibelelwano ezikhoyo kule ngxaki, kodwa kuyimfuneko ukuhlola enoba uza kuphinda izinto ukuba izibonelelo ngokwazo ukutshintsha ukuba indima enkulu idlalwa odolo zazo, kwakunye nezinye izinto.

Ingxaki combinatorial anokuba eziliqela nemida na kubekwa ezimbaxa. Kulo mzekelo, kuya kufuneka ukuba babale bonke isigqibo sakhe ukujonga, ingaba ezi zithintelo unayo nayiphi na impembelelo ukudityaniswa onke amacandelo. Ukuba isiphumo ngenene apho, kufuneka ukhangele ukuba yintoni na.

ukuqala phi?

Okokuqala kufuneka sifunde ukusombulula iingxaki sabaqalayo combinatorial. Wabagagamela izinto ezilula ukuvumela ukuba sifunde ukuqonda imisebenzi enzima kakhulu. Sicebisa ukuba uqale ukusombulula le ngxaki kunye nemiqobo ukuba azithathelwa ngqalelo xa ukhetho elula ngakumbi.

Kukwacetyiswa kwakhona ukuba ukuzama ukusombulula loo ngxaki kuqala, apho kufanele kuqwalaselwe inani elincinci izinto ezifanayo. Ukuze uqonde umgaqo wokudala eesampuli ukufunda kwixesha elizayo ngokwabo ukuba ukudala kubo. Ukuba umsebenzi apho imfuneko yokusebenzisa combinatorial siqulathe indibanisela, kucetyiswa eziliqela elula ukusombulula kuyo iindawo.

iingxaki Combinatorial

iingxaki ezinjalo inokubonakala elula isigqibo, kodwa combinatorics kakhulu nzima ukuphuhlisa, ezinye zazo musani ukuba isisombululo kule minyaka ilikhulu idlulileyo. Omnye wemisebenzi ezigqamileyo kukuqinisekisa inani izikwere magic ye inkqubo ekhethekileyo apho inani le n mkhulu kuno-4.

ingxaki Combinatorial izalana ngokusondeleyo kwithiyori lilonke, owayebonakele kumaxesha aphakathi. Amathuba imvelaphi isiganeko othile ibalwe kuphela ukusetyenziswa combinatorics, kulo mzekelo kuya kufuneka alternate phakathi zonke izinto kwezinye iindawo ukufumana isisombululo kangangoko.

Ukwanelisa mngeni

iingxaki Combinatorial ngesisombululo ezisetyenziselwa ekuqeqesheni abafundi kunye abafundi ukuba basebenze ngale nto. Xa sithetha nje ngokubanzi, kufuneka benze umntu umdla nomnqweno ukufumana isisombululo esifanayo. Ukongeza izibalo, kuyimfuneko ukuba basebenzise ntshikilelo engqondweni kwaye usebenzise uqikelelo.

Xa inkqubo yokusombulula iingxaki umntwana lowo uya kuba nakho ukuphuhlisa ukucamanga kwabo kunye nesikhundla imathematika combinatorial, kusenokuba nzulu kuba luncedo kuye kwixesha elizayo. Ngokuthe ngcembe, izinga mbaxa imisebenzi ekufuneka uphucule, ukuba umlibale ulwazi ekhoyo ongeze kuwo.

Indlela 1. Iterate

Zokufuya zokusombulula iingxaki combinatorial zahlukile kakhulu enye kwenye, kodwa ingasetyenziswa impendulo umfundi. Omnye umsebenzi olula, kodwa ngaxeshanye kunye ndlela inde ukuya umhlola. Xa kuyimfuneko ukuzama nje zonke izisombululo kunokwenzeka ngaphandle kokwenza nayiphi na imizobo kunye neetafile.

Njengoko umthetho, lo mbuzo ingxaki enjalo enxulumene iinketho imvelaphi isiganeko esithile, ezifana: yintoni amanani nga kuyilwa ngamanani-2, 4, 8, 9? Ngokuzama zonke iinketho zabuya impendulo eyenziwa lwendibaniso ezenzekayo. Loo ndlela efanelekileyo ukuba inani iinketho lincinane kakhulu.

2. Indlela Mthi lwalo

Ezinye iingxaki combinatorial ingasombululwa kuphela ngokwenza icebo, apho ulwazi malunga into nganye iya kudweliswa ngokweenkcukacha. Ukuzoba up Bungumthi iinketho - ngenye indlela ukuze ufumane impendulo. Kufanelekile ukuba izisombululo hayi imisebenzi enzima kakhulu, apho kukho imeko olongezelelweyo.

Umzekelo le ngxaki:

• Yintoni amanani anomvo ezintlanu ukuze kwakheke dijithi 0, 1, 7, 8? Ukusombulula imfuneko ukwakha ngumthi zonke lwendibaniso ezenzekayo, ngoxa kukho imeko olongezelelweyo - inani ayikwazi ukuqala ukusuka ekuqaleni. Ngoko ke, impendulo iya kuqulatha onke amanani eziza kuqala ngo-1, 7 okanye 8.

Formation Indlela iitafile 3

iingxaki Combinatorial zingenziwa ngokusebenzisa ezitafileni. Bafana ukuya umthi iinketho kuba inikeza isisombululo icace le meko. Ukuze ufumane impendulo eyiyo ufuna ukwenza itafile, kwaye oko kuya weempawu oxwesileyo kunye neemeko nkqo ziyafana.

iimpendulo kunokwenzeka ziya zingafumaneka ekudibaneni lwemihlathi kunye imikrozo. Kulo mzekelo, iimpendulo ukuya kuhlangana nekholam nakuluhlu abayi kufumana iinkcukacha ezifanayo, ekudibaneni kufuneka ingakumbi uphawu, ukuba mazingabhidaniswa ekwenzeni impendulo lokugqibela. Olu hlobo rhoqo kakhulu ukukhetha abafundi, abaninzi bakhetha umthi kunye iinketho.

Indlela 4. Multiplication

Kukho nenye indlela apho ukusombulula iingxaki combinatorial - umthetho-phindo. Yena ugqibelele kwimeko, xa imeko akuyomfuneko ukuba udwelise zonke izisombululo kunokwenzeka, wena nje kufuneka bafumane inani eliphezulu. Le ndlela nguye kuphela ngohlobo lwayo, isetyenziswa rhoqo kakhulu, xa uqala nje ukusombulula iingxaki combinatorial.

Umzekelo le ngxaki ukuze kwenziwe ngolu hlobo lulandelayo:

• abantu 6 balindele kwiholo leemviwo le. Zingaphi iindlela zingasetyenziswa ukubeka kubo kuluhlu? Kuba Phendula kuyimfuneko ukuba ucacise ukuba bangaphi kubo kuba ngabokuqala, kodwa ngomhla wesibini, nowesithathu, njalo njalo. D. Impendulo iya kuba inombolo 720.

Combinatorics neentlobo zayo

ingxaki Combinatorial ayikho izixhobo zezikolo kuphela, abafundi baseyunivesithi nabo ukufunda kuyo. Ngesayensi, kukho iindidi ezininzi combinatorics, yaye ngamnye kubo injongo yayo. lokufaka Combinatorial kufuneka siqwalasele iingxaki kwi ukhutshelo ubalo sisimo kunokwenzeka kunye neemeko ezongezelelweyo.

combinatorics zolwakhiwo njengenxalenye yenkqubo high school, oko uhlolisisa le ngcamango matroids kunye neegrafu. combinatorics kakhulu kwakhona inento yokwenza izinto high school, yaye naba umda wabo. Enye candelo - ingcamango Ramsey kufundwa lweepateni kwiiyantlukwano random lweziqalelo. Kukho kwakhona combinatorics olumnandi, nto leyo liqwalasela lo zokungahambisani izinto ezithile phakathi kwabo.

Iindlela zokufundisa iingxaki combinatorial

Ngokutsho kwikharityhulam, ubudala babafundi, nto leyo yenzelwe kwabazana lokuqala kunye ezo zinto zifundwayo kunye nokusombulula ingxaki combinatorial - class 5. Kwaba apho okokuqala esi sihloko okunikelwa abafundi, ukuba uqhelane kunye mkhuba combinatorial kwaye uzame ukusombulula imisebenzi yabo. Kubaluleke kakhulu ukuba indlela ezisetyenziswa kuqulunqo ingxaki combinatorial xa abantwana bekwi ukufumana iimpendulo kwimibuzo.

Phakathi kwezinye izinto, emva kokufunda esi sihloko kuya kuba lula kakhulu ukwazisa isigama impembelelo kwaye usebenzise yona ukuxazulula zibalo, imisebenzi njalo njalo. Ngoko ke, combinatorial ludlala indima ebalulekileyo kwimfundo eqhubekayo.

iingxaki Combinatorial: ntoni na bona?

Ukuba uyazi ukuba kukho iingxaki combinatorial, akukho ubunzima kunye isigqibo sabo nawe uya kufumana. Iindlela zokusombulula ngazo kungaba luncedo, ukuba kuyimfuneko, ukuhlela, iishedyuli zomsebenzi, kwakunye izibalo ezintsonkothileyo izibalo, kuba apho intsebenzo ayikho izixhobo ezifanelekileyo ze-elektroniki.

Kwizikolo olunzulu ukufunda imathematika nenzululwazi yekhompyutha iingxaki combinatorial zihlolisiswe ngakumbi, kuba oko okhethekileyo izifundo, iincwadi, kunye nemisebenzi. Njengomgaqo, ezininzi iingxaki olu hlobo kunokuba ube yinxalenye yale loviwo karhulumente elimanyeneyo zemathematika, zisoloko "ezifihliweyo" in Part C.

Indlela yokusombulula ingxaki combinatorial ngokukhawuleza?

Kubalulekile ukuba umntu akwazi ukubona ingxaki combinatorial ngokukhawuleza, ekubeni ukuba nesigqubuthelo amagama, kubaluleke ngakumbi xa uthatha uviwo, apho zonke ukubalwa ngomzuzu. Bhala zodwa ulwazi ozibona kwisicatshulwa ingxaki, kwi iphepha, uze uzame ukuhlalutya ukusuka kwindawo ngenxa yeendlela ezine odumileyo.

Ukuba uyakwazi ukubeka ulwazi ngendlela spreadsheet okanye elinye iqumrhu, zama ukuyisombulula ngayo. Ukuba hlela nto, wena awukwazi, kule meko kungcono uzakuwushiya ixesha elifutshane badlulele kwezinye imisebenzi, ukuze bachithe ixesha ezixabisekileyo. Le meko inokuphetshwa kwangaphambili poreshat mali ethile le hlobo ngxaki.

ndokufunela phi eminye imizekelo?

Inye kuphela eya kukunceda ufunde indlela yokucombulula iingxaki combinatorial - imizekelo. Ukuba inokufumaneka ngokuqokelela ezizodwa zemathematika, ezo zithengiswa ezivenkileni iincwadi zemfundo. Noko ke, kukho ingafunyanwa ulwazi kuphela kubafundi bezikolo zamabanga aphakamileyo, abafundi kuya kufuneka ukuba afumane imisebenzi eyongezelelweyo zithande ukuba owasungula umsebenzi bonke ootitshala.

oonjingalwazi University bakholelwa ukuba abafundi kufuneka baqeqeshe kwaye ngamaxesha onke kuzo iincwadi zokufundisa ezongezelelweyo. Enye yeengqokelela best njenge 'Iindlela Uhlalutyo ngokuqhubekayo ekucombululeni iingxaki combinatorial ", ebhalwe ngo-1977 iveliswayo ngokuphindaphindiweyo ekhokela nezindlu zokupapasha weli lizwe. Nantso loo apho unako ukufumana imisebenzi ezihambelana ngexesha size sihlale esemthethweni namhlanje.

Kufuneka wenze ntoni xa ufuna ukwenza ingxaki combinatorial?

Amaninzi umsebenzi combinatorial, kufuneka sibe ngabafundisi ekufuneka ukuba bafundise abafundi ukuba bacinge unconventionally. Apha yonke into iya kuxhomekeka amandla ezinobuchule umsunguli. Kucetyiswa ukuba anikele ingqalelo kwingqokelela ekhoyo uzame ukwenza lo msebenzi ukuze luhlanganisa iindlela ezininzi zokusombulula kuyo, yaye yayahlukile data ncwadi.

ootitshala University kule nkalo sikolo ethe kakhulu, bona zisoloko abafundi yam ukuza umsebenzi yi iingxaki combinatorial kunye nezisombululo eneenkcukacha neengcaciso iindlela. Ukuba akukho mntu okanye omnye, uyakwazi ukucela uncedo oluvela kwabo ngokwenene ukwazi indawo, kwakunye okuqesha komfundisi labucala. Enye iyure academic kwanele ukudala imisebenzi emininzi efanayo.

Combinatorics - inzululwazi elizayo?

Iingcali ezininzi endle yemathematika kunye zemvelo bakholelwa ukuba ingxaki combinatorial isekude uphuhliso Sciences zobugcisa. Kwanele ukuba indlela non-eqhelekileyo ukuba isisombululo ezinye iingxaki, ze emva koko uphendule imibuzo kakade kwiinkulungwane eziliqela ethandwa izazinzulu. Abanye babo kakhulu agcine loo combinatorics sisixhobo yonke inzululwazi mihla, ingakumbi ukuhambahamba esibhakabhakeni. Kulula kakhulu ukuba ukubala isikhokelo yeflayithi iinqanawa usebenzisa iingxaki combinatorial, njengoko iya kuqinisekisa indawo ngqo izidumbu ezithile yasezulwini.

Ukuphunyezwa kwe Indlela non-standard sele kudala iqalile kumazwe aseAsia, apho abafundi nokuba imisebenzi esisiseko-phindo, ukuthabatha, ukudibanisa neyantlukwano isigqibo ngokusebenzisa iindlela combinatorial. Ukuze ukumangala izazinzulu ezininzi eYurophu, le ndlela iyasebenza ngokwenene na. Izikolo yaseYurophu ukuza kuthi ga ngoku uqalisile kuphela ukufunda namava abalingane babo. Xa combinatorics abe ngomnye amasebe eziphambili nemathematika, ukuba bathwale nzima. Ngoku isayensi ufundwa zizazinzulu aphambili ehlabathini abafuna yazi loo nto.