Umsebenzi inkolelo-mbono yokuziphendukela okungenzeka nge isinqumo. Okungenzeka Theory ngoba Dummies

Mathematics Yiqiniso ulungisa abafundi eziningi lezimanga, enye yazo - kungumsebenzi imfundiso yokuziphendukela okungenzeka. Nge isinqumo imisebenzi enjalo abafundi kunenkinga cishe sasiyikhulu namashumi amaphesenti isikhathi. Ukuze uqonde futhi ukuqonda lo mbuzo, kumelwe wazi imithetho eyisisekelo, axioms, izincazelo. Ukuze uqonde umbhalo encwadini, odinga ukukwazi wonke ukusikeka. thina Konke lokhu ukuphakamisa ukufunda.

Isayensi uhlelo lwayo lokusebenza

Njengoba sinikela isifundo sokusaphazeka "Theory ka Okungenzeka For Dummies", kufanele uqale ufake nemiqondo eyisisekelo kanye incwadi izifinyezo. Ukuze uqale ukuchaza umqondo "okungenzeka theory". Hlobo luni isayensi ikuphi yona? Okungenzeka theory - ke ingenye amagatsha wezibalo ukuthi etadisha imihlola kanye namagugu okungahleliwe. Wabuye uhlola amaphethini, properties kanye imisebenzi eyenziwa nalezi eziguquguqukayo okungahleliwe. Kuqakatheke ngani? isayensi Yande kwaba ekuhloleni zemvelo. Noma yimuphi ezingokwemvelo nasezintweni esiwabona ngamehlo ngeke akwazi ukukwenza ngaphandle kobukhona randomness. Ngisho noma ngesikhathi sokuhlolwa zalotshwa ngokunembe ngangokunokwenzeka imiphumela, uma okuphindaphindiwe test efanayo awokuthi umphumela ngeke kuphinde kube njengasekuqaleni.

Izibonelo zezinkinga e okungenzeka theory sizocabangela ukuthi ungabona ngokwakho. Umphumela kuxhomeke ezicini eziningi ezahlukene, okuyizinto cishe akunakwenzeka ukuba acabangele noma ukubhalisa, kodwa nokho banayo umthelela omkhulu umphumela isilingo. izibonelo Obvious kukhona inkinga yokunquma trajectory amaplanethi noma ukuzimisela isimo sezulu, ematfuba kokuhlangana omjwayele endleleni ukusebenza nokuzimisela ukuphakama umsubathi gxuma. Libuye imfundiso yokuziphendukela Kungenzeka ukusizwa kakhulu wabathengi kwi isitokwe Ukuhwebelana. Umsebenzi inkolelo-mbono yokuziphendukela okungenzeka, isinqumo elalikade kwadingeka izinkinga eziningi kuyoba ngawe trifle yangempela emva izibonelo ezintathu noma ezine ngezansi.

imicimbi

Njengoba kushiwo ngaphambili, isayensi uyafundelwa izenzakalo. Okungenzeka theory, izibonelo ekuxazululeni izinkinga, sizocabangela kamuva, uhlobo oluthanda ukutadisha eyodwa kuphela - okungahleliwe. Noma kunjalo, kumelwe wazi ukuthi izenzakalo kungaba izinhlobo ezintathu:

• Akunakwenzeka.
• Esinokwethenjelwa.
• Okungahleliwe.

Sinikeza kancane liyasho ngamunye wabo. umcimbi Impossible akusoze kwenzeke ngaphansi kwanoma yiziphi izimo. Izibonelo: okokuqandisa yamanzi ezingeni lokushisa ngenhla zero Extruding cube isikhwama amabhola.

umcimbi ezithile kuthatha njalo indawo ngesiqinisekiso ngokuphelele, uma zonke izimo. Ngokwesibonelo, oyitholile inkokhelo ngomsebenzi wabo, wathola i-diploma ye-ephakeme imfundo professional, uma wafunda ngokwethembeka, wadlula ezivivinyweni wasivikela idiploma zabo nokunye.

Nge zenzakalo ezivele zenzeke nje kancane more xaka: ngokuhamba ukuhlola, kungase kwenzeke noma cha, isibonelo, ukudonsa ace kusukela emphemeni ikhadi, ngokwenza enkulu yemizamo ezintathu. Umphumela ingatholakala nge umzamo wokuqala, futhi ngakho, ngokuvamile, akusho ukuthola. Kungenzeka umsuka umcimbi futhi efunda ngesayensi.

Amathuba

Kuvamise ukuhlola kungenzeka ukuthi lokhu kwakuyoba nomphumela ngempumelelo isipiliyoni, lapho umcimbi kwenzeka. Amathuba Kulinganiselwa ezingeni qualitative, ikakhulukazi uma ukuhlolwa ambalwa noma okunzima. Umsebenzi inkolelo-mbono yokuziphendukela okungenzeka nge isinqumo, noma kunalokho ne nokuhlolwa Amathuba umcimbi, kusho lokuthola isabelo kungenzeka kakhulu ukuthi lokhu kwakuyoba nomphumela ngempumelelo. Okungenzeka mathematics - a izici zezinombolo lomcimbi. Kuthatha amanani asuka zero komunye, okhonjiswe incwadi P. Uma P kulingana zero, lo mcimbi awukwazi zenzeka uma iyunithi, umcimbi kuyokwenzeka nge okungenzeka ngokuphelele. I P ngaphezulu osondela ubunye, namandla amathuba okuba umphumela ube yimpumelelo, futhi okuphambene nalokho, uma iseduze zero, kanye umcimbi kuzokwenzeka nge okungenzeka ongaphakeme.

izifinyezo

Umsebenzi inkolelo-mbono yokuziphendukela okungenzeka, nge isinqumo okuyinto uzohlangana ngokushesha, ingase iqukathe nezifinyezo ezilandelayo:

• !;
• {};
• N;
• P no P (X);
• A, B, C, njll .;
• n;
• m.

Kukhona ezinye abanye: I-echaza zizokwenziwa esidingekile. Siphakamisa ukuba siqale, ukuchaza ukunciphisa ethulwa ngenhla. Okokuqala kuhla lwethu itholakala ngokwesimo. Ukuze kucace, sikunikeza izibonelo: 5 = 1 * 2 * 3 * 4 * 5 noma 3 = 1 * 2 * 3 !. Ngaphezu kwalokho, e-besokunxele babhala predetermined sebuningini, isibonelo {1; 2; 3; 4; ..; n} noma {10; 140; 400; 562}. I notation ezilandelayo - iqoqo izinombolo zemvelo akuve kuvamile ukuba imisebenzi kwemfundiso yokuziphendukela okungenzeka. Njengoba kushiwo ngaphambili, P - iyona amathuba, kanye P (X) - kuyinto ematfuba izenzakalo umcimbi nesenzakalo H. zamagama latin ezikhonjiswe, isibonelo: A - wabanjwa ezimhlophe ibhola B - blue, C - abomvu noma, ngokulandelana ,. incwadi Small n - inombolo yonkhe imiphumela kungenzeka, futhi m - nenani acebile. Ngakho, senza ukuthola umthetho classical lokuthola okungenzeka imisebenzi aphansi: F = m / n. Imfundiso yokuziphendukela okungenzeka "ngoba Dummies", cishe, futhi kungagcini ulwazi. Manje ukuze uvikele kwathatha isixazululo.

Inkinga 1. Combinatorics

Student Iqembu enezisebenzi amathathu, zazo kumelwe ukhethe umdala, iPhini lakhe futhi ongumphathi esitolo. Udinga ukuthola izindlela eziningi ukwenza lesi senzo. isabelo esinjalo kungaba senziwe uzihlole. Theory ecatshangelwayo, ukuthi imisebenzi manje izincwadi esizifundayo, kungafaka phakathi imisebenzi enkambweni combinatorics, Amathuba okuthola a classic, Jomethri nalabo nezinjongo ifomula eziyisisekelo. Kulesi sibonelo, thina ukuxazulula umsebenzi combinatorics Yiqiniso. Thina uqhubekele isinqumo. Lo msebenzi ulula:

1. n1 = 30 - stewards kungenzeka leqembu umfundi;
2. n2 = 29 - labo kungathatha sephini;
3. n3 = abantu 28 ngokufaka isicelo esitolo umphathi.

Konke kumele ukwenze ukuthola okungcono lezinketho, okungukuthi wanda zonke izibalo. Ngenxa yalokho, sithola: 30 * 29 * 28 = 24360.

Lokhu kuyoba impendulo yalo mbuzo.

Inkinga 2. Hlela kabusha

Engqungqutheleni 6 ababambiqhaza, oda kunqunywa wawenzela inkatho. Sidinga ukuthola inombolo ongakhetha kungenzeka draw. Kulesi sibonelo, sicabangela permutation izici eziyisithupha, okungukuthi, sidinga ukuthola 6!

Isigaba ukusikeka sekushiwo, ukuthi kuyini nokuthi ukubala. Inani kuvela ukuthi kukhona 720 ongakhetha for the draw kukhona. Uma uthi nhlá, umsebenzi onzima kuyinto isixazululo mfushane kakhulu futhi elula. Lona umsebenzi ukuthi uhlola imfundiso yokuziphendukela okungenzeka. Indlela ukuxazulula izinkinga ezingeni eliphakeme, sizobe sibheke izibonelo ezilandelayo.

umsebenzi 3

Iqembu labafundi kusuka amadoda angamashumi amabili nanhlanu kufanele zihlukaniswe ngamaqembu amathathu nesithupha, ayisishiyagalolunye neshumi. Sine: n = 25, k = 3, n1 = 6, n2 = 9, n3 = 10. It uhlala ukuze kufakwe esikhundleni amagugu efanele ku-formula, sithola: N25 (6,9,10). Ngemva izibalo ezilula sithola impendulo - 16,360,143 800. Uma umsebenzi alisho ukuthi kubalulekile ukuthola isixazululo zezinombolo, singahlinzeka ke ngesimo amafakthoriyali.

umsebenzi 4

Abantu abathathu inombolo engaziwa komunye kuya kweyishumi. Thola ematfuba ukuthi umuntu ngeke kwalingana nenani. Okokuqala sidinga ukwazi inani yonkhe imiphumela - kulesi simo, inkulungwane, okungukuthi, okuyishumi degree lwesithathu. Manje sithola inani ongakhetha ezenza zigcwaliseka zonke izinombolo ezahlukene ukuthi wande kwabayishumi, ayisishiyagalolunye nesishiyagalombili. Lapho benza lezi zinombolo? Eyokuqala ecabanga izinombolo anakho eziyishumi ongakhetha, eyesibili eziyisishiyagalolunye, futhi eyesithathu ingakhetfwa kusukela eziyisishiyagalombili ezisele, ukuze uthole 720 ongakhetha kunokwenzeka. Njengoba siye kakade okukhulunywe ngazo ngenhla, bonke ezahlukeneyo 1000, futhi 720 ngaphandle ukuphindaphinda, Ngakho-ke, sinesithakazelo ekutheni lo 280. asele Manje sidinga ifomula lokuthola amathuba classical: P =. Sithole impendulo: 0,28.