Umsebenzi thiyori amathuba kunye nesigqibo. Kwenzeke Theory for Dummies

Ikhosi Mathematics ulungiselela abafundi eninzi izimanga, enye yazo - Ngumsebenzi kwithiyori lilonke. Nesigqibo imisebenzi enjalo abafundi kukho ingxaki phantse ikhulu elinye ekhulwini ixesha. Ukuze siqonde kwaye ukuqonda lo mbuzo, kufuneka wazi ezingundoqo imithetho, elikuwo, iinkcazelo. Ukuze siyiqonde okubhaliweyo kule ncwadi, kufuneka wazi zonke ukucuthwa. Konke oku sicebisa ukuba sifunde.

Science and isicelo yayo

Ekubeni idini ikhosi crash "Theory of Ingqikelelo For Dummies", kufuneka kuqala ufake nezimaphambili ezingundoqo kunye nezishunqulelo ileta. Ukuqala ukuchaza ingcamango "theory lilonke". Loluphi uhlobo inzululwazi kwaye yintoni na ukuba? Kwenzeke theory - yenye amasebe yemathematika ukuba ufunda nesenzeko kunye nemilinganiselo random. Kwakhona uhlolisisa iipateni, iimpawu kunye nemisebenzi eyenziwa nezi variables random. Kutheni kuyimfuneko? isayensi kwande waba izifundo ngezenzeko zendalo. Naziphi na iinkqubo zendalo kunye emzimbeni akakwazi ukwenza ngaphandle phambi randomness. Nokuba phakathi nokuhlola zirekhodwe ngokuchanekileyo kangangoko kunokwenzeka iziphumo, ukuba waphinda uvavanyo efanayo kunye namathuba eliphezulu akayi kuba efanayo isiphumo.

Imizekelo iingxaki theory amathuba siza kuxubusha ukuba uyakwazi uzibonele ngokwakho. Isiphumo kuxhomekeke kwizinto ezininzi ezahlukeneyo, ezo kwakungenakwenzeka ukuba ukuthatha ingqalelo okanye irejista, kodwa kunjalo ke kuba negalelo elikhulu kwisiphumo nokuhlola. Imizekelo ezicacileyo zezona ngxaki yokufumanisa isikhokelo iiplanethi okanye ukumiselwa sezulu, amathuba ukuhlangana umhlobo endleleni eya emsebenzini kunye nokuzimisela ukuphakama njuze yemidlalo. Kwakhona imfundiso parameter na uncedo olukhulu abarhwebi kwi Stock Exchange. Umsebenzi kwengcamango ngokuqinisekileyo, ngaphambili iingxaki ezininzi ziya kuba wena akwazuza wokwenene emva ezintathu okanye ezine imizekelo ngezantsi isigqibo ngawo.

izenzakalo

Njengoko kuchaziwe ngaphambili, isayensi ukufunda iziganeko. theory kwenzeke, imizekelo iingxaki iingxaki, siza kuqwalasela kamva, ukufunda uhlobo olunye kuphela - ejikelezayo. Nakuba kunjalo, kufuneka wazi ukuba izenzakalo kube kweentlobo ezintathu:

• Ayinakwenzeka.
• Ezinokuthenjwa.
• Random.

Sinikezela kancinane zibeka ngamnye kubo. isiganeko Ayinakwenzeka soze kwenzeke phantsi kwazo naziphi na iimeko. Imizekelo: qhwa lamanzi lobushushu ngentla zero Extruding cube ibhegi iibhola.

isiganeko esithile kusoloko uthatha indawo ingqinisekiso, ukuba zonke iimeko. Umzekelo, nalamkelayo umvuzo ngomsebenzi wabo, wafumana idiploma yemfundo ephakamileyo umsebenzi, ukuba wafunda ngokuthembeka, abaphumelele iimviwo kwaye zikhuselwe idiploma yazo njalo njalo.

Nge iziganeko random isuntswana ezinobunzima: ebudeni olu lingelo, le nto inokwenzeka okanye hayi, umzekelo, ukutsala i-ACE evela ikhadi kumgangatho, ukwenza iinzame ezili ezintathu. Isiphumo zingafumaneka njengokuba kunye lilinge lokuqala, kwaye kunjalo, ngokubanzi, ukuba ningabi nakufumana nto noko. Kusenokwenzeka imvelaphi esi siganeko kwaye befunda ngenzululwazi.

Amathuba okuba

Oku ukuhlola ngokubanzi ithuba isiphumo ngempumelelo amava, apho kwenzeka isiganeko. Amathuba Kuqikelelwa kwinqanaba qualitative, ingakumbi xa uvavanyo oluninzi akunakwenzeka okanye enzima. Umsebenzi thiyori amathuba kunye isigqibo, okanye mandithi kunye uvavanyo amathuba isiganeko, kuthetha ukufumana isabelo isiphumo yimpumelelo kunokwenzeka kakhulu. Kwenzeke kwimathematika - kukho iimpawu ngamanani siganeko. Kuthatha amanani ukusuka kwiqanda ukuya kwenye, zibonakaliswe yileta P. Ukuba P ilingana zero, lo mcimbi ngeke kwenzeke ukuba i-unit, lo mcimbi uya kuqhubeka nge okuba epheleleyo. Le P ngaphezulu osondela umanyano, ngokuqina ukuba umntu ukuphumelela, kwaye vice versa, ukuba asondele zero, kwaye isiganeko siza kwenzeka kunye namathuba eliphantsi.

izifinyezo

Umsebenzi kwengcamango ngokuqinisekileyo, isigqibo oya nazo ngokukhawuleza, inokuba liqulathe izifinyezo zilandelayo:

• !;
• {};
• N;
• P kunye P (X);
• A, B, C, njl .;
• n;
• m.

Kukho ezinye abanye; ngokuba ingcaciso ezongezelelweyo ziya kwenziwa xa kuyimfuneko. Sicebisa ukuba siqale, chaza nokunciphisa uchazwe apha ngasentla. Okokuqala kuluhlu lwethu ufunyaniswe impembelelo. Ukuze ndiyibonakalalise, sinika imizekelo: 5 = 1 * 2 * 3 * 4 * 5 okanye 3 = 1 * 2 * 3 !. Ngaphezu koko, kwi braces engenakubhalwa kwangaphambili nobuninzi, umzekelo {1, 2, 3, 4; ..; n} okanye {10; 140; 400; 562}. Le notation ilandelayo - iseti yamanani zendalo kakhulu eqhelekileyo imisebenzi e-worldwork theory lilonke. Njengoko kuchaziwe ngaphambili, P - yindlela, kwaye P (X) - yindlela iziganeko isiganeko nasisihlo H. alphabet latin zibonakaliswe, umzekelo: A - ukubanjwa emhlophe ibhola B - oluhlaza, C - ebomvu okanye, ngokulandelelana ,. Small incwadi n - linani zonke iziphumo kunokwenzeka, kwaye m - inani ithengiswayo. Ngenxa yoko, nathi ukufumana ulawulo ezivunywa ekufumaneni amathuba lwemisebenzi nezakhiwo: F = m / n. Ithiyori kungenzeka "for Dummies", mhlawumbi, kwaye kuphela ulwazi. Ke kaloku, ukuze kukhuselwe kwinguqu esa isisombululo.

Ingxaki 1. Combinatorics

Group Student iqeshe abantu abangamashumi amathathu, apho kufuneka ukhethe i enkulu, isekela lakhe indlamafa evenkileni. Kufuneka ufumane eziliqela iindlela zokwenza oku. Loo isabelo kunokwenzeka uzihlole. Theory of kungenzeka, ukuba imisebenzi ngoku ucinga, kungaquka imisebenzi kwikhondo combinatorics, kungenzeka ukufumana i yamandulo, zejometri kunye neenjongo le formula esisiseko. Kulo mzekelo, siya ukucombulula umsebenzi combinatorics khosi. Siya kuphinda isigqibo. Lo msebenzi ilula:

1. uN1 = 30 - namagosa kwiqela umfundi enokwenzeka;
2. N2 = 29 - abo banako ukuthatha isithuba isekela;
3. N3 = abantu 28 isicelo ligosa ivenkile.

Sonke kufuneka ukwenze kufumana abona ukhetho, oko kukuthi zande onke amanani. Ngenxa yoko, sifumana: 30 * 29 * 28 = 24360.

Oku kuya kuba impendulo yalo mbuzo.

Ingxaki 2. silungisa

Kule nkomfa nxaxheba 6, indlela emiselwe ngamaqashiso. Kufuneka ukufumana inani iinketho kunokwenzeka ukuba draw. Kulo mzekelo, ucinge lobeko lwe izakhi ezintandathu, oko kukuthi, kufuneka sibe nako ukufumana 6!

cuts Umhlathi sele kuchaziwe, yintoni na nendlela yokubala. Ezihanjiswayo kuvela ukuba kukho 720 iindlela draw. Xa uqala kuqala, umsebenzi onzima na isisombululo kakhulu elifutshane kwaye ilula. Lo msebenzi undincinayo le ngcamango lilonke. Indlela yokusombulula iingxaki kwinqanaba eliphezulu, siza kujonga le mizekelo ilandelayo.

umsebenzi 3

Iqela labafundi abavela amadoda angamashumi amabini anesihlanu kufuneka yahlulwe amaqela amathathu ezintandathu, esithoba ezilishumi. Thina: n = 25, k = 3, N1 = 6, N2 = 9, N3 = 10. Kuhleli ukuba kufakwe amaxabiso ezichanekileyo ifomula, sifumana: N25 (6,9,10). Emva izibalo ezilula sifumana impendulo - 16,360,143 800. Ukuba umsebenzi ayitsho ukuba kuyimfuneko ukufumana isisombululo lwamanani, singakwazi ukubonelela ngayo ngohlobo factorials.

umsebenzi 4

abantu abathathu inani elingaziwayo ukusuka kwelinye ukuya kwishumi. Fumana amathuba ukuba umntu kuzakutelekisa inani. Okokuqala kufuneka sazi inani zonke iziphumo - kulo mzekelo, iwaka, oko kukuthi, alishumi kumlinganiselo wesithathu. Ngoku sifumana inani iinketho ukuba kube yinyaniso onke amanani ahlukeneyo ande ukuya ezilishumi, asithoba anesibhozo. Uvelaphi la manani? Eyokuqala ecinga amanani ukuba ineenketho ezilishumi, owesibini ezilithoba, kwaye eyesithathu kufuneka zikhethwe warn aseleyo, ukuze ukufumana iinketho 720 kunokwenzeka. Njengoko sele sibonile ngentla apha, zonke ezahlukeneyo ka 1000 no-720 ngaphandle phindo, ke ngoko, siye nomdla 280. ezisele Ngoku sifuna ifomula okufumana amathuba classical: P =. Siye safumana impendulo: 0,28.