Nezigaba nokumodela zemathematika, ezoqoqosho kunye nenzululwazi yekhompyutha

Xa lwalo, imodeli isikali imele imephu umfanekiso, umzobo othile, inkcazelo, umfanekiso efumaneka okanye inkqubo. Le meko ibizwa woqobo zemathematika okanye imifuziselo kwezoqoqosho.

Yintoni lwavuka?

Ngumzekelo sisifundo inkqubo ethile into. Ukuze sibe nokumiliselwa yakhiwe kwaye zihlalutywe nomzekelo.

Zonke Ukulinganisa sigaba sibandakanya lwesayensi, into leyo imodeli abstract okanye injongo. Xa wenza into ethile nokuhlola endaweni scheme okanye imodeli lula (copy). Kwezinye iimeko, babuthe imodeli ukusebenza yomzekelo yayo ukuqonda indlela yokusebenza, kukuhlalutya kwezoqoqosho yokuphumeza iziphumo amava kuqoqosho emarikeni. Isenzeko kuyafana ingqalelo imifuziselo ezahlukeneyo.

Umphandi kufuneka ukhethe amanqanaba eziyimfuneko yokubumba, ukusetyenziswa ngokuyimpumelelo kwazo. Ukusetyenziswa iimodeli ezifanelekileyo kwiimeko apho into yokwenene ayifumaneki, okanye asebenzise kuyo enxulumene neengxaki ezinkulu zokusingqongileyo. Le modeli langoku lisetyenziswa kwiimeko apho ulwazi lokwenene ibandakanya iindleko ezibalulekileyo zemali.

Iimpawu yokubumba zezibalo

Ngesayensi, imifuziselo zemathematika kubalulekile, kwakunye izixhobo kubo - izakhono zemathematika. Eminyaka eziliqela, bona wayiqokelela, yala maxesha. Kwimathematika mihla kukho iindlela jikelele nenamandla zophando. Naziphi na izinto njenge "ukumkanikazi inzululwazi", zimele indlela zezibalo. Ukuze uhlalutyo oluneenkcukacha into ekhethiweyo ezikhethiweyo amanqanaba umzekelo zezibalo. Ngoncedo lwabo bahlule iinkcukacha, iimpawu, iimpawu, weemeko ulwazi, ukwenza inkcazelo epheleleyo le into.

semthethweni Mathematical ibandakanya nokuphathwa uphando kweekhonsepthi ezizodwa: umsebenzi matrix, esukela, likumgangatho ophantsi, amanani. Ezo ubudlelwane kunye Intanethi ukuba ukufumana kwi into phantsi isifundo phakathi kwezakhi abasemthethweni kunye iinkcukacha abhalwe ubudlelwane zemathematika: zibalo, ukungalingani, equalities. Ngenxa yoko, into yalungiselelwa inkcazelo zezibalo zenkqubo kunye, ngoko ke, imodeli yayo zezibalo.

Imithetho ukufunda imodeli zezibalo

Kukho umyalelo ezithile amanyathelo yokulinganisa, nto leyo evumela ukuba wenze unxibelelwano phakathi unobangela kunye nesiphumo. I-central Inqanaba Uyilo inkqubo phando ukwakha imodeli ngokupheleleyo zezibalo. Yeyona umgangatho imisebenzi eyenziwa ngqo kuxhomekeke uhlalutyo ngakumbi into. Ukwakhiwa imodeli yemathematika okanye kwezoqoqosho na amanyathelo asemthethweni. Kufuneka kamnandi ukusetyenziswa, oluchanekileyo, ukuba akukho ubugqwetha kwiziphumo zohlalutyo.

Ngomhla ukuhlelwa imifuziselo zezibalo

iintlobo ezimbini: deterministic kunye stochastic imifanekiso. imifuziselo Deterministic zibonisa ukusekwa kwe-one-to-one imbalelwano phakathi kwezinto ezisetyenzisiweyo ukuchaza isenzeko okanye into.

Loo ndlela isekelwe phezu ulwazi isimiso ukusebenza le into. Kwiimeko ezininzi, isenzeko eyenziwe uba isakhiwo entsonkothileyo, ukuze uyivule kuthatha ixesha elininzi kunye nolwazi. Kwiimeko ezinjalo, zikhethwa zigaba ucikizeko yokuba kuya kuqhubeka yemifuniselo yokuqala, enze inkqubo yeziphumo, ngaphandle kokuya kwi iimpawu theoretical component into. Eyona nto basoloko manani kunye nethiyori lilonke. Isiphumo umfuziselo stochastic. Kuyo kukho unxulumano random phakathi kwezinto. Inani elikhulu lemiba ezahlukeneyo yiseti random eziguquguqukayo, esibonakala ngayo into okanye into.

izigaba Ukulinganisa Modern zisetyenziselwa imifuziselo ezimile kunye neguquguqukayo. inkcazelo kwamagxa lweentlobo lobudlelane phakathi kwezinto nesenzeko eyenziwe bengakuqapheli utshintsho ingqalelo xa parameters eziphambili ixesha. imifuziselo Dynamic bachaza unxibelelwano phakathi yezahlukileyo ikhutshwa phandle kuthathelwa ingqalelo ixesha utshintsho.

Iintlobo imifanekiso:

• okuqhubekayo;
• ezahlukene;
• hybrid

izigaba ezahlukeneyo yokubumba lweMathematika ukuvumela ukuba ukuchaza imifuziselo kumgama owazisayo, ubudlelwane kunye nemisebenzi usebenzisa variables ikhonkco ngqo.

Ziintoni ezifunekayo wayifanisa?

• Nsimbi. Le modeli kufuneka ibe umboniso epheleleyo yazo zonke iipropati ezendeleyo ukuya into yokwenene.
• Ukwanela. iimpawu ezibalulekileyo yento kufuneka ngaphezulu ixabiso kwangaphambili esiphoso.
• Ukuchaneka. Ephawula iqondo iimpawu kuqondana into ekhona eneneni, kunye efanayo parameters afunyenwe kwisifundo uReeva.
• Economy. Le modeli kufuneka ubuncinane iindleko eziphathekayo.

izigaba yokubumba

Eyona engundoqo izigaba umzekelo zezibalo.

• Task yoKhetho. Ekhethiweyo ekudlalelwa Injongo yesi sifundo, iindlela ukusetyenziswa kwayo, isicwangciso eveliswe nokuhlola ekhethiweyo. Esi sigaba kubandakanya umsebenzi kakhulu. Kuxhomekeke ukuchaneka umsebenzi kuxhomekeke ekupheleni ngenxa Ukulinganisa.

• Uhlalutyo iziseko yeengcingane, UPawulos yonke ingcaciso ayifumene malunga into. Inyathelo kubandakanya ukhetho okanye indalo le ngcamango. Xa engekho ulwazi theoretical malunga into ukuseka ubudlelwane kobude phakathi zonke ezitshintshayo ekhethiweyo ukuchaza isenzeko okanye into. Kweli nqanaba, isigqibo sokuqala nesokugqibela hypothesize data.
• Semthethweni. Isetyenziselwa khetha inkqubo yeesimboli ezizodwa ukunceda irekhodi ngohlobo amabinzana zezibalo, ubudlelwane phakathi amacandelo into.

Izongezelelo ukuya algorithm

Emva ukubeka model parameters ezikhethiweyo indlela ethile okanye indlela isisombululo.

• Ukuphunyezwa kwale modeli kuphuhliswa. Emva kokuba inkqubo ekhethiweyo eqongeni umzekelo, umisele inkqubo leyo lusavavanywa kwaye kusetyenziswa ukusombulula le ngxaki.
• Uhlalutyo ulwazi oluqokelelweyo. Isifaniso phakathi msebenzi sisombululo ufumene ixhomekeke ebonisa isiphoso.
• Ukukhangela le fit le modeli ukuya into yokwenene. Ukuba ngaba kukho umahluko omkhulu, imodeli entsha phakathi kwabo. Kude kube ngoko, de ubulungeleyo olucokisekileyo singangumzekelo analogu yayo yokwenene, eyayibanjelwe iling'awukazi, ukutshintsha iindawo.

Faka kwasetyen-

Phakathi kwinkulungwane yokugqibela ebomini womntu mihla uvele computing oomatshini, ukwanda ezingokubaluleka iindlela zezibalo ukuba ukufunda izinto ezinzulu. Kwakukho amacandelo afana "Mathematical Chemistry", "Ezolimi zemathematika", "ezoqoqosho zemathematika", abazinikele ekufundweni nesenzeko, izinto zayilwa zigaba eziphambili umzekelo.

njongo yabo iphambili yaba kwingqikelelo kokuma ezicwangcisiweyo, ukufunda izinto ezithile. Ukongeza, encediswa Ukulinganisa Unokufunda ihlabathi, ukuba ukujonga iindlela ukulawula kubo. Ukufeza Ukulinganisa ikhompyutha azithathele kwiimeko apho ihambo ayisebenzi ngoku. Emva kokuba kuqaliswe ngolwakhiwo imodeli yemathematika ye isenzeko phantsi ukufunda ngokusebenzisa computer banokufunda udubulo zenyukliya, isibetho njalo njalo. D.

Iingcali bachonga izigaba ezithathu yokubumba kwemathematika, yaye ngamnye uneempawu zawo:

• Ukwakhiwa imodeli. Esi sigaba kubandakanya umsebenzi isicwangciso koqoqosho, ezi izenzakalo yendalo, uyilo, inkqubo yemveliso. Ngokucacileyo ukuchaza imeko kule meko kunzima. Okokuqala kufuneka ukuchonga ingakumbi isenzeko, ukufumanisa ubudlelwane phakathi kuyo kunye nezinye izinto. Ke zonke iimpawu qualitative ziguqulelwa kulwimi zemathematika, wakha imodeli zezibalo. Eli nqanaba kuba nzima kakhulu kuyo yonke le nkqubo yokubumba.
• IsiGaba nesisombululo ingxaki zezibalo linxulunyaniswa ekuphuhliseni ubuchule, iindlela zokusombulula le ngxaki kwiteknoloji computer, ekuchongweni iimpazamo yomlinganiselo.
• Translation of ulwazi efunyenwe ngexesha izifundo ngolwimi indawo apho olu lingelo lwenziwa.

Ezi zigaba ezintathu yokubumba zemathematika zincediswe ekungqinweni ngokupheleleyo imodeli onesiphumo. Uhlola ukuvumelana phakathi iziphumo ezifunyenweyo kwi linga ngolwazi theoretical component. Ukuba kuyimfuneko, kukho loyamano imodeli wadala. Nzima okanye lula oko, kuxhomekeka kwiziphumo.

lwavuka ingakumbi kwezoqoqosho

amanyathelo 3 zibandakanya ukusetyenziswa yokubumba kwemathematika-aljibra, umehluko zibalo. Yakha izinto ezintsonkothileyo esebenzisa theory grafu. Oku kubandakanya isethi iingongoma isithuba okanye inxalenye moya iimbambo enxibeleleneyo. Izigaba ezingundoqo olungumzekelo elibonisa izibonelelo ezahlukeneyo, usasazo, kuthathelwa zothutho akhawunti, izicwangciso womnatha. Yintoni ayikho linyathelo Ukulinganisa? Kunzima ukuba uphendule lo mbuzo ayintsokothanga, konke oko kuxhomekeka kwimeko ethile. Izigaba ezingundoqo inkqubo zomzekelo kucingelwa iinjongo eyoqulunqo kunye nezifundo zophando, ukukhethwa iimpawu ezingundoqo ukufezekisa injongo, ubudlelwane phakathi inkcazelo imodeli elinazibini. izibalo ezingakumbi yenziwa ngokusebenzisa iifomyula zemathematika.

Umzekelo, theory nkonzo ingxaki tyhu. Kubalulekile ukufumana ungqinelwano phakathi ixabiso izixhobo kunye nesiqulatho ukuze ahlale iindleko efolisiweyo. Emva kokuba kuqaliswe ngolwakhiwo inkcazelo olusesikweni izibalo imodeli olwenziwe usebenzisa ubuchule azo nabaqiqayo. Unokufumana iimpendulo yonke imibuzo kweli imodeli ukuyilwa qualitative. Ukuba imodeli okubi, akunakwenzeka ukuba baqonde indlela nyathelo ayikho linyathelo Ukulinganisa.

Usizo na umbandela yokwenene nokuvavanya ukwanela isenzeko okanye imodeli. Multicriteria model, kuquka iinketho ifoun, injongo ekujongwe kuqulunqo. Kodwa indlela yokuphumeza oku eyahlukileyo. Phakathi iingxaki ezinokwenzeka kule nkqubo, kufuneka ziphawuliwe:

• kwinkqubo phakathi kwezakhi, kukho unxibelelwano ezininzi;
• kunzima ukuthatha yonke imiba random ingqalelo, kuphononongwe inkqubo lenene;
• nzima ukuthelekisa izixhobo zemathematika kunye neziphumo ukuba ufuna ukufumana

Ngenxa iingxaki ezininzi ezivelayo inkqubo ukufunda iinkqubo yoyilo, Ukulinganisa iye yaphuhliswa. Libhekisela iseti iinkqubo ezizodwa iikhompyutha, nto leyo echaza umsebenzi eziqalelo ngamnye kwenkqubo kunye nobudlelwane phakathi kwabo. Ukusetyenziswa variables random kubandakanya uphindaphindo amalinge, processing izibalo kweziphumo. Ukusebenza kunye nenkqubo Ukulinganisa yi umfuniselo ukuba yenziwa ngokusebenzisa ikhompyutha. Ziziphi iingenelo kwale nkqubo? Ngokufanayo, unako ukufikelela kufuphi ngakumbi inkqubo lenene, akunakwenzeka kwimeko imodeli zezibalo. Ukusebenzisa umgaqo block kunokwenzeka ukuba ukuhlalutya iibhloko ngamnye phambi kokuba ezifakwe kwinkqubo enye. Loo khetho likuvumela ukusetyenziswa izixhomekeki enobuzaza ayinakuchazwa ubuhlobo eziqhelekileyo zezibalo.

Phakathi bobubi inkqubo yokulinganisa, ukubeka iindleko ngexesha nezibonelelo, kwakunye nemfuneko yokusebenzisa ubugcisa computer mihla.

Amanqanaba uphuhliso Ukulinganisa efana neenguqu ezenzeka eluntwini. Ngokusetyenziswa zonke iimodeli yahlulwe iinkqubo zoqeqesho, abaqeqeshi, izixhobo ezibonwayo zemfundo. AMAGQABAZA ▸ kungancitshiswa iikopi zezinto yokwenene (iimoto). embodiments Scientific and yobugcisa nqwelo zenzelwe bombane uhlalutyo. Imifuziselo Ukulinganisa nje abonisa ubunyani langoku, ukuba befuma kuvavanywa neempuku elebhu, amalinge kwinkqubo yemfundo. Mbumbulu kubonwa njengendlela ngamava abuhlungu.

Kukho icandelo zonke iimodeli iinketho thaca. imifuziselo Physical kuthiwa substantive. ezahlukeneyo ezifana afakwa ezineempawu zejometri ngokwasemzimbeni ngenxa lokuqala, ukuba aguqulelwe ekhoyo. model ulwazi akunakwenzeka ukuba umchukumise. Bona agcwele karhulumente kunye neempawu into ngaye, nesenzeko, inkqubo, nokunxibelelana bona ehlabathini lokwenene. ongakhetha yomlomo ziquka imifuziselo ulwazi kuphunyezwa ngohlobo oluthethwayo okanye ngokwasengqondweni. imibono angumqondiso oluvakaliswe ukusetyenziswa iimpawu ezithile ezininzi ulwimi lwezibalo.

isiphelo

ucikizeko Mathematical njengendlela ulwazi lwenzululwazi wabonakala ngaxeshanye kunye ezisisiseko yemathematika ngaphezulu. Indima ebalulekileyo kwinkqubo onjalo edlalwa yi-Isaac Newton, Descartes, Leibniz. imifuziselo Mathematical zaye kuqala kwakhiwa Fermat, B. Pascal. nokumodela Mathematical kwi imveliso, uqoqosho uhlawule ingqalelo V. V. Mafikozolo, uV Novozhilov, A. L. Lure. Namhlanje, eyongeziweyo lobeko efanayo yenjongosenzi isifundo nasiphi na isenzeko lisetyenziswa kwiinkalo ezahlukeneyo umsebenzi. Kwiinkqubo eyenzelwe iinjineli uphando nesenzeko ezinjalo kunye neenkqubo ezingenako zihlalutywe kwiimeko yokwenene.

Uphando nge kwasetyen- esetyenziswa kumaxesha amandulo, ekugqibeleni bathimba iintlobo ezahlukeneyo ulwazi lwezenzululwazi: lwezakhiwo, zobunjineli, imichiza, ulwakhiwo, physics, ibhayoloji, eziphilayo, ukuma, kunye nezifundo zentlalo. Xa inkqubo na umzekelo usebenzisa izinto ezintathu: intloko, injongosenzi, imodeli. Kakade ke, uphononongo yokulinganisa into okanye isenzeko kungaphelelanga apho, zikhona nezinye iindlela zokufumana ulwazi oluyimfuneko.