Theory Number: theory and practice

Kukho iingcaciso ezininzi elithi "ingcamango amanani." Omnye wabo uthi ukuba isebe eyodwa kwimathematika (izibalo okanye ngaphezulu), ejongisisa ngokweenkcukacha wonke amanani kunye nezinto ezifana kubo.

Enye inkcazelo ikhankanya ukuba eli sebe kwemathematika ukufunda iimpawu amanani kunye nokuziphatha kwabo kwiimeko ezahlukeneyo.

Ezinye izazinzulu zikholelwa ukuba imfundiso likhulu kangangokuba anike inkcazelo ngqo akunakwenzeka, kwaye uwahlule nje niye neengcamango volume ngaphantsi.

Cwangcisa efanele xa wasungula kwithiyori amanani, oko akwenzeki. Noko ke, nje ifakiwe: namhlanje omdala, kodwa hayi uxwebhu kuphela ukuba ubonisa umdla kwithiyori yamandulo amanani, na isiqwengana encinane icwecwe lodongwe 1800 BC. Oku - inani ebizwa ngokuba yi-kathathu kaPythagoras (amanani zendalo), ezininzi kuzo zibandakanya amanqaku amahlanu. A Inani enkulu kathathu akudibanisi ukhetho lwabo mechanical. Oku kubonisa ukuba umdla kubonakala ukuba imfundiso amanani kwavela ngaphambili kakhulu kunokuba izazinzulu babecinga ekuqaleni.

Abadlali ezigqamileyo ekuphuhlisweni kolwazi olumayela Pythagoreans ingqalelo Euclid kunye Diophantus, ababehlala kumaXesha Aphakathi Indians Aryabhata, Brahmagupta kunye Bhaskara, yaye kamva - Fermat, Euler, आयडेंटीफिकेशन iSazisi.

Ngenkulungwane yokuqala yamashumi theory nani liye utsale ingqalelo buchopho zezibalo ezifana A. N. Korkin, E. I. Zolotarov, A. A. Markov, B. N. Delone, DK Faddeev, I. M. Vinogradov, G .Veyl Selberg.

Ukuphuhlisa nzulu izibalo kunye nezifundo zemathematika bamandulo, bazisa ingcamango ukuya kwinqanaba entsha, aphezulu kakhulu, eziquka iindawo ezininzi. In-kubunzulu uphando kunye ukukhangela ubungqina obutsha kwaye kwakhokelela ukufunyanwa iingxaki ezintsha, ezinye ezingaphunyezwanga kufundwe kude kube ngoku. Hlala vula: hypothesis Artin of etsala ngamabona ezininzi, umbuzo yenani engenasiphelo of etsala, nezinye ezininzi.

Okwangoku iinkalo eziphambili, ezo yahlulwe ithiyori inombolo, ithiyori zezi: samabanga aphantsi, amanani amakhulu amanani random, analytical, algebra.

theory inani iyevakala lijongana ukufunda integers, ngaphandle zokuzoba ubuchule kunye iikhonsepthi kwamanye amasebe lwemathematika. amanani Fibonacci, encinane theorem lokugqibela Fermat kaThixo, - ezi zezona zixhaphakileyo, kakuhle kwaziwa concepts besikolo kule ngcamango.

Imfundiso amanani amakhulu (okanye umthetho amanani amakhulu) - theory amathuba kwicandelwana, ufuna ukungqina ukuba imin yokalo emileyo (kwi kwenye - avareji lobhontsi) kwisampuli elikhulu kufutshane silindele (ekwabizwa ngokuba ngumlinganiselo theoretical component) isampula phantsi imeko ye eliqingqiweyo.

Imfundiso amanani random, yahlukanisa zonke iziganeko kwi ngezwi elingaqondakaliyo, deterministic kunye ngequbuliso, ukuzama ukufumanisa amathuba lwenzekile oku ezintsonkothileyo kweziganeko ezilula. Eli candelo libandakanya iimpawu baphicothwa enemiqathango kunye theorem yazo phindo, nantoni na awayefike sele theorem (idla ngokuba Bayes 'ifomula) njalo njalo.

theory inani zicazulule, njengokuba kucacile ukuba igama layo; ngokuba isifundo omyinge zemathematika kunye neempawu ngamanani iindlela kunye namacebo zohlalutyo zezibalo. Enye yezona ndlela iphambili kweli ithiyori - ubungqina (ngokusebenzisa uhlalutyo leqela) kunikezo yamanani yinkulumbuso.

Aljibra Number Theory isebenza ngqo kunye amanani analogue zazo (umz, amanani aljibra), izifundo ithiyori iqela, umahluli cohomology umsebenzi Dirichlet njl

Inkangeleko kunye nophuhliso le ngcamango kwenza iinzame eminyaka ubudala ukungqina theorem Fermat kaThixo.

De kwinkulungwane yamashumi amabini, le thiyori amanani yayijongwa inzululwazi nje, "vutshila esulungekileyo yemathematika", yokungabi ngokupheleleyo akukho zicelo ezenziwayo okanye ngevangeli. Namhlanje, oku kusetyenziswa xa kubalwa i-elandelwayo icryptographic, ibale trajectories-Hewana kunye ixhokonxa isithuba, kweenkqubo. Economics, ezezimali, inzululwazi ikhompyutha, yokuma - zonke ezi inzululwazi namhlanje ayinakwenzeka ngaphandle kwithiyori amanani.