Coronavirus uye Masvomhu Dzidzo - Zvikamu Zvakatumwa Kuunganidzwa

Utachiona hwakatitapurira huri kuita kuti dzidzo ivandudzwe nokukurumidza. kunyanya pazvidzidzo zvepamusoro. Unogona kunyora chinyorwa chakareba pane iyi musoro; zvirokwazvo pachave nerukova rwezvidzidzo zvechiremba panzira dzekudzidza kure. Kubva pane imwe nzvimbo yekuona, uku ndiko kudzoka kune mavambo uye kukanganwa maitiro ekuzvidzidzira. Izvi ndizvo zvakaitika, semuenzaniso, muchikoro chesekondari cheKremenets (muKremenets, ikozvino muUkraine, yaivepo muna 1805-31, yakamera kusvika 1914 uye yakasangana nekukura kwayo muna 1922-1939). Vadzidzi vakadzidza ipapo vega - mushure mekunge vadzidza ndipo vadzidzisi vakauya nekugadzirisa, kujekesa kwekupedzisira, rubatsiro munzvimbo dzakaoma, nezvimwewo. d. Pandakava mudzidzi, vakatiwo tinofanira kuwana zivo isu pachedu, kuti makirasi epayunivhesiti anogona kuodwa chete uye kutumirwa. Asi zvino yaingova dzidziso...

Muchirimo cha2020, handisi ndega ndakaona kuti zvidzidzo (zvinosanganisira hurukuro, maekisesaizi, nezvimwewo) zvinogona kuitwa nemazvo kure (Google Sangana, Microsoft Teams, nezvimwewo), nemubhadharo webasa rakawanda. kune chikamu chemudzidzisi uye chido chete "kuwana dzidzo" kune rumwe rutivi; asiwo nekunyaradzwa: Ndinogara kumba, muchigaro changu chemaoko, uye muhurukuro dzechivanhu, vadzidzi vaiwanzoitawo chimwe chinhu. Mhedzisiro yekudzidziswa kwakadai inogona kunge iri nani pane yechinyakare, kubva kuMiddle Ages, kirasi-chidzidzo system. Chii chichasara kwaari kana utachiona hwaenda kugehena? Ndinofunga ... zvikuru. Asi tichaona.

Nhasi ndichataura nezve chikamu chakaodha seti. Zviri nyore. Sezvo hukama hwebhinari mune isina-chinhu seti X inodaidzwa kuti hukama hwekurongeka kana paine

(Tadeusz Kotarbinski, 1886-1981, muzivi,

Mutungamiri wePolish Academy yeSainzi muna 1957-1962).

1. Reflexive, i.e. kune yega yega ∈ pane ",
2. Mupfuuri, i.e. kana ", uye", ", ipapo",
3. Semi-asymmetrical, i.e. ("∧")→ =

Mutsara seti ine chivakwa chinotevera: kune chero maviri maelementi, iyo seti ye" kana y". Antichain ndiyo ...

Mira, mira! Pane chimwe cheizvi chinogona kunzwisiswa here? Chokwadi ndizvo. Asi pane mumwe weVaverengi (achiziva neimwe nzira) atonzwisisa zviri pano?

Handifungi! Uye iyi ndiyo kanoni yekudzidzisa masvomhu. Kuchikorowo. Kutanga, tsananguro yakanaka, yakasimba, uyezve, avo vasina kurara kubva mukufinhwa vachanyatsonzwisisa chimwe chinhu. Iyi nzira yakaiswa nevadzidzisi "vakuru" vemasvomhu. Anofanira kungwarira uye kuomesa. Ichokwadi kuti izvi ndizvo zvazvinofanira kunge zvakaita pakupedzisira. Masvomhu anofanira kunge ari sainzi chaiyo (onawo: ).

Ndinofanira kureurura kuti payunivhesiti yandinoshanda mushure mekurega kubva kuYunivhesiti yeWarsaw, ndakadzidzisawo kwemakore akawanda. Mukati mayo chete maiva nebhakiti rakakurumbira remvura inotonhora (regai igare yakadaro: pakanga pane chido chebhakiti!). Pakarepo, kutorwa kwepamusoro kwakava chiedza uye kunofadza. Isa pfungwa: nyore hazvirevi nyore. Iyo light boxer inewo nguva yakaoma.

Ndinonyemwerera nendangariro dzangu. Ndakadzidziswa zvidzidzo zvemasvomhu nomukuru wedhipatimendi panguva iyoyo, nyanzvi yemasvomhu yakanga ichangosvika ichibva kuUnited States kwenguva refu, iyo panguva iyoyo yakanga ichishamisa pachayo. Ndinofunga akanga ari munyai zvishoma paakakanganwa chiPolish zvishoma. Akashandisa chiPolish chekare "chii", "saka", "azalea" uye akagadzira izwi rokuti: "semi-asymmetric relationship". Ndinoda kuishandisa, ndeyechokwadi. Ndinofarira. Asi ini handidi izvi kubva kuvadzidzi. Izvi zvinowanzonzi "low antisymmetry". Dzakanaka gumi.

Kare kare, nokuti mumakore makumi manomwe (yezana remakore rapfuura) shanduko huru, inofadza yedzidziso yemasvomhu yakaitwa. Izvi zvakaenderana nekutanga kwenguva pfupi yekutonga kwaEduard Gierek - kuvhurwa chaiko kwenyika yedu kupasirese. “Vana vanogonawo kudzidziswa masvomhu akakwirira,” vakadanidzira kudaro Vadzidzisi Vakuru. Pfupiso yehurukuro yeyunivhesiti "Fundamentals of Mathematics" yakagadzirirwa vana. Ichi chaive chimiro kwete muPoland chete, asi muEurope yose. Kugadzirisa equation hakuna kukwana; zvese zvaifanira kutsanangurwa. Kuti zvisave zvisina hwaro, imwe neimwe yeVaverengi inogona kugadzirisa iyo equation system:

asi vadzidzi vaifanira kupembedza nhanho imwe neimwe, vachitarisa kuzvirevo zvine chekuita nazvo, nezvimwewo. Uku kwaive kuwedzeredza kwechimiro pane zviri mukati. Zviri nyore kuti ndishore manje. Iniwo, ndakambova mutsigiri wemaitiro aya. Zvinonakidza... kune vechidiki vanoda zvemasvomhu. Izvi, hongu, zvaive (uye, nekuda kwekutarisisa, ini).

Asi zvakaringana kudzikisira, ngatidzikei kubhizinesi: hurukuro yaive "inoretically" yakaitirwa sophomores yePolytechnic uye ingadai yakawoma senge coconut flakes kana zvisiri zvake. Ndiri kuwedzera zvishoma...

Mangwanani kwamuri. Nyaya yanhasi ndeyekucheneswa zvishoma. Aiwa, ichi hachisi chidimbu chekuchenesa zvisina hanya. Kuenzanisa kuri nani kunenge kuri kufunga kuti ndezvipi zviri nani: sopu yemadomasi kana keke yekrimu. Mhinduro yakajeka: zvinoenderana nei. Ye dessert - makuki, uye yekudya kunovaka muviri: soup.

Mumasvomhu, tinobata nenhamba. Vanorongedzerwa: ivo vakakura uye vashoma, asi yenhamba mbiri dzakasiyana, imwe inogara iri shoma, izvo zvinoreva kuti imwe yakakura. Iwo akarongwa munhevedzano, semavara ari muarufabheti. Mumagazini yekirasi, urongwa hunogona kuva hunotevera: Adamchik, Baginskaya, Khoinitsky, Derkovsky, Elget, Filipov, Gzhechnik, Kholnitsky (ivo ishamwari uye vaunodzidza navo kubva mukirasi yangu!). Isu hatinawo mubvunzo kuti Matusyak "Matushelyansky" Matushevsky "Matisyak. Mucherechedzo wekuti "double kusaenzana" une chirevo che "kare".

Muchikwata changu chekufamba, tinoedza kuita mazita e-alfabheti, asi nezita, semuenzaniso, Alina Wrońska "Warvara Kaczarska", Cesar Bouschitz, etc. Muzvinyorwa zvepamutemo, kurongeka kwaizodzorerwa. Nyanzvi dzeMasvomhu dzinoreva kurongeka kwearufabheti semataurirwo emashoko (lexicon is more or less like a duramazwi). Kune rumwe rutivi, kurongeka kwakadaro, umo mune zita rine zvikamu zviviri (Michal Shurek, Alina Wronska, Stanislav Smazhinsky) tinotanga kutarisa chikamu chechipiri, i-anti-lexicographic order yevanoongorora masvomhu. Mazita marefu, asi zviri nyore zvemukati.

1. Linear order: zviteshi nekumira panjanji yeHabovka-Zakopane kubva kuPodhale, yakavakwa muna 1899 (ndinosiya decoding yezvipfupiso kumuverengi).

Mirairo yese yakadai inonzi line orders. Isu tinoronga mukuchinjana: yekutanga, yechipiri, yechitatu. Zvese zviri mugwara, kubva pekutanga kusvika kune yekupedzisira. Hazvina musoro nguva dzose. Mushure mezvose, tinoronga mabhuku muraibhurari kwete seizvi, asi muzvikamu. Chete mukati medhipatimendi tinoronga zvine mutsetse (kazhinji alfabheti).

2. Linear order: patinotanga injini yemotokari, tinoita zviito nenzira inowirirana.

Nemapurojekiti akakura, kunyanya mukushanda kwechikwata, isu hatisisina mutsara wekurongeka. Ngatitarisei fig. 3. Tinoda kuvaka hotera diki. Tatova nemari (sero 0). Isu tinogadzira zvibvumirano, tinounganidza zvinhu, tinotanga kuvaka, uye panguva imwe chete tichiita mushandirapamwe wekushambadzira, kutsvaga vashandi, zvichingodaro. Kana tasvika "10", vaenzi vekutanga vanogona kutarisa (muenzaniso kubva munyaya dzaVaDombrowski nehotera yavo duku mumaguta eKrakow). Tine non-linear order - zvimwe zvinhu zvinogona kuitika zvakafanana.

Mune zvehupfumi, iwe unodzidza nezve iyo pfungwa yeiyo yakakosha nzira. Iro seti yezviito zvinofanirwa kuitwa zvakatevedzana (uye izvi zvinonzi cheni mumasvomhu, zvakanyanya pane izvi nechinguva chidiki), uye izvo zvinotora nguva yakawanda. Kuderedza nguva yekuvaka ndiko kurongekazve kwenzira yakakosha. Asi zvakanyanya pane izvi mune dzimwe hurukuro (rega ndikuyeuchidze kuti ndiri kupa "yunivhesiti hurukuro"). Tinotarisa pasvomhu.

Madhayagiramu akaita seMufananidzo 3 anonzi madhayagiramu eHasse (Helmut Hasse, nyanzvi yemasvomhu yekuGermany, 1898–1979). Kuedza kwese kwakaoma kunofanira kurongwa nenzira iyi. Tinoona kutevedzana kwezviito: 1-5-8-10, 2-6-8, 3-6, 4-7-9-10. Nyanzvi dzeMasvomhu dzinoti tambo. Pfungwa yese ine cheni ina. Kusiyana neizvi, mapoka ekuita 1-2-3-4, 5-6-7, uye 8-9 maantichains. Hezvo zvavanonzi. Ichokwadi ndechokuti mune rimwe boka, hapana chimwe chezviito chinoenderana nechakapfuura.

4. Uyuwo mufananidzo weHasse.

handei ku mufananidzo 4. Chii chinoshamisa? Asi inogona kunge iri metro metro mune rimwe guta! Zvitima zvepasi pevhu zvinogara zvakaiswa mumitsara - hazvipfuuri kubva kune imwe kuenda kune imwe. Mitsetse mitsara yakasiyana. Muguta reFig. 4 iri bake mutsara (rangarira izvozvo bake rakanyorwa kuti "boldem" - muchiPolish inonzi semi-thick).

Mumufananidzo uyu (Fig. 4) pane pfupi yero ABF, nhanhatu-chiteshi ACFPS, yegirini ADGL, yebhuruu DGMRT, uye iyo yakareba tsvuku. Nyanzvi yemasvomhu ichati: iyi Hasse diagram ine bake maketani. Zviri pamutsetse mutsvuku vanomwe chiteshi: AEINRUW. Zvakadini neantichains? Varipo vanomwe. Muverengi atoona kuti ndanyora mutsetse wezwi vanomwe.

Antichain iyi seti yezviteshi zvekuti hazvigoneke kubva kune imwe yadzo kuenda kune imwe pasina kutamiswa. Kana isu "tichanzwisisa" zvishoma, tichaona anotevera antichains: A, BCLTV, DE, FGHJ, KMN, PU, ​​SR. Ndokumbira utarise, semuenzaniso, hazvigoneke kufamba kubva kune chero yezviteshi zveBCLTV kuenda kune imwe BCTLV pasina kutamiswa, zvakanyanya: pasina kudzokera kuchiteshi chinoratidzwa pazasi. Mangani maantichain aripo? Seven. Hukuru chii? Bake (zvakare mune bold).

Unogona kufungidzira, vadzidzi, kuti kusangana kwenhamba idzi hakusi netsaona. Ichi chi. Izvi zvakawanikwa uye zvakaratidzwa (kureva nguva dzose) muna 1950 naRobert Palmer Dilworth (1914-1993, American masvomhu). Nhamba yemitsara inodiwa kuvhara seti yose yakaenzana nehukuru hwe antichain yakakura, uye zvakasiyana-siyana: nhamba yeantichains yakaenzana nehurefu hwehurefu hwakareba antichain. Izvi zvinogara zvakadaro mune chikamu chakarairwa seti, i.e. imwe inogona kuonekwa. Hassego diagram. Iyi haisi tsanangudzo yakaoma uye yakarurama. Izvi ndizvo zvinodaidzwa nevemasvomhu kuti “working definition”. Izvi zvakati siyanei ne "kushanda tsananguro". Iyi izano rekuti unganzwisisa sei zvikamu zvakaodha seti. Ichi chikamu chakakosha chekudzidziswa kupi zvako: ona kuti zvinoshanda sei.

Chidimburidzo cheChirungu ndechekuti - iri izwi rinonzwika rakanaka mumitauro yeSlavic, zvishoma serukato. Ziva kuti rukato rine mataviwo.

Yakanaka kwazvo, asi ndiani anoida? Imi, vadzidzi vanodiwa, munoida kuti mupase bvunzo, uye ichi chingave chikonzero chakanaka chekuidzidza. Ndiri kuteerera, mibvunzo ipi? Ndiri kuteerera, muchinda uri pasi pehwindo. Oo, mubvunzo ndewokuti, izvi zvichazombobatsira here kuna Ishe muhupenyu hwako? Zvichida kwete, asi kune mumwe munhu akachenjera kupfuura iwe, zvechokwadi ... Pamwe nokuda kwekuongorora nzira yakaoma mune chirongwa chehupfumi chakaoma?

Ndiri kunyora chinyorwa ichi pakati paChikumi; sarudzo dzerector dziri kuitika kuYunivhesiti yeWarsaw. Ndakaverenga akati wandei kubva kune vashandisi veInternet. Pane huwandu hunoshamisa hweruvengo (kana "ruvengo") kune "vanhu vakadzidza." Mumwe munhu akanyora zvakajeka kuti vanhu vane dzidzo yokuyunivhesiti vanoziva zvishoma pane vane dzidzo yokuyunivhesiti. Ini, chokwadi, handizopindi muhurukuro. Ndiri kungosuwa kuti pfungwa iripo muPolish People's Republic yekuti zvese zvinogona kuitwa nesando uye chisel zviri kudzoka. Ndiri kudzokera kusvomhu.

Dillworth's theorem ine zvakawanda zvinofadza zvekushandisa. Mumwe wavo anozivikanwa se theorem yewanano.fig. 6). 

Kune boka revakadzi (asi vasikana) uye boka revarume vakati kurei. Musikana wese anofunga chimwe chinhu chakadai: "Ndaigona kuroora uyu, kune mumwe, asi kwete muhupenyu hwangu kwechitatu." Uye zvichingodaro, munhu wese ane zvaanoda. Isu tinodhirowa dhayagiramu, inotungamira kune mumwe nemumwe wavo museve kubva kumurume waasina kuramba semumiriri weatari. Mubvunzo: Vaviri vanogona kufananidzwa here kuti mumwe nemumwe awane murume waanotambira?

Theorem yaPhilip Hall, inotaura kuti izvi zvinogona kuitwa - zvichienderana nemamwe mamiriro ezvinhu, izvo zvandisingazotauri pano (zvino muhurukuro inotevera, vadzidzi, ndapota). Cherechedza, zvisinei, kuti kugutsikana kwevarume hakuna kutaurwa zvachose pano. Sezvaunoziva, vakadzi ndivo vanotisarudza, uye kwete zvakasiyana, sezvatinofunga (regai ndikuyeuchidzei kuti ini ndini munyori, kwete munyori).

Mamwe masvomhu akakomba. Ko theorem yaHall inotevera sei kubva kuDilworth? Zviri nyore kwazvo. Ngatitarisei zvakare paMufananidzo 6. Maketani aripo mapfupi zvikuru: ane urefu hwe2 (achimhanya munzira). Seti yevarume vadiki ndeye antichain (chaizvo nekuti miseve inongonongedza kune imwe neimwe). Nenzira iyi iwe unogona kuvhara muunganidzwa wose nemaantichains akawanda sezvaanoita varume. Saka, mukadzi wese achava nemuseve. Zvichireva kuti angaite kunge mukomana waanobvuma!!!

Mirira, mumwe munhu achabvunza, ndizvo here? Izvi ndizvo zvese here? Mahomoni neimwe nzira anowirirana uye nei masvomhu? Chekutanga, iyi haisi iyo yese application, asi imwe chete yemahombe akateedzana. Ngatitarisei chimwe chazvo. Regai (Fig. 6) zvinoreva kwete vamiririri pabonde nani, asi pane prosaic vatengi, uye aya mabhureki, semuenzaniso, motokari, washing machine, uremu zvigadzirwa, zvinopiwa kubva masangano kufamba, etc. Mutengi mumwe nomumwe ane mhando kuti anogamuchira uye anoramba. Pane chingaitwa here kutengesa chimwe chinhu kumunhu wese uye sei? Apa ndipo panopera majee chete, asiwo ruzivo rwemunyori wechinyorwa pamusoro penyaya iyi. Chandinoziva ndechekuti ongororo yacho yakavakirwa pane mamwe masvomhu akaoma kunzwisisa.

Kudzidzisa masvomhu muchikoro kudzidzisa maalgorithms. Ichi chikamu chakakosha chekudzidza. Asi zvishoma nezvishoma tiri kuenda kukudzidzisa kwete zvakanyanya masvomhu senzira yemasvomhu. Hurukuro yanhasi yaingove nezveizvi: tiri kutaura nezve abstract mental kuvaka, isu tiri kufunga nezve hupenyu hwemazuva ese. Isu tiri kutaura nezve cheni uye antichains mumaseti ane inverse, transitive uye humwe hukama hwatinoshandisa mumhando dzemutengesi-mutengi. Komputa ichaita macalculations ese kwatiri. Haasati agadzira masvomhu mamodheru. Tichiri kukunda nekufunga kwedu. Zvisinei, ndinovimba kwenguva yakareba sezvinobvira!