Coronavirus ndi Masamu Maphunziro - Zosonkhanitsidwa Mwapang'ono

Kachilombo kameneka kakutipatsira kachilomboka kakupangitsa kuti maphunziro asinthe mwachangu. makamaka pamaphunziro apamwamba. Nkhani yayitali ikhoza kulembedwa pamutuwu; padzakhaladi zolemba zambiri za udokotala panjira zophunzirira patali. Kuchokera kumalingaliro ena, uku ndikubwerera ku chiyambi ndi zizoloŵezi zoiwalika za kudziphunzira. Izi zinali choncho, mwachitsanzo, kusukulu ya sekondale ya Kremenets (ku Kremenets, yomwe tsopano ili ku Ukraine, yomwe inalipo mu 1805-31, idamera mpaka 1914 ndipo idakumana ndi nthawi yake mu 1922-1939). Ophunzirawo adaphunzira okha kumeneko - atangophunzira kumene aphunzitsi adabwera ndikuwongolera, kulongosola komaliza, thandizo m'malo ovuta, ndi zina zotero. d. Nditaphunzira, ananenanso kuti tiyenera kudzipezera tokha chidziwitso, kuti makalasi a ku yunivesite atha kuyitanidwa ndikutumizidwa. Koma ndiye inali chiphunzitso chabe...

Kumayambiriro kwa chaka cha 2020, sindine ndekha amene ndinazindikira kuti maphunziro (kuphatikiza maphunziro, masewera olimbitsa thupi, ndi zina zotero) amatha kuchitikira kutali (Google Meet, Microsoft Teams, etc.), pamtengo wa ntchito yambiri. kumbali ya mphunzitsi ndi chikhumbo chabe "kupeza maphunziro" kumbali ina; komanso ndi chitonthozo china: Ndimakhala kunyumba, pampando wanga, komanso pa maphunziro achikhalidwe, ophunzira nawonso nthawi zambiri ankachita zina. Zotsatira za maphunziro otere zitha kukhala zabwinoko kuposa momwe zimakhalira ndi maphunziro a m'kalasi, kuyambira ku Middle Ages. Kodi chidzatsala ndi chiyani pamene kachilomboka kapita ku gehena? Ndikuganiza ... kwambiri. Koma tiwona.

Lero ndilankhula za ma seti olamulidwa pang'ono. Ndi zophweka. Popeza ubale wa binary mu seti yopanda kanthu X umatchedwa mgwirizano wapang'ono pomwe pali

(Tadeusz Kotarbinski, 1886-1981, philosopher,

Purezidenti wa Polish Academy of Sciences mu 1957-1962).

1. Reflexive, i.e. pa chilichonse ∈ pali ",
2. Wodutsa, i.e. ngati ", ndi ", ndiye",
3. Semi-asymmetrical, i.e. (“∧“)→ =

Mzere ndi seti yokhala ndi zinthu zotsatirazi: pazigawo ziwiri zilizonse, ndi seti ya "kapena y". Antichain ndi ...

Imani, siyani! Kodi tingamvetse kalikonse kuchokera pamenepa? Inde ndi choncho. Koma kodi aliyense wa Owerenga (omwe sadziwa mwanjira ina) wamvetsetsa kale zomwe zili pano?

Musaganize! Ndipo iyi ndi mndandanda wamaphunziro a masamu. Komanso kusukulu. Choyamba, kutanthauzira koyenera, kokhwima, ndiyeno, iwo omwe samagona chifukwa chotopa adzamvetsetsadi china chake. Njira iyi idakhazikitsidwa ndi aphunzitsi "akulu" a masamu. Ayenera kukhala waudongo komanso wokhwimitsa zinthu. N’zoona kuti umu ndi mmene ziyenera kukhalira pamapeto pake. Masamu ayenera kukhala sayansi yeniyeni (onaninso: ).

Ndiyenera kuvomereza kuti ku yunivesite kumene ndimagwira ntchito nditapuma ntchito pa yunivesite ya Warsaw, ndinaphunzitsanso kwa zaka zambiri. Chokhacho chinali ndi chidebe chodziwika bwino chamadzi ozizira (chilekeni chikhale momwemo: pankafunika chidebe!). Mwadzidzidzi, kutulutsa kwakukulu kunakhala kopepuka komanso kosangalatsa. Khazikitsani mfundo: zosavuta sizitanthauza kuti ndizosavuta. Woponya nkhonya wopepuka nayenso amavutika.

Ndimwetulira pokumbukira zanga. Ndinaphunzitsidwa masamu ndi mkulu wa faculty wa panthaŵiyo, katswiri wa masamu yemwe anali atangofika kumene kuchokera ku United States kuchokera kudziko lakale kwambiri, ndipo panthaŵiyo zinali zodabwitsa kwambiri. Ndikuganiza kuti anali wopusa pang'ono pomwe anayiwala Chipolishi pang'ono. Anagwiritsa ntchito mopitirira muyeso wakale wa Chipolishi "kuti", "choncho", "azale" ndipo adabwera ndi mawu awa: "ubale wa semi-asymmetrical". Ndimakonda kuzigwiritsa ntchito, ndizolondola. Ndimakonda. Koma sindikufuna izi kwa ophunzira. Izi zimatchedwa "low antisymmetry". khumi okongola.

Kalekale, chifukwa m'zaka za makumi asanu ndi awiri (zaka zapitazo) kusintha kwakukulu, kosangalatsa kwa chiphunzitso cha masamu kunachitika. Izi zinagwirizana ndi chiyambi cha nthawi yochepa ya ulamuliro wa Eduard Gierek - kutsegula kotsimikizika kwa dziko lathu kudziko lapansi. “Ana angaphunzitsidwenso masamu apamwamba,” anafuula motero Aphunzitsi Aakulu. Chidule cha nkhani ya kuyunivesite yakuti “Mfundo Zazikulu za Masamu” inasonkhanitsidwa kwa ana. Izi zinali chizolowezi osati ku Poland kokha, komanso ku Europe konse. Kuthetsa equation sikunali kokwanira; chilichonse chimayenera kufotokozedwa. Kuti asakhale opanda maziko, aliyense wa Owerenga akhoza kuthetsa dongosolo la equations:

koma ophunzira amayenera kulungamitsa sitepe iliyonse, kutchula ziganizo zoyenera, ndi zina zotero. Ndizosavuta kwa ine kutsutsa tsopano. Inenso, nthawi ina ndinali wochirikiza njira imeneyi. Ndizosangalatsa ... kwa achinyamata omwe amakonda masamu. Zinalidi (ndipo, chifukwa cha chidwi, ine).

Koma kupitirira kwapang'onopang'ono kwanyimbo, tiyeni tifike pamfundoyi: phunziro lomwe "mwamwano" linali lopangidwira ophunzira a polytechnic achaka chachiwiri ndipo likanakhala louma ngati coconut flakes ngati sichoncho. Ndikukokomeza pang'ono...

Mmawa wabwino kwa inu. Mutu wa lero ndi kuyeretsa pang'ono. Ayi, izi sizikutanthauza kuyeretsa mosasamala. Kuyerekeza bwino kungakhale kuganizira zomwe zili bwino: supu ya phwetekere kapena keke ya kirimu. Yankho ndilomveka: zimatengera chiyani. Kwa mchere - makeke, ndi chakudya chopatsa thanzi: supu.

Mu masamu timachita ndi manambala. Iwo amalamulidwa: iwo ndi aakulu ndi ochepa, koma a ziwerengero ziwiri zosiyana, nthawi zonse zimakhala zochepa, zomwe zikutanthauza kuti winayo ndi wamkulu. Amasanjidwa mwadongosolo, monga zilembo za zilembo. Mu chipika cha kalasi, dongosolo likhoza kukhala: Adamczyk, Baginskaya, Chojnicki, Derkovsky, Elget, Filipov, Grzecnik, Kholnicki (iwo ndi abwenzi ndi anzanga a m'kalasi mwanga!). Sitikukayikiranso kuti Matusiak "Matusheliansky" Matuszewski "Matysiak. Chizindikiro cha "kusagwirizana kawiri" chimatanthauza "kutsogola".

Mu kalabu yanga yoyendamo timayesa kupanga mndandanda wa zilembo, koma ndi dzina, mwachitsanzo, Alina Wronska "Warwara Kaczarowska", Cesar Boushitz, ndi zina zotero. Akatswiri a masamu amatcha alfabetical order lexicographical (lexicon imakhala yocheperako ngati dikishonale). Komano, dongosolo ili, limene mu dzina wopangidwa ndi zigawo ziwiri (Michal Szurek, Alina Wronska, Stanislav Smarzynski) choyamba tiyang'ane pa gawo lachiwiri, ndi dongosolo odana lexicographic kwa masamu. Maina aatali, koma osavuta kwambiri.

1. Linear Order: masiteshoni ndi maimidwe panjira ya Habovka - Zakopane njanji yochokera ku Podhale, yomangidwa mu 1899 (ndikusiya kumasulira kwachidule kwa owerenga).

Malamulo onsewa amatchedwa ma line order. Timayitanitsa mwadongosolo: choyamba, chachiwiri, chachitatu. Chilichonse chili mwadongosolo, kuyambira poyambira mpaka pomaliza. Izi sizikhala zomveka nthawi zonse. Kupatula apo, timakonza mabuku mu laibulale osati monga chonchi, koma m'zigawo. Pokhapokha mu dipatimenti yomwe timayikonza motsatira (nthawi zambiri motsatira zilembo).

2. Dongosolo la mzere: poyambitsa injini yagalimoto, timachita zinthu mogwirizana.

Ndi mapulojekiti akuluakulu, makamaka ntchito yamagulu, tilibenso dongosolo la mzere. Tiyeni tionepo chith. 3. Tikufuna kumanga hotelo yaying'ono. Tili ndi ndalama kale (selo 0). Timakonza zilolezo, kusonkhanitsa zipangizo, kuyamba kumanga, ndipo panthawi imodzimodziyo timapanga kampeni yotsatsa malonda, kuyang'ana antchito, ndi zina zotero. Tikafika "10", alendo oyambirira akhoza kuyang'ana (chitsanzo kuchokera ku nkhani za Bambo Dombrowski ndi hotelo yawo yaing'ono m'midzi ya Krakow). Tili ndi dongosolo nonlinear -Zinthu zina zimatha kuchitika nthawi imodzi.

Muzachuma, mumaphunzira za lingaliro la njira yovuta. Ndi gulu la zochita zomwe ziyenera kuchitidwa motsatizana (ndipo izi zimatchedwa unyolo mu masamu, zambiri pa izi pakamphindi), zomwe zimatenga nthawi yambiri. Kuchepetsa nthawi yomanga ndikukonzanso njira yovuta. Koma zambiri pa izi mu maphunziro ena (ndiroleni ndikukumbutseni kuti ndikupereka "nkhani yakuyunivesite"). Timaganizira kwambiri masamu.

Zithunzi monga Chithunzi 3 zimatchedwa zithunzi za Hasse (Helmut Hasse, katswiri wa masamu wa ku Germany, 1898-1979). Ntchito iliyonse yovuta iyenera kukonzedwa motere. Timawona kutsatizana kwa zochita: 1-5-8-10, 2-6-8, 3-6, 4-7-9-10. Akatswiri a masamu amawatcha kuti zingwe. Lingaliro lonse lili ndi maunyolo anayi. Mosiyana, magulu a ntchito 1-2-3-4, 5-6-7 ndi 8-9 ndi antichains. Ndi chimene iwo amatchedwa. Zoona zake n’zakuti m’gulu linalake, palibe chochita chilichonse chimene chimadalira m’mbuyomo.

4. Ichinso ndi chithunzi cha Hasse.

tiyeni tipite ku chithunzi 4. Chochititsa chidwi ndi chiyani? Koma awa akhoza kukhala mapu a metro mumzinda wina! Njanji zapansi panthaka nthawi zonse zimagawidwa m'mizere - sizimapita kumodzi. Mizere ndi mizere payekha. Mumzinda, mpunga. 4 inde kuphika mzere (kumbukirani kuti kuphika olembedwa "boldem" - mu Chipolishi amatchedwa theka-thick).

Pachithunzichi (mkuyu 4) pali ABF yachikasu yachikasu, ACFKPS yachisanu ndi chimodzi, ADGL yobiriwira, DGMRT ya buluu ndi yofiira kwambiri. Katswiri wa masamu adzati: pa chithunzi cha Hasse ichi pali kuphika unyolo. Ili pa mzere wofiira zisanu ndi ziwiri siteshoni: AEINRUV. Nanga bwanji antichains? Iwo ali kumeneko zisanu ndi ziwiri. Wowerenga waona kale kuti mawuwa ndidawalemba kawiri zisanu ndi ziwiri.

Kuyembekezera Awa ndi masiteshoni kotero kuti ndizosatheka kuchoka kwa aliyense wa iwo kupita kwina popanda kusamutsa. "Tikazindikira" pang'ono, tiwona ma antichain awa: A, BCLTV, DE, FGHJ, KMN, PU, ​​SR. Chonde onani, mwachitsanzo, kuchokera ku masiteshoni aliwonse a BCLTV sikutheka kupita ku BCTLV ina osasintha, kapena ndendende: popanda kubwereranso kusiteshoni yomwe ili pansipa. Kodi pali ma antichain angati? Zisanu ndi ziwiri. Ndi kukula kwake kotani? Kuphika (kachiwiri mochedwa).

Inu mukhoza kulingalira, ophunzira, kuti mwangozi manambala amenewa si mwangozi. Izi. Izi zidapezeka ndikutsimikiziridwa (mwachitsanzo nthawi zonse) mu 1950 ndi Robert Palmer Dilworth (1914-1993, katswiri wa masamu waku America). Chiwerengero cha mizere yofunikira kuti chiphimbe seti yonseyi ndi yofanana ndi kukula kwa antichain yayikulu, ndipo mosiyana: chiwerengero cha antichains ndi chofanana ndi kutalika kwa antichain yaitali kwambiri. Izi nthawi zonse zimachitika mu dongosolo lokhazikitsidwa pang'ono, i.e. yomwe ikhoza kuwonetsedwa. Chithunzi cha Hassego. Ili si tanthauzo lokhazikika komanso lolondola. Izi ndi zomwe akatswiri a masamu amatcha "tanthauzo la ntchito". Izi ndizosiyana pang'ono ndi "tanthauzo la ntchito". Ili ndi lingaliro la momwe mungamvetsetse ma seti oyitanidwa pang'ono. Ili ndi gawo lofunikira pamaphunziro aliwonse: onani momwe amagwirira ntchito.

Chidule cha Chingerezi ndi - mawu awa amamveka bwino m'zilankhulo za Asilavo, ngati nthula. Chonde dziwani kuti nthula zimakhalanso ndi nthambi.

Zokongola kwambiri, koma ndani akuzifuna? Inu, ophunzira okondedwa, mumafunikira kuti mupambane mayeso ndipo, mwina, ichi ndi chifukwa chabwino chophunzirira. Ndikumvetsera, mafunso otani? Ine ndikumvetsera, bwana, pansi pa zenera. O, funso ndilakuti, kodi izi zidzakhala zothandiza kwa Ambuye m'moyo wanu? Mwina ayi, koma kwa wina wanzeru kuposa inu motsimikiza ... Mwinamwake pofufuza njira yovuta mu ntchito yovuta yachuma?

Ndikulemba nkhaniyi mkati mwa June; zisankho za rector zili mkati ku yunivesite ya Warsaw. Ndawerenga ndemanga zingapo kuchokera kwa ogwiritsa ntchito intaneti. Pali chidani chodabwitsa (kapena "chidani") kwa "anthu ophunzira." Munthu wina analemba mosapita m’mbali kuti anthu amene ali ndi maphunziro a ku yunivesite amadziwa zochepa poyerekezera ndi amene ali ndi maphunziro a ku yunivesite. Ine, ndithudi, sindidzalowa mu zokambirana. Ndine wachisoni kuti malingaliro omwe alipo ku Polish People's Republic kuti chilichonse chikhoza kuchitika ndi nyundo ndi chisel chikubwerera. Ndikubwerera ku masamu.

Theorem ya Dillworth ili ndi mapulogalamu angapo osangalatsa. Chimodzi mwa izo chimadziwika kuti chiphunzitso chaukwati.chith. 6). 

Pali gulu la amayi (ochuluka atsikana) ndi gulu lokulirapo pang'ono la amuna. Mtsikana aliyense amaganiza motere: “Ndikhoza kukwatiwa ndi uyu, uyu, uyu, koma osati wachitatu m’moyo wanga.” Ndi zina zotero, aliyense ali ndi zokonda zake. Timajambula chithunzi, chotsogolera kwa aliyense wa iwo muvi kuchokera kwa munthu yemwe samakana ngati woimira pa guwa. Funso: Kodi maanja angafanane kuti aliyense apeze mwamuna amene amamuvomereza?

Theorem ya Philip Hall, akunena kuti izi zikhoza kuchitika - malinga ndi zikhalidwe zina, zomwe sindidzakambirana pano (ndiye mu phunziro lotsatira, ophunzira, chonde). Dziwani, komabe, kuti kukhutitsidwa kwa amuna sikunatchulidwe konse pano. Monga mukudziwa, ndi amayi omwe amatisankha, osati mosiyana, monga momwe timaganizira (ndiroleni ndikukumbutseni kuti ine ndine wolemba, osati wolemba).

Masamu ena akulu. Kodi theorem ya Hall ikutsatira bwanji kuchokera ku Dilworth? Ndi zophweka kwambiri. Tiyeni tionenso Chithunzi 6. Maunyolo omwe alipo ndi aafupi kwambiri: ali ndi kutalika kwa 2 (kuthamanga kumbali). Gulu la amuna ang'onoang'ono ndi antichain (ndendende chifukwa mivi imangolozerana). Mwanjira iyi mutha kuphimba gulu lonse ndi ma antichain ambiri monga momwe alili amuna. Choncho, mkazi aliyense adzakhala ndi muvi. Kutanthauza kuti atha kuwoneka ngati mnyamata yemwe amamuvomereza!!!

Dikirani, wina afunsa, sichoncho? Kodi iyi ndi ntchito yonse? Mahomoni mwanjira inayake amalumikizana ndipo chifukwa chiyani masamu? Choyamba, iyi si ntchito yonse, koma imodzi yokha mwa mndandanda waukulu. Tiyeni tione imodzi mwa izo. Tiyeni (mkuyu 6) sikutanthauza oimira kugonana bwino, koma ogula prosaic, ndipo izi ndi zopangidwa mwachitsanzo, magalimoto, makina ochapira, katundu kuwonda, amapereka kwa mabungwe oyendayenda, etc. Wogula aliyense ali ndi zizindikiro zomwe amavomereza. ndipo amakana. Kodi pali chilichonse chomwe chingachitike kuti mugulitse wina aliyense ndipo bwanji? Apa ndi pamene osati nthabwala zokha, komanso chidziwitso cha wolemba nkhani pamutuwu. Zomwe ndikudziwa ndikuti kusanthula kumatengera masamu ena ovuta kwambiri.

Kuphunzitsa masamu kusukulu ndikuphunzitsa ma algorithms. Ichi ndi gawo lofunikira la maphunziro. Koma pang'ono ndi pang'ono tikupita kukaphunzitsa masamu ambiri monga njira ya masamu. Nkhani yamasiku ano inali yongonena izi: timalankhula zamalingaliro osamveka, timaganizira za moyo watsiku ndi tsiku. Tikukamba za maunyolo ndi ma antichains mu seti zokhala ndi maubwenzi osinthika, osinthika ndi ena omwe timagwiritsa ntchito pamitundu yogulitsa ogula. Kompyutayo idzatiwerengera zonse. Sadzapanganso zitsanzo zamasamu. Timapambanabe ndi maganizo athu. Mulimonsemo, ndikuyembekeza kwa nthawi yayitali momwe ndingathere!