Izifundo ngesiFrentshi
Ngokungacwangciswanga: Intshayelelo enokwenzeka – iCandelo loku-1 (POLYTECHNIQUE PARIS)
I-École Polytechnique, iziko elaziwayo, libonelela ngekhosi enomdla kwi-Coursera enesihloko esithi “Ngokungacwangciswanga: intshayelelo enokwenzeka – iCandelo loku-1”. Le khosi, ithatha malunga neeyure ezingama-27 ezisasazwa kwiiveki ezintathu, lithuba elikhethekileyo kuye nabani na onomdla kwiziseko zokwenzeka. Iyilwe ukuba ibe bhetyebhetye kwaye ihambelane nesantya somfundi ngamnye, le khosi ibonelela ngobunzulu kunye nendlela efikelelekayo kwithiyori enokwenzeka.
Inkqubo iqulethe iimodyuli ezibandakanyekayo ze-8, nganye ijongana nemiba ephambili yendawo enokwenzeka, imithetho efanayo enokwenzeka, ukulungelelanisa, ukuzimela, kunye nokuguquguquka okungahleliwe. Imodyuli nganye ityetyiswe ngeevidiyo ezicacisayo, ufundo olongezelelweyo kunye neekhwizi zokuvavanya kunye nokudibanisa ulwazi olufunyenweyo. Abafundi bakwanalo nethuba lokufumana isatifikethi ekwabelwana ngaso ekugqityweni kwekhosi, bongeza ixabiso elibalulekileyo kuhambo lwabo lobuchwephesha okanye lwezifundo.
Abahlohli, uSylvie Méléard, uJean-René Chazottes noCarl Graham, bonke abasebenzisana ne-École Polytechnique, bazisa ubuchule babo nothando lwabo lwezibalo, besenza esi sifundo singabi semfundo kuphela, kodwa sibe sikhuthaza. Nokuba ungumfundi wezibalo, ingcali ejonge ukwenza nzulu ulwazi lwakho, okanye ungumntu othanda isayensi, esi sifundo sikunika ithuba elikhethekileyo lokuphonononga kwihlabathi elinomdla lamathuba, ukhokelwa zezona ngqondo zibalaseleyo e-École Polytechnique.
Ngokungacwangciswanga: Intshayelelo enokwenzeka – iCandelo loku-2 (POLYTECHNIQUE PARIS)
Ukuqhubela phambili ukugqwesa kwezemfundo kwe-École Polytechnique, ikhosi "Ngokuzenzekelayo: intshayelelo enokwenzeka - iCandelo 2" kwi-Coursera kukuqhubekeka ngokuthe ngqo nokutyebisayo kwecandelo lokuqala. Le khosi, eqikelelwa kwiiyure ezili-17 eziya kusasazeka kwiiveki ezintathu, intywilisela abafundi kwiikhonsepthi eziphambili zethiyori enokwenzeka, ibonelela ngokuqonda okunzulu kunye nokusetyenziswa okubanzi kolu qeqesho lunomdla.
Ngeemodyuli ezi-6 ezakhiwe kakuhle, ikhosi ihlanganisa izihloko ezifana ne-random vectors, i-generalization of calculation of law, umthetho wamanani amakhulu i-theorem, indlela ye-Monte Carlo, kunye ne-central limit theorem. Imodyuli nganye ibandakanya iividiyo ezifundisayo, ukufundwa kunye nemibuzo, ukuze ube namava okufunda antywilayo. Le fomati ivumela abafundi ukuba bazibandakanye ngenkuthalo nemathiriyeli kwaye basebenzise iikhonsepthi ezifundiweyo ngendlela ebonakalayo.
Abahlohli, uSylvie Méléard, uJean-René Chazottes noCarl Graham bayaqhubeka nokukhokela abafundi kolu hambo lwemfundo ngobuchule babo nothando lwabo lwezibalo. Indlela yabo yokufundisa iququzelela ukuqondwa kweekhonsepthi ezintsonkothileyo kwaye ikhuthaza ukuphononongwa nzulu kwamathuba.
Le khosi ilungele abo sele benesiseko esomeleleyo ekunokwenzeka kwaye bafuna ukwandisa ukuqonda kwabo kunye nokukwazi ukusebenzisa ezi ngqikelelo kwiingxaki ezinzima ngakumbi. Ngokugqiba le khosi, abafundi banokufumana isatifikethi ekwabelwana ngaso, esibonisa ukuzinikela kunye nobuchule babo kule ndawo ikhethekileyo.
Intshayelelo kwithiyori yokusasaza (POLYTECHNIQUE PARIS)
Ikhosi "Intshayelelo kwithiyori yokusasazwa", enikezelwa ngu-École Polytechnique e-Coursera, imele uphononongo olukhethekileyo nolunzulu lwenkalo yezibalo ephucukileyo. Le khosi, ethatha malunga neeyure ezili-15 ezisasazwa kwiiveki ezintathu, yenzelwe abo bafuna ukuqonda ukuhanjiswa, ingcamango esisiseko kwimathematika esetyenziswayo kunye nohlalutyo.
Le nkqubo ineemodyuli ezili-9, nganye ibonelela ngomxube weevidiyo ezifundisayo, ukufundwa kunye neekhwizi. Ezi modyuli zibandakanya imiba eyahlukeneyo yethiyori yokusabalalisa, kubandakanywa nemiba enzima efana nokuchaza i-derivative ye-discontinuous function kunye nokusetyenziswa kwemisebenzi engapheliyo njengezisombululo kwii-equations ezahlukeneyo. Le ndlela icwangcisiweyo ivumela abafundi ukuba baqhelane ngokuthe ngcembe neekhonsepthi ezinokubonakala zoyikisa ekuqaleni.
Unjingalwazi uFrançois Golse noYvan Martel, bobabini abangamalungu abalaseleyo e-École Polytechnique, bazisa ubuchule obuninzi kwesi sifundo. Ukufundisa kwabo kudibanisa ukuqina kwezemfundo kunye neendlela ezintsha zokufundisa, ukwenza umxholo ufikeleleke kwaye ubandakanye abafundi.
Le khosi ifaneleke ngokukodwa abafundi bemathematika, ubunjineli, okanye amacandelo anxulumeneyo abajonge ukwenza nzulu ukuqonda kwabo izicelo ezintsonkothileyo zemathematika. Ngokugqiba le khosi, abathathi-nxaxheba abayi kufumana ulwazi oluxabisekileyo kuphela, kodwa baya kuba nethuba lokufumana isatifikethi ekwabelwana ngaso, esongeza ixabiso elibalulekileyo kwiprofayili yabo yobungcali okanye yezemfundo.
Intshayelelo yethiyori yeGalois (ISIKOLO ESIQHELEKILEYO ESEMPHUMILEYO PARIS)
Inikezelwa ngu-École Normale Supérieure kwi-Coursera, ikhosi "Intshayelelo ye-Galois Theory" luphononongo olunika umdla lwelona sebe linzulu nelinempembelelo kwimathematika yanamhlanje.Ithathe malunga neeyure ezili-12, le khosi intywilisela abafundi kwihlabathi elintsonkothileyo nelinomtsalane lethiyori yeGalois, uqeqesho oluye lwaguqula ukuqonda kobudlelwane phakathi kweeequation zepolynomial kunye nezakhiwo zealjibra.
Ikhosi igxininise ekufundweni kweengcambu zeepolynomials kunye nokubonakaliswa kwazo kwi-coefficients, umbuzo oyintloko kwi-algebra. Iphonononga ingcamango yeqela leGalois, elaziswa ngu-Évariste Galois, elidibanisa ne-polynomial nganye iqela le-permutations yeengcambu zayo. Le ndlela ivumela ukuba siqonde ukuba kutheni kungenakwenzeka ukuchaza iingcambu zeequation zepolynomial ezithile ngeefomula zealjibra, ngakumbi iipolynomials zedigri enkulu kunesine.
Imbalelwano yeGalois, eyona nto iphambili kule khosi, inxulumanisa ithiyori yecandelo kwithiyori yeqela, ibonelela ngembono eyodwa ekusombulukeni kwee-radical equations. Ikhosi isebenzisa iikhonsepthi ezisisiseko kwi-algebra yomgca ukusondela kwithiyori yemizimba kwaye yazise ingcamango yenani le-algebra, ngelixa iphonononga amaqela emvumelwano eyimfuneko yokufunda amaqela e-Galois.
Esi sifundo siphawuleka ngakumbi kubuchule baso bokuveza iikhonsepthi ezintsonkothileyo ze-algebra ngendlela efikelelekayo nelula, evumela abafundi ukuba bafikelele ngokukhawuleza kwiziphumo ezinentsingiselo kunye nobuncinci be-formalism engabonakaliyo. Ilungile kubafundi bezibalo, befiziksi, okanye bobunjineli, kunye nabo bathanda imathematika abajonge ukwenza nzulu ukuqonda kwabo izakhiwo zealjibra kunye nokusetyenziswa kwazo.
Ngokugqiba le khosi, abathathi-nxaxheba abayi kufumana ukuqonda okunzulu kuphela kwethiyori yeGalois, kodwa baya kuba nethuba lokufumana isatifikethi ekwabelwana ngaso, bongeza ixabiso elibalulekileyo kwiprofayili yabo yobungcali okanye yezemfundo.
Uhlalutyo I (icandelo 1): Isandulela, iimbono ezisisiseko, amanani okwenene (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ikhosi "Uhlalutyo I (inxalenye ye-1): I-Prelude, iingcamango ezisisiseko, amanani okwenene ", enikezelwa yi-École Polytechnique Fédérale de Lausanne kwi-edX, isingeniso esinzulu kwiingcamango ezisisiseko zohlalutyo lwangempela. Le khosi yeeveki ezi-5, ifuna malunga neeyure ezi-4-5 zokufunda ngeveki, yenzelwe ukuba igqitywe ngesantya sakho.
Umxholo wekhosi uqala ngengabula-zigcawu ebuyela kwakhona kwaye yenza nzulu iingcamango zemathematika ezibalulekileyo ezifana nemisebenzi ye-trigonometric (isono, i-cos, i-tan), imisebenzi ehambelanayo (exp, ln), kunye nemithetho yokubala yamagunya, iilogarithms kunye neengcambu. Ikwabandakanya iiseti ezisisiseko kunye nemisebenzi.
Undoqo wekhosi ugxile kwiisistim zamanani. Ukuqala kwingcinga ecacileyo yamanani endalo, ikhosi ichaza ngokungqongqo amanani aqikelelwayo kwaye iphonononga iipropati zabo. Ingqalelo ngokukodwa ihlawulwa kumanani okwenene, aziswa ukuze kuzaliswe izithuba kumanani a-rational. Ikhosi ibonisa inkcazo ye-axiomatic yamanani okwenene kunye nokufunda iipropati zabo ngokweenkcukacha, kubandakanywa neekhonsepthi ezifana ne-infimum, i-supremum, ixabiso elipheleleyo kunye nezinye iimpawu ezongezelelweyo zamanani okwenene.
Le khosi ifanelekile kwabo banolwazi olusisiseko lwemathematika kwaye bafuna ukwenza nzulu ukuqonda kwabo uhlalutyo lwehlabathi lokwenyani. Iluncedo ngakumbi kubafundi bemathematika, fiziksi, okanye ubunjineli, kunye naye nabani na onomdla wokuqonda ngokungqongqo iziseko zemathematika.
Ngokugqiba le khosi, abathathi-nxaxheba baya kufumana ukuqonda okuqinileyo kwamanani okwenene kunye nokubaluleka kwabo kuhlalutyo, kunye nethuba lokufumana isatifikethi ekwabelwana ngaso, ukongeza ixabiso elibalulekileyo kwiprofayili yabo yobungcali okanye yezemfundo.
Uhlalutyo I (icandelo 2): Intshayelelo kumanani antsonkothileyo (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ikhosi "Uhlalutyo I (icandelo 2): Intshayelelo kumanani antsonkothileyo ", enikezelwa yi-École Polytechnique Fédérale de Lausanne kwi-edX, isingeniso esichukumisayo kwihlabathi lamanani anzima.Le khosi yeeveki ezi-2, ifuna malunga neeyure ezi-4-5 zokufunda ngeveki, yenzelwe ukuba igqitywe ngesantya sakho.
Ikhosi iqala ngokujongana ne-equation z^2 = -1, engenaso isisombululo kwiseti yamanani okwenene, R. Le ngxaki ikhokelela ekuqalisweni kwamanani anzima, C, intsimi equlethe i-R kwaye ivumela ukuba sisombulule ezinjalo. iiequations. Ikhosi iphonononga iindlela ezahlukeneyo zokumela inani elintsonkothileyo kwaye ixoxa ngezisombululo kwiinxaki zemo z^n = w, apho u-n engoka-N* kunye no-w ukuya ku-C.
Eyona nto ibalaseleyo kwesi sifundo kufundo lwethiyori esisiseko yealgebra, esisiphumo esingundoqo kwimathematika. Ikhosi ikwabandakanya izihloko ezifana nokumelwa kweCartesian yamanani anzima, iipropathi zawo ezisisiseko, into eguquguqukayo yokuphindaphinda, i-Euler kunye ne-de Moivre formula, kunye nefom yepolar yenombolo eyinkimbinkimbi.
Le khosi ifanelekile kwabo sele benolwazi oluthile lwamanani okwenene kwaye bafuna ukwandisa ukuqonda kwabo kumanani anzima. Iluncedo ngakumbi kubafundi bezibalo, fiziksi, okanye ubunjineli, kunye naye nabani na onomdla wokuqonda nzulu ialjebra kunye nokusetyenziswa kwayo.
Ngokugqiba le khosi, abathathi-nxaxheba baya kufumana ukuqonda okuqinileyo kwamanani antsokothileyo kunye nendima yabo ebalulekileyo kwimathematika, kunye nethuba lokufumana isatifikethi ekwabelwana ngaso, esongeza ixabiso elibalulekileyo kwiprofayili yabo yobungcali okanye yezemfundo.
Uhlalutyo I (icandelo 3): Ulandelelwano lwamanani okwenene I no-II (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ikhosi "Uhlalutyo I (icandelo 3): Ukulandelelana kwamanani okwenene I kunye no-II ", enikezelwa yi-École Polytechnique Fédérale de Lausanne kwi-edX, igxile ekulandeleni amanani okwenene. Le khosi yeeveki ezi-4, ifuna malunga neeyure ezi-4-5 zokufunda ngeveki, yenzelwe ukuba igqitywe ngesantya sakho.
Ingcamango engundoqo yale khosi ngumda wokulandelelana kwamanani okwenene. Iqala ngokuchaza ulandelelwano lwamanani okwenene njengomsebenzi ukusuka ku-N ukuya ku-R. Umzekelo, ulandelelwano a_n = 1/2^n luhlolisisiwe, lubonisa indlela esondela ngayo kwi-zero. Ikhosi ijongana ngokungqongqo inkcazo yomda wokulandelelana kwaye iphuhlise iindlela zokuseka ubukho bomda.
Ukongeza, ikhosi iseka ikhonkco phakathi kwengqikelelo yomda kunye naleyo ye-infimum kunye ne-supremum yeseti. Ukusetyenziswa okubalulekileyo kolandelelwano lwamanani okwenene kubonakaliswa yinto yokuba inani lokwenyani ngalinye linokuthathwa njengomda wokulandelelana kwamanani a-rational. Ikhosi iphinda iphonononge ulandelelwano lweCauchy kunye nolandelelwano oluchazwe ngokufakwa komgca, kunye ne-Bolzano-Weierstrass theorem.
Abathathi-nxaxheba baya kufunda kwakhona malunga nothotho lwamanani, kunye nentshayelelo kwimizekelo eyahlukeneyo kunye neendlela zokuhlangana, ezifana nekhrayitheriya ye-d'Alembert, ikhrayitheriya yeCauchy, kunye nekhrayitheriya yeLeibniz. Ikhosi iphetha ngokufunda uluhlu lwamanani kunye nepharamitha.
Le khosi ifanelekile kwabo banolwazi olusisiseko lwemathematika kwaye bafuna ukwenza nzulu ukuqonda kwabo ulandelelwano lwamanani lokwenyani. Iluncedo ngakumbi kubafundi bemathematika, ifiziksi okanye ubunjineli. Ngokugqiba le khosi, abathathi-nxaxheba baya kutyebisa ukuqonda kwabo imathematika kwaye banokufumana isatifikethi ekwabelwana ngaso, i-asethi yophuhliso lwabo lobungcali okanye lwezifundo.
Ukufunyanwa kweMisebenzi yokwenyani kunye neQhubekekayo: Uhlalutyo I (icandelo 4) (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ku "Uhlalutyo I (icandelo 4): Umda womsebenzi, imisebenzi eqhubekayo", i-École Polytechnique Fédérale de Lausanne inikezela ngohambo olunomdla kufundo lwemisebenzi yokwenyani yoguquko lwangempela.Le khosi, ehlala iiveki ezi-4 kunye ne-4 kwiiyure ze-5 zokufunda ngeveki, iyafumaneka kwi-edX kwaye ivumela ukuqhubela phambili ngesantya sakho.
Eli candelo lekhosi liqala ngokungeniswa kwemisebenzi yokwenyani, kugxininiswa kwiipropati zabo ezifana ne-monotonicity, i-parity, kunye ne-periodicity. Ikwaphonononga imisebenzi phakathi kwemisebenzi kwaye yazisa imisebenzi ethile efana nemisebenzi ye-hyperbolic. Ingqwalasela eyodwa inikwa kwimisebenzi echazwe ngokwenyathelo, kubandakanywa iSignum kunye nemisebenzi ye-Heaviside, kunye nokuguqulwa kwe-affine.
Ingundoqo yekhosi igxininise kumda obukhali womsebenzi kwinqanaba, ukubonelela ngemizekelo ephathekayo yemida yemisebenzi. Ikwabandakanya iingqikelelo zemida yasekhohlo nasekunene. Okulandelayo, ikhosi ijonga imida engapheliyo yemisebenzi kwaye ibonelela ngezixhobo ezibalulekileyo zokubala imida, njenge-cop theorem.
Inkalo ephambili yekhosi kukungeniswa kwengcamango yokuqhubeka, echazwe ngeendlela ezimbini ezahlukeneyo, kunye nokusetyenziswa kwayo ukwandisa imisebenzi ethile. Ikhosi iphela ngesifundo sokuqhubekeka kwamathuba avulekileyo.
Le khosi lithuba elityebisayo kwabo bajonge ukuqinisa ukuqonda kwabo imisebenzi yokwenyani kunye neqhubekayo. Ilungele abafundi bemathematika, ifiziksi okanye ubunjineli. Ngokugqiba le khosi, abathathi-nxaxheba abayi kwandisa i-horizons yabo yemathematika kuphela, kodwa baya kuba nethuba lokufumana isatifikethi esivuzayo, okuvula umnyango kwiimbono ezintsha zemfundo okanye zobungcali.
Ukuphonononga imisebenzi eyahlukeneyo: Uhlalutyo I (icandelo 5) (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
I-École Polytechnique Fédérale de Lausanne, ekuboneleleni kwayo ngemfundo kwi-edX, inikezela "Uhlalutyo I (icandelo 5): Imisebenzi eqhubekayo kunye nemisebenzi eyahlulayo, umsebenzi ophumayo". Le khosi yeeveki ezine, ifuna malunga neeyure ze-4-5 zokufunda ngeveki, kuphononongo olunzulu lweengcamango zokuhlukana kunye nokuqhubeka kwemisebenzi.
Ikhosi iqala ngophando olunzulu lwemisebenzi eqhubekayo, egxininisa kwiipropati zabo kwixesha elivaliweyo. Eli candelo linceda abafundi baqonde ubuninzi kunye nobuncinci bemisebenzi eqhubekayo. Ikhosi ke yazisa indlela yokucanda kabini kwaye ibonise iithiyori ezibalulekileyo ezifana nethiyori yexabiso eliphakathi kunye nethiyori yenqaku elimiselweyo.
Inxalenye esembindini yekhosi inikezelwe ekuhlukeni kunye nokungafani kwemisebenzi. Abafundi bafunda ukutolika la magama kunye nokuqonda ukulingana kwawo. Ikhosi ke ijonga ulwakhiwo lwe-derivative function kwaye iphonononga iipropati zayo ngokweenkcukacha, kubandakanywa nokusebenza kwealjibra kwimisebenzi ephuma kuyo.
Umba obalulekileyo wekhosi kuphononongo lweempawu zemisebenzi enokuhlukaniswa, njengokuphuma kokubunjwa komsebenzi, ithiyori kaRolle, kunye nethiyori yokunyusa isiphelo. Ikhosi iphinda iphonononge ukuqhubeka komsebenzi ophumayo kunye neempembelelo zayo kwi-monotonicity yomsebenzi ohlukeneyo.
Le khosi lithuba elihle kakhulu kwabo bafuna ukwenza nzulu ukuqonda kwabo ngemisebenzi eyahlulahluko kunye neqhubekayo. Ilungele abafundi bemathematika, ifiziksi okanye ubunjineli. Ngokugqiba le khosi, abathathi-nxaxheba abayi kwandisa nje ukuqonda kwabo iikhonsepthi ezisisiseko zemathematika, kodwa baya kuba nethuba lokufumana isatifikethi esivuzayo, bevula umnyango kumathuba amatsha emfundo okanye ubungcali.
Ukuzinzisa kuHlahlelo lweMathematika: Uhlalutyo I (icandelo 6) (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ikhosi "Uhlalutyo I (inxalenye ye-6): Izifundo zemisebenzi, uphuhliso olulinganiselweyo ", olunikezwa yi-École Polytechnique Fédérale de Lausanne kwi-edX, kuphononongo olunzulu lwemisebenzi kunye nophuhliso lwabo olulinganiselweyo. Le khosi ithatha iiveki ezine, enomthwalo onzima weeyure ezi-4 ukuya kwezi-5 ngeveki, ivumela abafundi ukuba baqhubele phambili ngokwesantya sabo.
Esi sahluko sekhosi sigxile kuphononongo olunzulu lwemisebenzi, kusetyenziswa iithiyori ukuphonononga ukwahluka kwazo. Emva kokujongana nethiyori yokunyuswa kwesiphelo, ikhosi ijonga ngokubanzi. Umba obalulekileyo wokufunda imisebenzi kukuqonda ukuziphatha kwabo ngokungenasiphelo. Ukwenza oku, ikhosi yazisa umgaqo weBernoulli-l'Hospital, isixhobo esibalulekileyo sokumisela imida enzima yee-quotients ezithile.
Ikhosi ikwaphonononga ukumelwa kwemizobo yemisebenzi, iphonononga imibuzo efana nobukho bendawo okanye i-global maxima okanye i-minima, kunye ne-convexity okanye i-concavity yemisebenzi. Abafundi baya kufunda ukuchonga ii-asymptotes ezahlukeneyo zomsebenzi.
Enye ingongoma eyomeleleyo yekhosi kukungeniswa kokwandiswa okulinganiselweyo komsebenzi, okubonelela ngokuqikelelwa kwe-polynomial kwindawo ekufutshane nenqaku elinikiweyo. Olu phuhliso lubalulekile ukwenza lula ukubalwa kwemida kunye nophononongo lweempawu zemisebenzi. Ikhosi ikwaquka uthotho olupheleleyo kunye neradiyasi yokuhlangana, kunye nothotho lweTaylor, isixhobo esinamandla sokumela imisebenzi enokuhlukaniswa ngokungenasiphelo.
Le khosi sisixhobo esixabisekileyo kwabo bafuna ukwenza nzulu ukuqonda kwabo imisebenzi kunye nokusetyenziswa kwabo kwimathematika. Ibonelela ngembono etyebisayo neneenkcukacha kwiikhonsepthi eziphambili kuhlalutyo lwemathematika.
Ubuchule boManyano: Uhlalutyo I (icandelo 7) (ISIKOLO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Ikhosi "Uhlalutyo I (inxalenye ye-7): Iindibaniselwano ezingapheliyo kunye ezicacileyo, ukudibanisa (izahluko ezikhethiweyo)", ezinikezelwa yi-École Polytechnique Fédérale de Lausanne kwi-edX, ukuphononongwa okucacileyo kokuhlanganiswa kwemisebenzi. Le modyuli, ethatha iiveki ezine ngokubandakanyeka kweeyure ezi-4 ukuya kwezi-5 ngeveki, ivumela abafundi ukuba bafumanise ubucukubhede bokuhlanganisa ngesantya sabo.
Ikhosi iqala ngengcaciso yokudityaniswa okungapheliyo kunye nokudityaniswa okuqinisekileyo, ukwazisa okudityanisiweyo okuqinisekileyo nge-Riemann sums kunye nezibalo eziphezulu nezisezantsi. Emva koko ixoxa ngeempawu ezintathu eziphambili zee-integrals ezicacileyo: umgca we-integal, ulwahlulo lwe-domain yokudibanisa, kunye ne-monotonicity ye-integral.
Inqaku eliphambili kwikhosi yinkcazo yenkcazo yemisebenzi eqhubekayo kwicandelo, eliboniswe ngokweenkcukacha. Ikhosi ifikelela kuvutho-ndaba ngethiyori esisiseko ye-calculus edibeneyo, izisa ingcamango ye-antiderivative yomsebenzi. Abafundi bafunda iindlela ezahlukeneyo zokuhlanganisa, ezinje ngokudityaniswa ngamalungu, ukutshintsha izinto eziguquguqukayo, kunye nokudibanisa ngokufakwa.
Ikhosi iqukumbela ngesifundo sokudityaniswa kwemisebenzi ethile, kubandakanywa ukudityaniswa kokwandiswa okulinganiselweyo komsebenzi, ukudityaniswa koluhlu olupheleleyo, kunye nokudityaniswa kwemisebenzi eqhubekayo. Obu buchule buvumela ukudityaniswa kwemisebenzi kunye neefom ezikhethekileyo ukuba zibalwe ngokufanelekileyo. Okokugqibela, ikhosi iphonononga izinto ezidityanisiweyo ngokubanzi, ezichazwa ngokudlula umda kwizinto ezidityanisiweyo, kwaye zibonisa imizekelo ebambekayo.
Esi sifundo sisixhobo esixabisekileyo kwabo bafuna ukugqwesa ukumanyanisa, isixhobo esisisiseko kwimathematika. Ibonelela ngembono ebanzi nesebenzayo yokumanyanisa, ixhobisa izakhono zabafundi zemathematika.
Izifundo ngesiNgesi
Intshayelelo kwiiModeli zeLinear kunye ne-Matrix Algebra (eHarvard)
IYunivesithi yaseHarvard, ngeqonga layo leHarvardX kwi-edX, ibonelela ngesifundo "Intshayelelo kwiiModeli zeLinear kunye neMatrix Algebra". Nangona ikhosi ifundiswa ngesiNgesi, inika ithuba elikhethekileyo lokufunda iziseko ze-matrix algebra kunye neemodeli zemigca, izakhono eziyimfuneko kwiinkalo ezininzi zenzululwazi.
Le khosi yeeveki ezine, ifuna iiyure ezi-2 ukuya kwezi-4 zokufunda ngeveki, yenzelwe ukuba igqitywe ngesantya sakho. Ijolise ekusebenziseni ulwimi lweprogram ye-R ukusebenzisa iimodeli zelinear kuhlalutyo lwedatha, ngakumbi kwisayensi yobomi. Abafundi baya kufunda ukusebenzisa i-matrix algebra kwaye baqonde ukusetyenziswa kwayo kuyilo lovavanyo kunye nohlalutyo oluphezulu lwedatha.
Inkqubo ibandakanya i-matrix algebra notation, imisebenzi ye-matrix, ukusetyenziswa kwe-matrix algebra kuhlalutyo lwedatha, iimodeli zomgca, kunye nentshayelelo yokubola kwe-QR. Le khosi yinxalenye yoluhlu lwezifundo ezisixhenxe, ezinokuthi zithathwe ngabanye okanye njengenxalenye yezatifikethi ezimbini zobungcali kwi-Data Uhlalutyo lweSayensi yoBomi kunye neGenomic Data Analysis.
Le khosi ifanelekile kwabo bajonge ukufumana izakhono kwimodeli yamanani kunye nohlalutyo lwedatha, ngakumbi kumxholo wesayensi yobomi. Ibonelela ngesiseko esiluqilima kwabo banqwenela ukuphonononga ngakumbi i-matrix algebra kunye nokusetyenziswa kwayo kwiinkalo ezahlukeneyo zenzululwazi kunye nophando.
I-Master Probability (eHarvard)
LUluhlu lokudlalwayo lwe- "Statistics 110: Inokwenzeka" kuYouTube, efundiswa ngesiNgesi nguJoe Blitzstein weYunivesithi yaseHarvard, sisixhobo esixabiseke kakhulu kwabo bajonge ukukhulisa ulwazi lwabo lokwenzeka.. Uluhlu lokudlalayo lubandakanya iividiyo zesifundo, izixhobo zokuphonononga, kunye nokuzivocavoca okungaphezulu kwama-250 kunye nezisombululo ezineenkcukacha.
Le khosi yesiNgesi yintshayelelo ebanzi yokwenzekayo, enikezelwa njengolwimi olubalulekileyo kunye neseti yezixhobo zokuqonda izibalo, isayensi, umngcipheko kunye nokungakhethi. Iikhonsepthi ezifundiswayo ziyasebenza kwiinkalo ezahlukeneyo ezifana namanani, isayensi, ubunjineli, uqoqosho, imali kunye nobomi bemihla ngemihla.
Izihloko ezigutyungelwe zibandakanya iziseko ezinokwenzeka, ukuguquguquka okungahleliwe kunye nokuhanjiswa kwazo, ukusabalalisa okungafaniyo kunye ne-multivariate, ii-theorems zokukhawulela, kunye ne-Markov chains. Ikhosi ifuna ulwazi lwangaphambili lwecalculus eguquguqukayo enye kunye nokuqhelana nematrices.
Kwabo bakhululekileyo ngesiNgesi kwaye banomdla wokuphonononga ilizwe elinokwenzeka nzulu, olu ngcelele lwezifundo zeHarvard lubonelela ngamathuba okufunda atyebisayo. Unokufikelela kuluhlu lokudlala kunye nemixholo yalo eneenkcukacha ngokuthe ngqo kuYouTube.
Ubunokwenzeka buchaziwe. Ikhosi enemibhalo engezantsi yesiFrentshi (eHarvard)
Ikhosi ethi "Ithuba lokutyeba: Ukunokwenzeka ukusuka kwi-Ground Up," enikezelwa ngu-HarvardX kwi-edX, yintshayelelo enomdla kumathuba kunye namanani. Nangona ikhosi ifundiswa ngesiNgesi, iyafikeleleka kubaphulaphuli abathetha isiFrentshi ngenxa yemibhalo engezantsi yesiFrentshi ekhoyo.
Le khosi yeeveki ezisixhenxe, ifuna iiyure ezi-3 ukuya kwezi-5 zokufunda ngeveki, yenzelwe abo baqalayo ukufunda ukuba kunokwenzeka okanye abafuna uphononongo olufikelelekayo lweekhonsepthi eziphambili phambi kokubhalisa kwikhosi yezibalo. I-“Fat Chance” igxininisa ekuphuhliseni ukucinga ngemathematika kunokunkqaya amagama neefomula.
Iimodyuli zokuqala zazisa izakhono zokubala ezisisiseko, ezithi ke zisetyenziswe kwiingxaki ezilula ezinokwenzeka. Iimodyuli ezilandelayo ziphonononga ukuba ezi mbono kunye nobuchule bunokulungiswa njani ukujongana noluhlu olubanzi lweengxaki ezinokwenzeka. Ikhosi iphetha ngentshayelelo yezibalo ngeengcinga zexabiso elilindelekileyo, umahluko kunye nokuhanjiswa okuqhelekileyo.
Le khosi ilungele abo bafuna ukwandisa izakhono zabo zokuqiqa kunye nokuqonda iziseko zokwenzeka kunye neenkcukacha-manani. Ibonelela ngembono etyebisayo malunga nemo eyongezelekayo yemathematika kunye nendlela esebenza ngayo ekuqondeni umngcipheko nokungakhethi buso.
Ukungeniswa koBalo kunye nokuModeli kuMfuniselo oPhakamileyo (iHarvard)
Ikhosi ye-"Statistical Inference and Modeling for High-throughput Experiments" ngesiNgesi igxininise kwiindlela zobuchule ezisetyenziselwa ukwenza i-statistical inference kwi-high-throughput data. Le khosi yeeveki ezine, ifuna i-2-4 iiyure zokufunda ngeveki, ngumthombo oxabisekileyo kwabo bafuna ukuqonda nokusebenzisa iindlela zamanani eziphambili kwizicwangciso zophando olunzulu.
Inkqubo ihlanganisa izihloko ezahlukeneyo, kubandakanywa ingxaki yokuthelekisa ezininzi, amazinga eempazamo, iinkqubo zokulawula izinga lempazamo, amazinga okufumanisa ubuxoki, amaxabiso e-q, kunye nohlalutyo lwedatha yokuhlola. Ikwazisa imodeli yeenkcukacha-manani kunye nokusetyenziswa kwayo kwidatha ephezulu, ixoxa ngosasazo lweparametric olufana ne-binomial, i-exponential, kunye ne-gamma, kunye nokuchaza uqikelelo olunokwenzeka oluphezulu.
Abafundi baya kufunda ukuba ezi ngqikelelo zisetyenziswa njani kumxholo onjengolandelelwano lwesizukulwana esilandelayo kunye nedatha ye-microarray. Ikhosi ikwabandakanya iimodeli zoluhlu kunye ne-Bayesian empirics, kunye nemizekelo ebonakalayo yokusetyenziswa kwazo.
Le khosi ifanelekile kwabo bajonge ukwenza nzulu ukuqonda kwabo ngeenkcukacha-manani kunye nemodeli kuphando lwesayensi lwanamhlanje. Ibonelela ngembono enzulu kuhlalutyo lweenkcukacha-manani zedatha entsonkothileyo kwaye isisityebi esigqwesileyo kubaphandi, abafundi kunye neengcali kwiinkalo zenzululwazi yobomi, i-bioinformatics kunye nezibalo.
Intshayelelo kuKunokwenzeka (iHarvard)
Ikhosi "Intshayelelo yoKunokwenzeka", enikezelwa nguHarvardX kwi-edX, luphononongo olunzulu lokunokwenzeka, ulwimi oluyimfuneko kunye nesixhobo sokuqonda idatha, ithuba, kunye nokungaqiniseki. Nangona ikhosi ifundiswa ngesiNgesi, iyafikeleleka kubaphulaphuli abathetha isiFrentshi ngenxa yemibhalo engezantsi yesiFrentshi ekhoyo.
Le khosi yeeveki ezilishumi, ifuna iiyure ezi-5-10 zokufunda ngeveki, ijolise ekuziseni ingqiqo kwihlabathi elizaliswe ngamathuba kunye nokungaqiniseki. Iya kubonelela ngezixhobo ezifunekayo ukuqonda idatha, isayensi, ifilosofi, ubunjineli, uqoqosho kunye nezezimali. Awuyi kufunda kuphela indlela yokusombulula iingxaki ezinzima zobugcisa, kodwa kunye nendlela yokusebenzisa ezi zisombululo kubomi bemihla ngemihla.
Ngemizekelo esusela kuvavanyo lwezonyango ukuya kuqikelelo lwezemidlalo, uya kufumana isiseko esiluqilima sophononongo lothelekiso lwamanani, iinkqubo zestochastic, i-algorithms engacwangciswanga, kunye nezinye izihloko apho okunokwenzeka kuyimfuneko.
Le khosi ilungele abo bajonge ukwandisa ukuqonda kwabo ukungaqiniseki kunye nethuba, ukwenza uqikelelo olulungileyo, kunye nokuqonda okuguquguqukayo okungahleliwe. Ibonelela ngembono etyebisayo kunikezelo olunokwenzeka oluqhelekileyo olusetyenziswa kwizibalo nakwisayensi yedatha.
Ikhalculum esetyenzisiweyo (eHarvard)
Ikhosi ye-“Calculus Applied!”, enikezelwa nguHarvard kwi-edX, luphononongo olunzulu lokusetyenziswa kwezibalo ezinoguquko olunye kwezentlalo, ubomi, kunye nenzululwazi yendalo. Le khosi, ngokupheleleyo ngesiNgesi, lithuba elihle kakhulu kwabo bafuna ukuqonda ukuba icalculus isetyenziswa njani kwiimeko zobuchwephesha behlabathi bokwenyani.
Ihlala iiveki ezilishumi kwaye ifuna phakathi kwe-3 kunye neeyure ze-6 zokufunda ngeveki, le khosi ihamba ngaphaya kweencwadi zendabuko. Usebenzisana neengcali ezivela kwiinkalo ezahlukeneyo ukubonisa indlela icalculus esetyenziswa ngayo ukuhlalutya kunye nokusombulula iingxaki zehlabathi lokwenyani. Abafundi baya kuphonononga izicelo ezahlukeneyo, ukusukela kuhlalutyo lwezoqoqosho ukuya kwimodeli yebhayoloji.
Iprogram ibandakanya ukusetyenziswa kwezinto eziphuma kwi-derivatives, integrals, differential equations, kwaye igxininisa ukubaluleka kweemodeli zemathematika kunye neeparamitha. Yenzelwe abo banokuqonda okusisiseko kwe-calculus eguquguqukayo enye kwaye banomdla kwizicelo ezisebenzayo kwiinkalo ezahlukeneyo.
Le khosi ifanelekile kubafundi, ootitshala, kunye neengcali ezijonge ukwenza nzulu ukuqonda kwazo ngecalculus kwaye zifumanise usetyenziso lwayo lwehlabathi lokwenyani.
Intshayelelo yokuqiqa kwemathematika (eStanford)
Ikhosi “yentshayelelo yokuCinga ngeMathematika”, efundiswa yiYunivesithi yaseStanford eCoursera, kukuntywila kwihlabathi lokuqiqa kwemathematika. Nangona ikhosi ifundiswa ngesiNgesi, iyafikeleleka kubaphulaphuli abathetha isiFrentshi ngenxa yemibhalo engezantsi yesiFrentshi ekhoyo.
Le khosi yeeveki ezisixhenxe, ifuna malunga neeyure ezingama-38 zizonke, okanye malunga neeyure ezili-12 ngeveki, yenzelwe abo banqwenela ukuphuhlisa indlela yokucinga yemathematika, ngokwahlukileyo ekuqheliseleni nje imathematika njengoko isoloko iboniswa kwinkqubo yesikolo. Esi sifundo sigxininisa ekuphuhliseni indlela yokucinga “engaphandle kwebhokisi”, isakhono esibalulekileyo kwihlabathi lanamhlanje.
Abafundi baya kuphonononga indlela iingcali zemathematika ezicinga ngayo ukusombulula iingxaki zehlabathi lokwenene, nokuba zivela kwihlabathi lemihla ngemihla, kwisayensi, okanye kwimathematika ngokwayo. Ikhosi inceda ekuphuhliseni le ndlela ibalulekileyo yokucinga, idlulela ngaphaya kweenkqubo zokufunda ukusombulula iingxaki ezibambekayo.
Le khosi ifanelekile kwabo bajonge ukomeleza ukuqiqa kwabo kobungakanani kunye nokuqonda iziseko zokuqiqa kwemathematika. Ibonelela ngembono etyebisayo malunga nemo eyongezelekayo yemathematika nokusetyenziswa kwayo ekuqondeni iingxaki ezinzima.
Ufundo-manani kunye no-R (eStanford)
Ikhosi ye-“Statistical Learning with R”, ebonelelwa nguStanford, yintshayelelo yenqanaba eliphakathi kwimfundo ebekwe esweni, egxile ekubuyeleni umva kunye neendlela zokuhlela. Le khosi, ngokupheleleyo ngesiNgesi, sisixhobo esixabisekileyo kwabo bafuna ukuqonda nokusebenzisa iindlela zobalo kwicandelo lenzululwazi yedatha.
Ithathe iiveki ezilishumi elinanye kwaye ifuna iiyure ezi-3-5 zokufunda ngeveki, ikhosi ibandakanya zombini iindlela zemveli kunye nezichulumancisayo kwimodeli yamanani, kunye nendlela yokuzisebenzisa kulwimi lwenkqubo ye-R. Ikhosi yahlaziywa ngo-2021 kuhlelo lwesibini lwe incwadi yesifundo.
Izihloko ziquka ukuguqulwa komgca kunye ne-polynomial regression, ukuguqulwa kwezinto kunye nokuhlalutya okucaluliweyo, ukuqinisekiswa kwe-cross-validation kunye ne-bootstrapping, ukhetho lwemodeli kunye neendlela eziqhelekileyo (i-ridge kunye ne-lasso), imizekelo engabonakaliyo, i-splines kunye neemodeli ezongezelelweyo ngokubanzi, iindlela ezisekelwe kwimithi, amahlathi angaqhelekanga kunye nokunyusa, Ukuxhasa oomatshini be-vector, iinethiwekhi ze-neural kunye nokufunda okunzulu, iimodeli zokusinda, kunye novavanyo oluninzi.
Le khosi ifanelekile kwabo banolwazi olusisiseko lwezibalo, i-algebra yomgca, kunye nesayensi yekhompyutha, kwaye abafuna ukuqinisa ukuqonda kwabo ukufunda ngezibalo kunye nokusetyenziswa kwayo kwisayensi yedatha.
Uzifunda njani izibalo: Ikhosi yomntu wonke (eStanford)
Ikhosi “yeSifundo seMathematika: yaBafundi”, efundiswa nguStanford. Yikhosi yasimahla ye-intanethi yabafundi bawo onke amanqanaba ezibalo. Ngokupheleleyo ngesiNgesi, idibanisa ulwazi olubalulekileyo malunga nengqondo kunye nobungqina obutsha malunga neendlela ezilungileyo zokufikelela kwimathematika.
Ihlala iiveki ezintandathu kwaye ifuna i-1 ukuya kwiiyure ze-3 zokufunda ngeveki. Ikhosi yenzelwe ukutshintsha ubudlelwane babafundi nemathematika. Abantu abaninzi baye baba namava angalunganga ngezibalo, nto leyo ekhokelela ekuzicaphukiseni okanye ekusileleni. Le khosi ijolise ekunikeni abafundi ulwazi abaludingayo ukuze bayonwabele imathematika.
Kugutyungelwe izihloko ezifana nengqondo kunye nokufunda izibalo. Iintsomi malunga nezibalo, indlela yokucinga, iimpazamo kunye nesantya nazo ziyaqukwa. Ukuguquguquka kwamanani, ukuqiqa ngemathematika, uqhagamshelwano, iimodeli zamanani nazo ziyinxalenye yeprogram. Ukubonakaliswa kweemathematika ebomini, kodwa nakwindalo kunye nasemsebenzini akulibaleki. Ikhosi iyilwe nge-pedagogy yothethathethwano esebenzayo, isenza ukufunda kunxibelelane kwaye kuguquguquke.
Sisixhobo esixabisekileyo kuye nabani na ofuna ukubona imathematika ngokwahlukileyo. Phuhlisa ukuqonda okunzulu nokwakhayo kolu qeqesho. Ifaneleke ngakumbi abo banamava angalunganga kwizibalo kwixesha elidlulileyo kwaye bajonge ukuyitshintsha le mbono.
Ulawulo olunokwenzeka (eStanford)
Ikhosi “yentshayelelo yoLawulo lokunokwenzeka”, enikezelwa nguStanford, yintshayelelo yoqeqesho lolawulo lokwenzekayo. Lo mmandla ugxile ekunxibelelana nasekubaleni ukungaqiniseki ngendlela yeetheyibhile zedatha eziphicothwayo ezibizwa ngokuba yiStochastic Information Packets (SIPs). Le khosi yeeveki ezilishumi ifuna i-1 kwiyure yokufunda ngeveki ye-5. Akungabazeki ukuba ngumthombo oxabisekileyo kwabo bafuna ukuqonda nokusebenzisa iindlela zobalo kwinkalo yesayensi yedatha.
Ikharityhulam yekhosi igubungela izihloko ezifana nokuqaphela "i-Flaw of Average," iseti yeempazamo ezicwangcisiweyo ezivela xa ukungaqiniseki kubonakaliswa ngamanani omnye, ngokuqhelekileyo i-avareji. Icacisa ukuba kutheni iiprojekthi ezininzi zifika emva kwexesha, zidlula kuhlahlo lwabiwo-mali kwaye ziphantsi kohlahlo lwabiwo-mali. Ikhosi ikwafundisa ukungaqiniseki kwe-Arithmetic, eyenza izibalo ngamagalelo angaqinisekanga, okukhokelela kwiziphumo ezingaqinisekanga apho unokubala iziphumo zokwenyani zomndilili kunye namathuba okufikelela kwiinjongo ezichaziweyo.
Abafundi baya kufunda ukwenza ukulinganisa okusebenzisanayo okunokwabelwana naye nawuphi na umsebenzisi we-Excel ngaphandle kokufuna ukongezwa okanye iimacros. Le ndlela ifanelekile ngokulinganayo kwiPython okanye nayiphi na imeko yeprogram exhasa ii-arrays.
Le khosi ilungele abo bakhululekileyo ngeMicrosoft Excel kwaye bajonge ukwenza nzulu ukuqonda kwabo ulawulo lokwenzeka kunye nokusetyenziswa kwayo kwisayensi yedatha.
Inzululwazi yokungaqiniseki kunye neDatha (MIT)
Ikhosi "Inokwenzeka - iSayensi yokungaqiniseki kunye neDatha", enikezelwa yiMassachusetts Institute of Technology (MIT). Yintshayelelo esisiseko kwisayensi yedatha ngokusebenzisa iimodeli ezinokwenzeka. Le khosi ithatha iiveki ezilishumi elinesithandathu, ifuna iiyure ezili-10 ukuya kwezili-14 zokufunda ngeveki. Ihambelana nenxalenye yenkqubo yeMIT MicroMasters kwizibalo kunye nesayensi yedatha.
Le khosi iphonononga ihlabathi lokungaqiniseki: ukusuka kwiingozi kwiimarike zemali ezingalindelekanga ukuya kunxibelelwano. Ukwenziwa komfuziselo okunokwenzeka kunye nenkalo enxulumeneyo yokuthelekelela ngokwamanani. Ngaba izitshixo ezibini zokuhlalutya le datha kunye nokwenza uqikelelo oluvakalayo ngokwesayensi.
Abafundi baya kufumanisa ubume kunye nezinto ezisisiseko zeemodeli ezinokwenzeka. Kubandakanya ukuguquguquka okungahleliwe, ukuhanjiswa kwazo, iindlela kunye nokwahluka. Ikhosi ikwabandakanya iindlela zokucinga. Imithetho yamanani amakhulu kunye nezicelo zabo, kunye neenkqubo ezizenzekelayo.
Le khosi ifanelekile kwabo bafuna ulwazi olusisiseko kwisayensi yedatha. Ibonelela ngembono ebanzi kwiimodeli ezinokwenzeka. Ukusuka kwizinto ezisisiseko ukuya kwiinkqubo ezingaqhelekanga kunye nokuqikelelwa kwamanani. Konke oku kuluncedo kakhulu kwiingcali kunye nabafundi. Ngokukodwa kwiinkalo zenzululwazi yedatha, ubunjineli kunye nezibalo.
Ukuba nokwenzeka koBalo kunye nokuQikelela (MIT)
I-Massachusetts Institute of Technology (MIT) inikezela ngesifundo se-"Computational Probability and Inference" ngesiNgesi. Inkqubo ibandakanya intshayelelo yenqanaba eliphakathi kuhlalutyo olunokwenzeka kunye nokuthelekelela. Le khosi yeeveki ezilishumi elinambini, ifuna iiyure ezi-4 ukuya kwezi-6 ngeveki, luphononongo olunika umdla lwendlela okunokwenzeka ngayo kunye nokuthelekelela ezisetyenziswa kwiindawo ezahlukeneyo njengokucoca i-spam, ukuhamba kwe-bot ehambayo, okanye nakwimidlalo yeqhinga efana ne-Jeopardy kunye ne-Go.
Kule khosi, uya kufunda imigaqo yokwenzeka kunye nokuthelekelela kunye nendlela yokuyiphumeza kwiinkqubo zekhompyuter eziqiqayo ngokungaqinisekanga kwaye wenze uqikelelo. Uya kufunda malunga nolwakhiwo lwedatha olwahlukeneyo lokugcina unikezelo lokwenzeka, njengemifuziselo yegraphical enokwenzeka, kwaye uphuhlise i-algorithms esebenzayo yokuqiqa ngolu luhlu lwedatha.
Ekupheleni kwesi sifundo, uya kukwazi ukuba ungayenza njani imodeli yeengxaki zehlabathi lokwenyani ngokunokwenzeka kunye nendlela yokusebenzisa iimodeli ezineziphumo zokuthelekelela. Awudingi ukuba namava angaphambili kwinto enokwenzeka okanye intelekelelo, kodwa kuya kufuneka ukhululeke ngesiseko senkqubo yePython kunye nokubala.
Le khosi sisixhobo esibalulekileyo kwabo bafuna ukuqonda nokusebenzisa iindlela zobalo kwicandelo lenzululwazi yedatha, ibonelela ngembono ebanzi kwiimodeli ezinokwenzeka kunye nokuthelekelela ngokwamanani.
Kwintliziyo yokungaqiniseki: I-MIT ichaza ukuba kunokwenzeka
Kwikhosi "Intshayelelo kwiCandelo le-II elinokwenzeka: Iinkqubo zokungeniswa", iMassachusetts Institute of Technology (MIT) ibonelela ngokuntywiliselwa okuphambili kwihlabathi lokunokwenzeka kunye nokuthelekelela. Le khosi, ngokupheleleyo ngesiNgesi, kukuqhubela phambili okunengqiqo kwecandelo lokuqala, ukungena nzulu kuhlalutyo lwedatha kunye nesayensi yokungaqiniseki.
Kwithuba leeveki ezilishumi elinesithandathu, kunye nokuzibophelela kweeyure ze-6 ngeveki, le khosi iphonononga imithetho yamanani amaninzi, iindlela ze-Bayesian inference, izibalo zeklasi, kunye neenkqubo ezizenzekelayo ezifana neenkqubo zePoisson kunye namatyathanga eMarkov. Olu luphononongo olungqongqo, olujoliswe kwabo sele benesiseko esiluqilima ngokunokwenzeka.
Le khosi ibalasele ngendlela yayo ecacileyo, ngelixa igcina ubukhali bezibalo. Ayibonisi nje iithiyori kunye nobungqina, kodwa ijolise ekuphuhliseni ukuqonda okunzulu kweekhonsepthi ngezicelo ezibambekayo. Abafundi baya kufunda ukwenza imodeli yeziganeko ezinzima kwaye batolike idatha yelizwe lokwenyani.
Ilungele iingcali zenzululwazi yedatha, abaphandi, kunye nabafundi, le khosi ibonelela ngembono eyodwa malunga nokuba kunokwenzeka njani kunye nokuthelekelela ukuqonda kwethu ihlabathi. Ifanelekile kwabo bajonge ukukhulisa ukuqonda kwabo kwisayensi yedatha kunye nohlalutyo lwamanani.
I-Analytical Combinatorics: Ikhosi yePrinceton yokuCinga iZakhiwo eziNxibelele (Princeton)
Ikhosi ye-Analytic Combinatorics, enikezelwa yiYunivesithi yasePrinceton, luphononongo olunomdla lwe-combinatorics yohlalutyo, uqeqesho oluvumela uqikelelo oluchanekileyo lobungakanani bezakhiwo ezidityanisiweyo ezintsonkothileyo. Le khosi, iphelele ngesiNgesi, sisixhobo esixabisekileyo kwabo bafuna ukuqonda nokusebenzisa iindlela eziphucukileyo kwicandelo lee-combintorics.
Ihlala iiveki ezintathu kwaye ifuna malunga neeyure ze-16 zizonke, okanye malunga neeyure ze-5 ngeveki, le khosi yazisa indlela yomfuziselo yokufumana ubudlelwane obusebenzayo phakathi kwemisebenzi eqhelekileyo, ecacileyo, kunye ne-multivariate yokuvelisa. Ikwaphonononga iindlela zohlalutyo oluntsonkothileyo lokufumana ii-asymptotics ezichanekileyo kwii-equations zemisebenzi yokuvelisa.
Abafundi baya kufumanisa ukuba i-combinatorics yohlalutyo ingasetyenziswa njani ukuqikelela amanani achanekileyo kwizakhiwo ezinkulu zokudityaniswa. Baya kufunda ukuxhaphaza izakhiwo ezidibeneyo kwaye basebenzise iindlela zokuhlalutya ezinzima ukuhlalutya ezi zakhiwo.
Le khosi ilungele abo bajonge ukuqinisa ukuqonda kwabo i-combinatorics kunye nokusetyenziswa kwayo ekusombululeni iingxaki ezinzima. Ibonelela ngembono eyodwa malunga nendlela i-combintorics yohlalutyo ibumba ukuqonda kwethu kwezibalo kunye nezakhiwo ezidibeneyo.
