Makosi muFrench
Random: Nhanganyaya kune Mukana - Chikamu 1 (POLYTECHNIQUE PARIS)
École Polytechnique, inzvimbo ine mukurumbira, inopa kosi inonakidza paCoursera ine musoro unoti "Random: sumo kune zvingangoitika - Chikamu 1". Iyi kosi, inogara maawa angangoita makumi maviri nemanomwe akapararira kwemavhiki matatu, mukana wakasarudzika kune chero munhu anofarira nheyo dzekugona. Yakagadzirwa kuti ishanduke uye ichienderana nekumhanya kwemudzidzi wega-wega, kosi iyi inopa yakadzama uye inosvikika nzira yekugona dzidziso.
Chirongwa ichi chine 8 inobata mamodule, imwe neimwe ichitaura zvakakosha zvezvingabvira nzvimbo, yunifomu mitemo yemukana, mamiriro, rusununguko, uye zvisingaite. Imwe neimwe moduli inokwenenzverwa nemavhidhiyo anotsanangura, yekuwedzera kuverenga uye quizzes yekuyedza nekubatanidza ruzivo rwakawanikwa. Vadzidzi vanewo mukana wekuwana chitupa chinogovaniswa kana vapedza kosi, vachiwedzera kukosha kurwendo rwavo rwehunyanzvi kana rwedzidzo.
Varairidzi, Sylvie Méléard, Jean-René Chazottes naCarl Graham, vese vakabatana neÉcole Polytechnique, vanounza hunyanzvi hwavo uye shungu dzemasvomhu, zvichiita kuti kosi iyi ive kwete yekudzidzisa chete, asiwo inokurudzira. Kunyangwe iwe uri mudzidzi wemasvomhu, inyanzvi iri kutsvaga kudzamisa ruzivo rwako, kana kungofarira sainzi, kosi iyi inopa mukana wakasarudzika wekuongorora munyika inonakidza yezvinogoneka, ichitungamirwa nedzimwe dzepfungwa dzakanaka paÉcole Polytechnique.
Random: Nhanganyaya kune Mukana - Chikamu 2 (POLYTECHNIQUE PARIS)
Kuenderera mberi nekunaka kwedzidzo kweÉcole Polytechnique, kosi "Random: sumo kune zvingangoitika - Chikamu 2" paCoursera kuenderera kwakananga uye kunopfumisa kwechikamu chekutanga. Kosi iyi, inofungidzirwa kuti inotora maawa gumi nemanomwe yakapararira kwemavhiki matatu, inonyudza vadzidzi mune imwe pfungwa yepamusoro-soro yezvingangoitika dzidziso, ichipa kunzwisisa kwakadzama uye mashandisirwo akazara eichi chirango chinonakidza.
Iine 6-yakanyatsorongeka mamodule, kosi inovhara misoro yakadai seasina mavheti, generalization yekuverenga mutemo, mutemo wenhamba huru theorem, iyo Monte Carlo nzira, uye yepakati muganhu theorem. Imwe neimwe module inosanganisira mavhidhiyo edzidzo, kuverenga uye quizzes, kune inonyudza yekudzidza chiitiko. Iyi fomati inobvumira vadzidzi kuti vabatane zvine mutsindo nezvinhu uye kushandisa pfungwa dzakadzidzwa nenzira inoshanda.
Varairidzi, Sylvie Méléard, Jean-René Chazottes naCarl Graham vanoramba vachitungamirira vadzidzi murwendo urwu rwedzidzo nehunyanzvi hwavo uye chido chesvomhu. Nzira yavo yekudzidzisa inofambisa kunzwisiswa kwepfungwa dzakaoma uye inokurudzira kuongorora kwakadzama kwezvingangoitika.
Iyi kosi yakanakira avo vanotova nehwaro hwakasimba mune mukana uye vanoda kuwedzera kunzwisisa kwavo uye kugona kushandisa aya pfungwa kumatambudziko akaomarara. Nekupedza kosi iyi, vadzidzi vanogona zvakare kuwana chitupa chinogovaniswa, vachiratidza kuzvipira kwavo uye kugona kwavo munzvimbo iyi yakasarudzika.
Nhanganyaya yekugovera dzidziso (POLYTECHNIQUE PARIS)
Kosi ye "Sumo yedzidziso yekugovera", inopihwa neÉcole Polytechnique paCoursera, inomiririra kuongorora kwakasiyana uye kwakadzama kwenzvimbo yepamusoro yemasvomhu. Iyi kosi, inogara maawa angangoita gumi nemashanu akapararira kwemavhiki matatu, yakagadzirirwa avo vari kutsvaga kunzwisisa kugovera, pfungwa yakakosha mukushandiswa kwemasvomhu uye ongororo.
Chirongwa ichi chine 9 module, imwe neimwe ichipa musanganiswa wemavhidhiyo edzidzo, kuverenga uye quizzes. Aya mamodule anovhara akasiyana siyana edzidziso yekugovera, kusanganisira nyaya dzakaomarara sekutsanangudza zvakabva kune risingaenderereki basa uye kushandisa discontinuous mabasa semhinduro kusiyanisa equations. Iyi nzira yakarongeka inobvumira vadzidzi kuti vazive zvishoma nezvishoma nemafungiro angaita seanotyisa pakutanga.
Mapurofesa François Golse naYvan Martel, vese vari nhengo dzakatanhamara dzeÉcole Polytechnique, vanounza hunyanzvi hukuru pafundo iyi. Dzidziso yavo inosanganisa kuomarara kwedzidzo uye nzira itsva dzekudzidzisa, zvichiita kuti zvirimo zviwanike uye zvine chekuita nevadzidzi.
Kosi iyi inonyanya kukodzera vadzidzi vesvomhu, mainjiniya, kana minda ine hukama vari kutarisa kudzamisa kunzwisisa kwavo kwemaitiro akaomarara esvomhu. Nekupedza kosi iyi, vatori vechikamu havangove vakawana ruzivo rwakakosha chete, asi vanozove nemukana wekuwana chitupa chinogovaniswa, vachiwedzera kukosha kwakakosha kune yavo hunyanzvi kana yezvidzidzo.
Nhanganyaya kuGalois theory (SUPERIOR NORMAL SCHOOL PARIS)
Inopihwa neÉcole normale supérieure paCoursera, kosi ye "Introduction to Galois Theory" iongororo inonakidza yeimwe yemapazi akadzama uye ane simba emasvomhu emazuva ano.Inotora maawa angangosvika gumi nemaviri, kosi iyi inonyudza vadzidzi munyika yakaoma uye inonakidza yedzidziso yeGalois, chirango chakashandura kunzwisisa kwehukama pakati pepolynomial equations uye algebraic zvimiro.
Kosi yacho inotarisa pakudzidza kwemidzi yemapolynomials uye kutaura kwavo kubva kucoefficients, mubvunzo wepakati mualgebra. Inoongorora pfungwa yeboka reGalois, rakaunzwa naÉvariste Galois, iyo inosanganisa imwe neimwe polynomial neboka remvumo yemidzi yayo. Maitiro aya anotibvumira kuti tinzwisise kuti sei zvisingabviri kuratidza midzi yeimwe polynomial equations nealgebraic formulas, kunyanya yemapolynomials edhigirii rakakura kupfuura mana.
Tsamba yeGalois, chinhu chakakosha chekosi, inobatanidza dzidziso yemunda kune dzidziso yeboka, ichipa maonero akasiyana eiyo solvability yeradical equations. Kosi yacho inoshandisa pfungwa dzekutanga mumutsara algebra kuswedera kudzidziso yemitumbi uye kusuma pfungwa yenhamba yealgebra, uku uchiongorora mapoka emvumo anodiwa pakudzidza kwemapoka eGalois.
Kosi iyi inonyanya kukosha pakugona kwayo kupa pfungwa dzakaoma dze algebra nenzira inosvikika uye yakapfava, zvichiita kuti vadzidzi vakurumidze kuwana mibairo ine musoro nehushoma hwechimiro chechimiro. Yakanakira masvomhu, fizikisi, kana vadzidzi veinjiniya, pamwe nevanofarira masvomhu vanotarisa kudzamisa kunzwisisa kwavo kwezvimiro zvealgebraic uye mashandisiro avo.
Nekupedza kosi iyi, vatori vechikamu havangowana nzwisiso yakadzama yedzidziso yeGalois, asi vanozove nemukana wekuwana chitupa chinogovaniswa, vachiwedzera kukosha kwakakosha kune yavo yehunyanzvi kana yezvidzidzo.
Ongororo I (chikamu 1): Prelude, pfungwa dzekutanga, nhamba chaidzo (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Kosi "Ongororo I (chikamu 1): Prelude, nheyo dzekutanga, nhamba chaidzo", inopihwa neÉcole Polytechnique Fédérale de Lausanne paedX, sumo yakadzama kune akakosha pfungwa dzekuongorora chaiko. Iyi kosi ye5-vhiki, inoda angangoita 4-5 maawa ekudzidza pasvondo, yakagadzirirwa kupedzwa nekumhanya kwako wega.
Zvinyorwa zvekosi zvinotanga nenhanganyaya inodzokorodza uye nekudzamisa pfungwa dzemasvomhu dzakakosha senge trigonometric mabasa (chivi, cos, tan), kudzorera mabasa (exp, ln), pamwe chete nemitemo yekuverenga yemasimba, logarithms nemidzi. Inosanganisirawo maseti ekutanga uye mabasa.
Nheyo yekosi inotarisa pane masisitimu enhamba. Kutanga kubva pane intuitive pfungwa yezvakasikwa manhamba, kosi yacho inotsanangura zvine mutsindo manhamba uye inoongorora zvimiro zvavo. Kunyanya kutariswa kunobhadharwa kunhamba chaidzo, dzinounzwa kuti dzizadze mapeji munhamba dzinonzwisisika. Kosi yacho inopa tsananguro yeaxiomatic yenhamba chaidzo uye inodzidza zvimiro zvadzo zvakadzama, kusanganisira pfungwa dzakadai se infimum, supremum, absolute kukosha uye zvimwe zvekuwedzera zvimiro zvenhamba chaidzo.
Iyi kosi yakanakira avo vane ruzivo rwekutanga rwemasvomhu uye vanoda kudzamisa manzwisisiro avo ekuongorora kwepasirese. Inonyanya kubatsira kuvadzidzi ve masvomhu, fizikisi, kana mainjiniya, pamwe nechero munhu anofarira kunzwisisa kwakasimba kwehwaro hwemasvomhu.
Nekupedza kosi iyi, vatori vechikamu vanowana kunzwisisa kwakasimba kwenhamba chaidzo uye kukosha kwadzo mukuongorora, pamwe nemukana wekuwana chitupa chinogovaniswa, zvichiwedzera kukosha kwakakosha kune yavo yehunyanzvi kana yedzidzo chimiro.
Ongororo I (chikamu 2): Nhanganyaya kunhamba dzakaoma (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Kosi "Ongororo I (chikamu 2): Nhanganyaya kunhamba dzakaoma", inopihwa neÉcole Polytechnique Fédérale de Lausanne paedX, sumo inokwezva kune nyika yenhamba dzakaoma.Iyi kosi ye2-vhiki, inoda angangoita 4-5 maawa ekudzidza pasvondo, yakagadzirirwa kupedzwa nekumhanya kwako wega.
Dzidzo inotanga nekugadzirisa equation z^ 2 = -1, iyo isina mhinduro mune imwe nhamba yenhamba chaidzo, R. Dambudziko iri rinotungamirira pakuiswa kwenhamba dzakaoma, C, munda une R uye unotibvumira kugadzirisa zvakadaro. equations. Kosi iyi inoongorora nzira dzakasiyana dzekumiririra nhamba yakaoma uye inokurukura mhinduro kuequation yefomu z^n = w, apo n ndeyaN* uye w kuC.
Chikuru chekosi iyi kudzidza kweiyo theorem yakakosha yealgebra, inova mhedzisiro yakakosha mumasvomhu. Iyo kosi zvakare inovhara misoro senge Cartesian inomiririra yenhamba dzakaoma, yavo yekutanga zvivakwa, inverse element yekuwedzera, iyo Euler uye de Moivre formula, uye polar fomu yenhamba yakaoma.
Iyi kosi yakanakira avo vanotova neruzivo rwenhamba chaidzo uye vanoda kuwedzera kunzwisisa kwavo kunhamba dzakaoma. Inonyanya kukosha kuvadzidzi vesvomhu, fizikisi, kana mainjiniya, pamwe chete nemunhu wese anofarira kunzwisisa kwakadzama kwealgebra nemashandisirwo ayo.
Nekupedza kosi iyi, vatori vechikamu vanowana kunzwisisa kwakasimba kwenhamba dzakaoma uye basa ravo rakakosha mumasvomhu, pamwe nemukana wekuwana chitupa chinogovaniswa, zvichiwedzera kukosha kwakakosha kune yavo nyanzvi kana yezvidzidzo.
Ongororo I (chikamu 3): Kutevedzana kwenhamba chaidzo I uye II (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Kosi "Ongororo I (chikamu 3): Kutevedzana kwenhamba chaidzo I uye II", inopihwa neÉcole Polytechnique Fédérale de Lausanne paedX, inotarisa pakutevedzana kwenhamba chaidzo. Iyi kosi ye4-vhiki, inoda angangoita 4-5 maawa ekudzidza pasvondo, yakagadzirirwa kupedzwa nekumhanya kwako wega.
Pfungwa yepakati yeiyi kosi muganhu wekutevedzana kwenhamba chaidzo. Inotanga nekutsanangura kutevedzana kwenhamba chaidzo sebasa kubva kuN kusvika kuR. Semuenzaniso, kutevedzana a_n = 1/2 ^ n kunoongororwa, kuratidza kuti inosvika sei zero. Kosi yacho inobata zvakasimba tsananguro yemuganhu wekutevedzana uye inovandudza nzira dzekusimbisa kuvapo kwemuganhu.
Mukuwedzera, iyo kosi inogadza chinongedzo pakati pepfungwa yemuganhu uye iyo ye infimum uye iyo supremum yeti. Kushandiswa kunokosha kwenhevedzano dzenhamba chaidzo kunoratidzirwa neidi rokuti nhamba imwe neimwe chaiyoiyo inogona kurangarirwa somuganhu wenhevedzano yenhamba dzine mufungo. Iyo kosi zvakare inoongorora Cauchy kutevedzana uye kutevedzana kunotsanangurwa nemutsara induction, pamwe neiyo Bolzano-Weierstrass theorem.
Vatori vechikamu vanozodzidzawo nezvenhamba dzakatevedzana, nechisumo chemienzaniso yakasiyana uye nzira yekushandura, senge d'Alembert criterion, Cauchy criterion, uye Leibniz criterion. Kosi yacho inopera nekudzidza kwenhamba dzakatevedzana ine parameter.
Iyi kosi yakanakira avo vane ruzivo rwekutanga rwemasvomhu uye vanoda kudzamisa kunzwisisa kwavo kwekutevedzana kwenhamba chaidzo. Inonyanya kukosha kune vadzidzi ve masvomhu, fizikisi kana engineering. Nekupedza kosi iyi, vatori vechikamu vanozowedzera kunzwisisa kwavo masvomhu uye vanogona kuwana chitupa chinogovaniswa, pfuma yehunyanzvi hwavo kana budiriro yedzidzo.
Kuwanikwa Kwechokwadi uye Anoenderera Mabasa: Ongororo I (chikamu 4) (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Mu "Ongororo I (chikamu 4): Muganho webasa, mabasa anoenderera mberi", iyo École Polytechnique Fédérale de Lausanne inopa rwendo runonakidza mukudzidza kwemabasa chaiwo ekuchinja chaiko.Iyi kosi, inogara mavhiki mana ne4 kusvika ku4 maawa ekudzidza kwevhiki, inowanikwa paedX uye inobvumira kufambira mberi nekumhanya kwako wega.
Ichi chikamu chekosi chinotanga nekuunzwa kwemabasa chaiwo, kusimbisa zvimiro zvavo senge monotonicity, parity, uye periodicity. Inoongororawo mashandiro pakati pemabasa uye inosuma mamwe mabasa akadai se hyperbolic mabasa. Kunyanya kutariswa kunopihwa kumabasa anotsanangurwa nhanho, kusanganisira Signum uye Heaviside mabasa, pamwe neaffine shanduko.
Nheyo yekosi inotarisa pamuganho wakapinza webasa pane imwe nzvimbo, ichipa kongiri mienzaniso yemiganhu yemabasa. Inovharawo pfungwa dzemiganhu yekuruboshwe nekurudyi. Tevere, kosi yacho inotarisa isingaperi miganhu yemabasa uye inopa zvakakosha maturusi ekuverenga miganhu, senge cop theorem.
Chinhu chakakosha chekosi kusuma pfungwa yekuenderera, inotsanangurwa nenzira mbiri dzakasiyana, uye kushandiswa kwayo kuwedzera mamwe mabasa. Kosi yacho inopera nekudzidza kwekuenderera mberi panguva dzakavhurika.
Iyi kosi mukana unopfumisa kune avo vari kutsvaga kudzamisa manzwisisiro avo echokwadi uye anoenderera mberi mabasa. Yakanakira vadzidzi ve masvomhu, fizikisi kana engineering. Nekupedza kosi iyi, vatori vechikamu havangowedzere masvomhu avo, asi vanozove nemukana wekuwana chitupa chinopa mubairo, vachivhura musuwo wemaonero matsva ezvidzidzo kana hunyanzvi.
Kuongorora Mabasa Akasiyana: Ongororo I (chikamu 5) (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Iyo École Polytechnique Fédérale de Lausanne, mune yayo yekudzidzisa inopa pa edX, inopa "Ongororo I (chikamu 5): Anoenderera mberi nemabasa uye anosiyanisa mabasa, iro rinobva kune iro basa". Iyi kosi yemavhiki mana, inoda maawa angangoita 4-5 ekudzidza pasvondo, kuongorora kwakadzama kwepfungwa dzekusiyanisa uye kuenderera kwemabasa.
Kosi yacho inotanga nekudzidza kwakadzama kwemabasa anoenderera, achitarisa pane yavo midziyo pamusoro penguva dzakavharwa. Ichi chikamu chinobatsira vadzidzi kunzwisisa huwandu uye hushoma hwemabasa anoenderera. Kosi yacho inobva yasuma nzira yekubatanidza uye inopa dzidziso dzakakosha senge yepakati kukosha theorem uye yakatarwa point theorem.
Chikamu chepakati chekosi chakatsaurirwa kusiyanisa uye kusiyanisa kwemabasa. Vadzidzi vanodzidza kududzira pfungwa idzi uye kunzwisisa kuenzana kwavo. Kosi yacho inozotarisa kuvakwa kweiyo derivative basa uye inoongorora zvimiro zvayo zvakadzama, kusanganisira algebraic mashandiro pazvinobuda.
Chinhu chakakosha chekosi iyi kudzidza kwezvimiro zvemabasa anosiyaniswa, senge rinobva kune basa rekuumbwa, Rolle's theorem, uye finite increment theorem. Iyo kosi zvakare inoongorora kuenderera kweiyo derivative basa uye zvarinoreva pane monotonicity yechinhu chinosiyanisa basa.
Iyi kosi mukana wakanakisa kune avo vanoda kudzamisa kunzwisisa kwavo kweanosiyanisa uye anoenderera mberi mabasa. Yakanakira vadzidzi ve masvomhu, fizikisi kana engineering. Nekupedza kosi iyi, vatori vechikamu havangowedzera kunzwisisa kwavo kweakakosha masvomhu pfungwa, asi vanozove nemukana wekuwana chitupa chinopa mubairo, vachivhura musuwo kumikana mitsva yezvidzidzo kana yehunyanzvi.
Kudzika muMasvomhu Analysis: Analysis I (chikamu 6) (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Iyo kosi "Ongororo I (chikamu 6): Zvidzidzo zvemabasa, mashoma budiriro, inopihwa neÉcole Polytechnique Fédérale de Lausanne paedX, iongororo yakadzama yemabasa uye mashoma ekuvandudza kwavo. Kosi iyi yemavhiki mana, ine basa remaawa mana kusvika mashanu pasvondo, inobvumira vadzidzi kuti vafambire mberi nekumhanya kwavo.
Ichi chitsauko chekosi chinotarisa pakudzidza kwakadzama kwemabasa, uchishandisa maoremu kuongorora kusiyana kwawo. Mushure mekubata iyo inogumira increment theorem, kosi inotarisa kuzara kwayo. Chinhu chakakosha pakudzidza mabasa ndiko kunzwisisa maitiro avo nekusingagumi. Kuti uite izvi, kosi inosuma mutemo weBernoulli-l'Hospital, chishandiso chakakosha chekutarisa miganho yakaoma yemamwe maquotients.
Iyo kosi zvakare inoongorora iyo graphical inomiririra yemabasa, ichiongorora mibvunzo senge kuvapo kwenzvimbo kana yepasi rose maxima kana minima, pamwe neiyo convexity kana concavity yemabasa. Vadzidzi vanozodzidza kuona akasiyana asymptotes ebasa.
Imwe pfungwa yakasimba yekosi iyi kusuma kweashoma ekuwedzera kwebasa, izvo zvinopa fungidziro yepolynomial munharaunda yenzvimbo yakapihwa. Zviitiko izvi zvakakosha kurerutsa kuverenga kwemiganhu uye kudzidza kwemaitiro emabasa. Iyo kosi zvakare inovhara akateedzana akateedzana uye radius yavo yekusangana, pamwe neTaylor nhevedzano, chishandiso chine simba chekumiririra nekusingaperi mabasa anosiyaniswa.
Iyi kosi yakakosha sosi kune avo vari kutsvaga kudzamisa kunzwisisa kwavo kwemabasa uye mashandisiro avanoita musvomhu. Inopa inopfumisa uye yakadzama maonero epfungwa dzakakosha mukuongorora kwemasvomhu.
Hunyanzvi hwekubatanidza: Ongororo I (chikamu 7) (CHIKORO POLYTECHNIQUE FEDERALE DE LAUSANNE)
Iyo kosi "Ongororo I (chikamu 7): Zvisingagumi uye zvakanyatsobatanidzwa, kubatanidzwa (zvitsauko zvakasarudzwa)", yakapihwa neÉcole Polytechnique Fédérale de Lausanne pa edX, iongororo yakadzama yekubatanidzwa kwemabasa. Iyi module, inotora mavhiki mana nekubatanidzwa kwe4 kusvika kumaawa mashanu pasvondo, inobvumira vadzidzi kuti vaone hunyengeri hwekubatanidzwa pamwero wavo.
Kosi yacho inotanga netsananguro yezvisinga verengeki zvakabatanidzwa uye yakanyatsobatanidzwa, kuunza chaiyo yekubatanidza kuburikidza neRiemann sums uye yepamusoro uye yakaderera sums. Inobva yakurukura zvinhu zvitatu zvakakosha zvezvakakosha zvakabatanidzwa: mutsara wezvakabatanidzwa, kupatsanurwa kwenzvimbo yekubatanidza, uye monotonicity yechinhu chakakosha.
Chinhu chepakati chekosi inoreva theorem yekuenderera mberi kwemabasa pachikamu, icho chinoratidzwa zvakadzama. Kosi yacho inosvika kumagumo neiyo theorem yakakosha ye integral calculus, ichiunza pfungwa ye antiderivative yebasa. Vadzidzi vanodzidza nzira dzakasiyana dzekubatanidza, dzakadai sekubatanidza nezvikamu, kushandura machinjiro, uye kubatanidza nekupinza.
Dzidzo inopedzisa nekudzidza kwekubatanidzwa kwemamwe mabasa, kusanganisira kubatanidzwa kwekuwedzera kuduku kwechiito, kubatanidzwa kwezvikamu zvakatevedzana, uye kubatanidzwa kwe piecewise inopfuurira mabasa. Aya maitiro anobvumira kubatanidzwa kwemabasa ane mafomu anokosha kuti averengerwe zvakanyanya. Chekupedzisira, kosi yacho inoongorora zvakajairwa, zvinotsanangurwa nekupfuura muganho mune zvakabatanidzwa, uye inopa mienzaniso chaiyo.
Iyi kosi chishandiso chakakosha kune avo vari kutsvaga kugona kubatanidza, chishandiso chakakosha mumasvomhu. Inopa maonero akazara uye anoshanda pakubatanidza, achipfumisa unyanzvi hwemasvomhu hwevadzidzi.
Makosi muChirungu
Nhanganyaya kune Linear Models uye Matrix Algebra (Harvard)
Harvard University, kuburikidza nepuratifomu yayo yeHarvardX paedX, inopa kosi "Kusuma kune Linear Models uye Matrix Algebra". Kunyangwe kosi yacho ichidzidziswa muChirungu, inopa mukana wakasarudzika wekudzidza hwaro hwematrix algebra uye mutsara modhi, hunyanzvi hwakakosha mune dzakawanda sainzi ndima.
Iyi kosi yemavhiki mana, inoda maawa maviri kusvika mana ekudzidza pasvondo, yakagadzirirwa kupedzwa nekumhanya kwako wega. Inotarisa pakushandisa iyo R programming mutauro kushandisa mutsara modhi mukuongorora data, kunyanya mune yehupenyu sainzi. Vadzidzi vanozodzidza kushandura matrix algebra uye vanonzwisisa mashandisiro ayo mukuyedza dhizaini uye yakakwirira-dimensional data kuongororwa.
Chirongwa ichi chinovhara matrix algebra notation, matrix mashandiro, kushandiswa kwematrix algebra kuongororo yedata, mutsara modhi, uye sumo yekuparara kweQR. Iyi kosi chikamu cheakatevedzana makosi manomwe, anogona kutorwa ega kana sechikamu chezvitupa zviviri zvehunyanzvi muData Analysis yeHupenyu Sayenzi uye Genomic Data Analysis.
Iyi kosi yakanakira avo vari kutsvaga kuwana hunyanzvi mukuenzanisira kwenhamba uye kuongororwa kwedata, kunyanya mumamiriro esainzi yehupenyu. Inopa hwaro hwakasimba kune avo vanoshuvira kuenderera mberi nekuongorora matrix algebra uye mashandisiro ayo munzvimbo dzakasiyana dzesainzi nekutsvaga.
Master Probability (Harvard)
LThe "Statistics 110: Probability" playlist paYouTube, inodzidziswa neChirungu naJoe Blitzstein weHarvard University, inzvimbo yakakosha kune avo vari kutsvaga kudzamisa ruzivo rwavo rwekubvira.. Rondedzero yekutamba inosanganisira mavhidhiyo ezvidzidzo, zvekuongorora, uye anopfuura mazana maviri nemakumi mashanu ekudzidzira maekisesaizi ane akadzama mhinduro.
Iyi kosi yechirungu sumo yakazara kune zvingangoitika, inoratidzwa semutauro wakakosha uye seti yezvishandiso zvekunzwisisa manhamba, sainzi, njodzi uye zvisina tsarukano. Mafungiro anodzidziswa anoshanda munzvimbo dzakasiyana senge nhamba, sainzi, engineering, economics, mari uye hupenyu hwezuva nezuva.
Misoro yakafukidzwa inosanganisira izvo zvekutanga zvezvingangoitika, zvisizvo zvakasiyana uye kugovera kwavo, univariate uye multivariate kugovera, miganhu theorems, uye Markov cheni. Kosi yacho inoda ruzivo rwepamberi yeimwe-inosiyanisa calculus uye kujairana nematrices.
Kune avo vakagadzika neChirungu uye vane shungu yekuongorora nyika yemukana zvakadzama, iyi Harvard kosi inoteedzana inopa mukana wekudzidza unopfumisa. Iwe unogona kuwana iyo yekutamba uye yakadzama zvirimo zvakananga paYouTube.
Probability Inotsanangurwa. Kosi ine French Subtitles (Harvard)
Kosi ye "Fat Chance: Probability from the Ground Up," inopihwa naHarvardX paedX, sumo inonakidza kune zvingangoitika uye nhamba. Kunyangwe kosi yacho ichidzidziswa muChirungu, inowanikwa kune vateereri vanotaura chiFrench nekuda kwezvinyorwa zvechiFrench zviripo.
Iyi kosi yemavhiki manomwe, inoda maawa matatu kusvika mashanu ekudzidza pasvondo, yakagadzirirwa avo vatsva pakudzidza zvingangoitika kana kutsvaga ongororo inogoneka yepfungwa dzakakosha vasati vanyoresa mukosi yehuwandu. “Fat Chance” inosimbisa kukudziridza kufunga kwemasvomhu pane kubata nomusoro mazwi nemafomula.
Mamodule ekutanga anosuma hunyanzvi hwekuverenga, hunobva hwaiswa kumatambudziko akareruka. Anotevera mamodule anoongorora kuti aya mazano uye matekiniki anogona kugadziridzwa sei kugadzirisa huwandu hwakakura hwematambudziko angangoitika. Kosi yacho inopera nenhanganyaya yezviverengero kuburikidza nepfungwa dzeukoshi hunotarisirwa, musiyano uye kugovera kwakajairika.
Iyi kosi yakanakira avo vari kutsvaga kuwedzera hunyanzvi hwavo hwekufunga uye kunzwisisa hwaro hwekugona uye nhamba. Inopa maonero anopfumisa pahuwandu hwemasvomhu uye kuti inoshanda sei pakunzwisisa njodzi uye kusarongeka.
Statistical Inference uye Modelling yePamusoro-Phroughput Experiments (Harvard)
Kosi ye "Statistical Inference and Modelling for High-throughput Experiments" muChirungu inotarisisa nzira dzinoshandiswa kuita manhamba padata repamusoro-soro. Iyi kosi yemavhiki mana, inoda 2-4 maawa ekudzidza pasvondo, chinhu chakakosha kune avo vari kutsvaga kunzwisisa nekushandisa nzira dzepamusoro dzenhamba mune data-yakadzika tsvagiridzo marongero.
Chirongwa ichi chinovhara nyaya dzakasiyana siyana, kusanganisira dambudziko rekuenzanisa kwakawanda, mitengo yekukanganisa, maitiro ekukanganisa kudzora, manyepo ekuwanikwa mareti, q-values, uye yekuongorora data data. Inosumawo manhamba ekuenzanisira uye mashandisiro ayo kune yakakwirira-kuburikidza data, ichikurukura parametric kugovera senge binomial, exponential, uye gamma, uye ichitsanangura yakanyanya mukana fungidziro.
Vadzidzi vanozodzidza mashandisirwo aya mazwi mumamiriro ezvinhu akadai sechizvarwa chinotevera kutevedzana uye microarray data. Iyo kosi zvakare inovhara mamodheru emhando uye Bayesian empirics, nemienzaniso inoshanda yekushandiswa kwavo.
Iyi kosi yakanakira avo vari kutsvaga kudzamisa manzwisisiro avo ehuwandu hwekufungidzira uye modhi mukutsvaga kwesainzi kwazvino. Inopa maonero akadzama pamusoro pekuongororwa kwenhamba dze data yakaoma uye inyanzvi yakanaka kune vaongorori, vadzidzi nenyanzvi muminda yesainzi yehupenyu, bioinformatics uye manhamba.
Nhanganyaya kune Probability (Harvard)
Iyo "Introduction to Probability" kosi, inopihwa neHarvardX paedX, iongororo yakadzama yezvingabvira, mutauro unokosha uye mudziyo wekunzwisisa data, mukana, uye kusavimbika. Kunyangwe kosi yacho ichidzidziswa muChirungu, inowanikwa kune vateereri vanotaura chiFrench nekuda kwezvinyorwa zvechiFrench zviripo.
Iyi kosi yemavhiki gumi, inoda maawa mashanu kusvika gumi ekudzidza pasvondo, ine chinangwa chekuunza pfungwa kune nyika izere nemukana uye kusagadzikana. Ichapa maturusi anodiwa kuti unzwisise data, sainzi, uzivi, mainjiniya, hupfumi uye mari. Iwe haungodzidzi chete kugadzirisa matambudziko akaomarara ehunyanzvi, asiwo maitiro ekushandisa aya mhinduro muhupenyu hwezuva nezuva.
Nemienzaniso kubva pakuyedzwa kwekurapa kusvika kufungidziro yemitambo, iwe unowana hwaro hwakasimba hwekudzidza kwehuwandu hwekufungidzira, stochastic process, random algorithms, uye mimwe misoro apo mukana unodiwa.
Iyi kosi yakanakira avo vari kutsvaga kuwedzera manzwisisiro avo ekusavimbika uye mukana, kuita fungidziro yakanaka, uye kunzwisisa zvakangosiyana zvakasiyana. Inopa maonero anopfumisa pane zvakajairika mukana wekugovera unoshandiswa muhuwandu uye data sainzi.
Applied Calculus (Harvard)
Kosi ye "Calculus Applied!", inopihwa naHarvard paedX, kuongorora kwakadzama kwemashandisirwo ecalculus inosiyana-siyana mumagariro, hupenyu, uye sainzi yemuviri. Iyi kosi, yakazara muChirungu, mukana wakanakisa kune avo vari kutsvaga kuti vanzwisise kuti Calculus inoshandiswa sei mumamiriro ehunyanzvi epasirese.
Inotora mavhiki gumi uye ichida pakati pe3 ne6 maawa ekudzidza pasvondo, kosi iyi inodarika mabhuku echinyakare. Anoshanda pamwe nenyanzvi kubva munzvimbo dzakasiyana siyana kuratidza mashandisirwo ecalculus kuongorora nekugadzirisa matambudziko epasirese. Vadzidzi vanozoongorora akasiyana maapplication, kubva pakuongorora hupfumi kusvika kune biological modelling.
Iyo purogiramu inovhara kushandiswa kwezvinobva, zvakabatanidzwa, zvakasiyana equations, uye inosimbisa kukosha kwemasvomhu modhi uye paramita. Yakagadzirirwa avo vane nzwisiso yekutanga yeimwe-inosiyanisa calculus uye vanofarira mashandisiro ayo anoshanda mundima dzakasiyana.
Iyi kosi yakanakira vadzidzi, vadzidzisi, uye nyanzvi dzinotarisa kudzamisa manzwisisiro avo ecalculus uye kuwana ayo chaiwo-enyika mashandisirwo.
Nhanganyaya kune masvomhu kufunga (Stanford)
Iyo "Introduction to Mathematical Thinking" kosi, inopihwa neStanford University paCoursera, inonyura munyika yekufunga kwemasvomhu. Kunyangwe kosi yacho ichidzidziswa muChirungu, inowanikwa kune vateereri vanotaura chiFrench nekuda kwezvinyorwa zvechiFrench zviripo.
Kosi iyi yemavhiki manomwe, inoda maawa angangosvika makumi matatu nemasere, kana maawa angangoita gumi nemaviri pasvondo, yakagadzirirwa avo vanoda kukudziridza kufunga kwemasvomhu, kwakasiyana nekungodzidzira masvomhu sezvainowanzoitwa muhurongwa hwechikoro. Kosi yacho inonangana nokukudziridza nzira yokufunga “kunze kwebhokisi,” unyanzvi hunokosha munyika yanhasi.
Vadzidzi vanozoongorora kuti nyanzvi dzemasvomhu dzinofunga sei kugadzirisa matambudziko epasirese, angave ari kubva munyika yemazuva ese, kubva kusainzi, kana kubva kusvomhu pachadzo. Iyo kosi inobatsira kukudziridza iyi yakakosha nzira yekufunga, ichipfuura nzira dzekudzidza kugadzirisa matambudziko akasarudzika.
Iyi kosi yakanakira avo vari kutsvaga kusimbisa kuwanda kwavo kufunga uye kunzwisisa hwaro hwemasvomhu kufunga. Inopa maonero anopfumisa pahuwandu hwemasvomhu uye mashandisirwo ayo mukunzwisisa matambudziko akaomarara.
Statistical Kudzidza neR (Stanford)
Kosi ye "Statistical Learning neR", inopihwa naStanford, sumo yepakati-soro pakudzidza kwakatariswa, ichitarisa kudzoreredza uye nzira dzekuronga. Iyi kosi, yakazara muChirungu, chishandiso chakakosha kune avo vari kutsvaga kunzwisisa nekushandisa nzira dzenhamba mumunda wesainzi yedata.
Masvondo gumi nerimwe anotora uye achida maawa matatu-3 ekudzidza pasvondo, kosi iyi inobata nzira itsva dzechinyakare uye dzinonakidza mukuenzanisira kwenhamba, uye mashandisirwo emutauro weR programming. bhuku rezvidzidzo.
Misoro yakafukidzwa inosanganisira mutsara uye polynomial regression, logistic regression uye linear kusarura ongororo, kuchinjika-kusimbisa uye bootstrapping, kusarudzwa kwemuenzaniso uye nzira dzekugadzirisa (ridge uye lasso), nonlinear modhi, splines uye generalized ekuwedzera modhi, miti-yakavakirwa nzira, masango asina kurongeka uye kuwedzera. , inotsigira vector michina, neural network uye kudzidza kwakadzama, mamodheru ekupona, uye kuyedzwa kwakawanda.
Iyi kosi yakanakira avo vane ruzivo rwekutanga rwehuwandu, mutsara algebra, uye sainzi yekombuta, uye vari kutsvaga kudzamisa kunzwisisa kwavo kwenhamba yekudzidza uye mashandisiro ayo musainzi yedata.
Maitiro Ekudzidza Math: Kosi Yemunhu wese (Stanford)
Iyo "Maitiro Ekudzidza Math: YeVadzidzi" kosi, inopihwa naStanford. Iyo yemahara online kosi yevadzidzi veese mazinga emasvomhu. Zvakazara muChirungu, inosanganisa ruzivo rwakakosha nezvehuropi nehumbowo hutsva pamusoro penzira dzakanakisa dzemasvomhu.
Kutora mavhiki matanhatu uye kunoda 1 kusvika kumaawa 3 ekudzidza pasvondo. Kosi iyi yakagadzirirwa kushandura hukama hwevadzidzi nemasvomhu. Vanhu vazhinji vakave nezviitiko zvisina kunaka nemasvomhu, zvichikonzera kuvenga kana kukundikana. Chidzidzo ichi chine chinangwa chekupa vadzidzi ruzivo rwavanoda kuti vafarire masvomhu.
Yakavharwa imisoro yakaita seuropi uye kudzidza masvomhu. Ngano pamusoro pemasvomhu, pfungwa, zvikanganiso uye kumhanya zvakafukidzwa zvakare. Numerical flexibility, masvomhu kufunga, kubatanidza, nhamba dzemhando zvakare chikamu chechirongwa. Izvo zvinomiririra masvomhu muhupenyu, asiwo mune zvakasikwa uye kubasa hazvikanganwiki. Kosi iyi yakagadzirwa neinoshingaira yekubatirana pedagogy, ichiita kuti kudzidza kupindirane uye kusimbaradze.
Icho chinhu chakakosha kune chero munhu anoda kuona masvomhu zvakasiyana. Ita kunzwisisa kwakadzama uye kwakanaka kwechirango ichi. Inonyanya kukodzera kune avo vakave nezviitiko zvakashata nemasvomhu munguva yakapfuura uye vari kutarisa kuchinja maonero aya.
Probability Management (Stanford)
Iyo "Introduction to Probability Management" kosi, yakapihwa naStanford, sumo yekuraira kwekugona manejimendi. Iyi ndima inotarisisa kutaurirana nekuverengera kusavimbika nenzira yematafura edata anotarisika anonzi Stochastic Information Packets (SIPs). Iyi kosi yevhiki gumi inoda 1 kusvika kuawa ye5 pasvondo.Iri pasina mubvunzo chinhu chakakosha kune avo vari kutsvaga kunzwisisa nekushandisa nzira dzenhamba mumunda wesainzi yedata.
Kosi yedzidzo inovhara misoro yakadai sekuziva "Kukanganisa kweAvhareji," seti yezvikanganiso zvakarongeka zvinomuka kana kusavimbika kunomiririrwa nenhamba imwe chete, kazhinji avhareji. Inotsanangura kuti sei mapurojekiti mazhinji akanonoka, pamusoro pebhajeti uye pasi pebhajeti. Iyo kosi zvakare inodzidzisa Kusavimbika Arithmetic, iyo inoita maverengero asina chokwadi mapimendi, zvichikonzera kusava nechokwadi kwezvinobuda kubva kwaunogona kuverenga echokwadi avhareji mhedzisiro uye mikana yekuzadzisa zvinangwa zvakatemwa.
Vadzidzi vanozodzidza kugadzira anodyidzana simulations anogona kugovaniswa chero mushandisi weExcel pasina kuda ma-add-ins kana macros. Iyi nzira inokodzera zvakaenzana kuPython kana chero nharaunda yepurogiramu inotsigira arrays.
Iyi kosi yakanakira avo vakagadzika neMicrosoft Excel uye vari kutsvaga kudzamisa kunzwisisa kwavo kwekugona manejimendi uye mashandisiro ayo mune data sainzi.
Sayenzi yekusavimbika uye data (MIT)
Iyo kosi "Kugona - Iyo Sainzi Yekusavimbika uye Dhata", inopihwa neMassachusetts Institute of Technology (MIT). Iko sumo yakakosha kune sainzi yedata kuburikidza nemamodheru anoenderana. Iyi kosi yemavhiki gumi nematanhatu, inoda maawa gumi kusvika gumi nemana ekudzidza pasvondo. Iyo inoenderana nechikamu cheMIT MicroMasters chirongwa muhuwandu uye data sainzi.
Iyi kosi inoongorora nyika yekusagadzikana: kubva mutsaona mumisika yezvemari isingafungidzirwe kusvika kune kutaurirana. Probabilistic modelling uye ine hukama ndima yehuwandu hwekufungidzira. Makiyi maviri ekuongorora iyi data uye kuita fungidziro ine hunyanzvi hwesainzi.
Vadzidzi vachawana chimiro uye zvinhu zvakakosha zve probabilistic modhi. Kusanganisira zvisizvo zvakasiyana, kugovera kwavo, nzira uye kusiyana. Iyo kosi zvakare inovhara nzira dzekufungidzira. Mitemo yenhamba huru uye mashandisiro adzo, pamwe nemaitiro asina kujairika.
Iyi kosi yakanakira avo vanoda ruzivo rwakakosha mune data sainzi. Inopa maonero akazara pane zvingangoitika modhi. Kubva kuzvinhu zvekutanga kuenda kune zvakangoitika maitiro uye manhamba inference. Zvese izvi zvinonyanya kubatsira kune nyanzvi uye vadzidzi. Kunyanya muminda yedata sainzi, engineering uye manhamba.
Computational Probability uye Inference (MIT)
Massachusetts Institute of Technology (MIT) inopa kosi ye "Computational Probability uye Inference" muChirungu. Pachirongwa, sumo yepakati-pamwero we probabilistic analysis uye inference. Iyi kosi yevhiki gumi nembiri, inoda maawa mana kusvika matanhatu ekudzidza pasvondo, iongororo inonakidza yekuti zvingangoitika uye fungidziro zvinoshandiswa sei munzvimbo dzakasiyana sesefa spam, mobile bot navigation, kana kunyange mumitambo yemazano seJeopardy neGo.
Muchidzidzo ichi, iwe unozodzidza misimboti yekugona uye kufungidzira uye maitiro ekuashandisa muzvirongwa zvekombuta zvinokonzeresa nekusaziva uye kufanotaura. Iwe unozodzidza nezve akasiyana data zvimiro zvekuchengetedza zvingangogoverwa kugovera, senge probabilistic graphical modhi, uye kugadzira algorithms anoshanda ekufunga neaya madhata zvimiro.
Pakupera kweiyi kosi, iwe unozoziva maitiro ekuenzanisira matambudziko epasirese ane mukana uye mashandisiro azvino uno mamodheru ekufungidzira. Iwe haufanire kuve neruzivo rwepamberi mune mukana kana kufungidzira, asi iwe unofanirwa kuve wakasununguka neiyo yakakosha Python programming uye Calculus.
Iyi kosi chishandiso chakakosha kune avo vari kutsvaga kunzwisisa nekushandisa nzira dzenhamba mumunda wesainzi yedata, ichipa tarisiro yakazara pane zvingangoitika modhi uye manhamba inference.
Pamwoyo Wekusavimbika: MIT Inodedza Kuitika
Mukosi ye "Sumo kune Probability Chikamu II: Inference Matanho", iyo Massachusetts Institute of Technology (MIT) inopa kunyudzwa kwepamberi munyika yekugona uye kufungidzira. Iyi kosi, yakazara muChirungu, ndeyekuenderera kune musoro kwechikamu chekutanga, kunyura mukati mekuongorora data uye sainzi yekusavimbika.
Kwenguva yemavhiki gumi nematanhatu, nekuzvipira kwemaawa matanhatu pasvondo, kosi iyi inoongorora mitemo yenhamba huru, nzira dzeBayesian inference, classical statistics, uye zvisina tsarukano maitiro akadai sePoisson maitiro nemaketani eMarkov. Uku kuongorora kwakasimba, kwakagadzirirwa avo vanotova nehwaro hwakasimba mune mukana.
Iyi kosi inomira pachena nekuda kwayo intuitive maitiro, uku ichichengetedza kuomarara kwemasvomhu. Izvo hazvingounze dzidziso uye humbowo, asi ine chinangwa chekusimudzira kunzwisisa kwakadzama kwepfungwa kuburikidza nekongiri yekushandisa. Vadzidzi vanozodzidza kuenzanisa zviitiko zvakaoma uye kududzira chaiyo-yepasi data.
Yakanakira data sainzi nyanzvi, vaongorori, uye vadzidzi, kosi iyi inopa yakasarudzika maonero ekuti zvingangoitika uye kufungidzira zvinogadzirisa sei kunzwisisa kwedu kwenyika. Yakakwana kune avo vari kutsvaga kudzamisa kunzwisisa kwavo kwesainzi yedata uye ongororo yenhamba.
Analytical Combinatorics: Kosi yePrinceton Yekutsanangura Zvimiro Zvakaoma (Princeton)
Iyo Analytic Combinatorics kosi, inopihwa nePrinceton University, inonakidza kuongorora kweanalytical combinatorics, chirango chinogonesa chaiyo yehuwandu hwekufanotaura kwezvakaoma combinatorial zvimiro. Iyi kosi, yakazara muChirungu, chishandiso chakakosha kune avo vari kutsvaga kunzwisisa uye kushandisa nzira dzepamusoro mumunda wecombinatorics.
Inotora mavhiki matatu uye ichida maawa angangoita 16 muhuwandu, kana angangoita maawa mashanu pasvondo, kosi iyi inosuma nzira yekufananidzira yekuwana hukama hwekushanda pakati pezvakajairwa, exponential, uye multivariate generating mabasa. Inoongorora zvakare nzira dzekuongorora kwakaoma kuti iwane chaiyo asymptotics kubva kune equation yekugadzira mabasa.
Vadzidzi vanozoona kuti analytical combinatorics inogona kushandiswa sei kufanotaura huwandu chaihwo muhombe combinatorial zvimiro. Ivo vanozodzidza kushandura zvimiro zvekubatanidza uye kushandisa yakaoma nzira dzekuongorora kuongorora izvi zvimiro.
Iyi kosi yakanakira avo vari kutsvaga kudzamisa kunzwisisa kwavo kwecombinatorics uye mashandisiro ayo mukugadzirisa matambudziko akaomarara. Inopa yakasarudzika maonero ekuti analytical combinatorics inoumba sei kunzwisisa kwedu kwemasvomhu uye combinatorial zvimiro.
