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.