{"id":3267,"date":"2022-03-05T09:39:21","date_gmt":"2022-03-05T08:39:21","guid":{"rendered":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/?page_id=3267"},"modified":"2026-02-26T11:47:34","modified_gmt":"2026-02-26T10:47:34","slug":"e9-22-eai001-matematicke-osnove-masinskog-ucenja","status":"publish","type":"page","link":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/?page_id=3267","title":{"rendered":"E9.22.EAI001 Matemati\u010dke osnove ma\u0161inskog u\u010denja, MAS Ve\u0161ta\u010dka inteligencija i ma\u0161insko u\u010denje"},"content":{"rendered":"\n
SEMESTAR<\/strong><\/td>1<\/td><\/tr>
ESPB<\/strong><\/td>6<\/td><\/tr>
FOND \u010cASOVA<\/strong><\/td>3+1+2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Sadr\u017eaj<\/h3>\n\n\n\n

1 Linearna algebra<\/h4>\n\n\n\n

1.1 Vektorski prostori, nezavisnost, baza
1.2 Linearne transformacije
1.3 Matrice, rang, sistemi linearnih jedna\u010dina
1.4 Norme, unutra\u0161nji proizvodi, du\u017eine, uglovi
1.5 Ortonormirana baza, ortogonalni komplement
1.6 Ortogonalne projekcije, rotacije
1.7 Unutra\u0161nji proizvodi funkcija
1.7 Determinanta i trag
1.8 Karakteristi\u010dni koreni i vektori
1.9 Cholesky dekompozicija
1.10 Dijagonalizacija
1.11 SVD<\/p>\n\n\n\n

2 Vektorski ra\u010dun sa funkcijama vi\u0161e promenljivih<\/h4>\n\n\n\n

2.1 Parcijalni izvodi i gradijenti
2.2 Gradijenti vektorskih funkcija i matrica
2.3 Korisni identiteti za ra\u010dunanje gradijenata
2.4 Izvodi vi\u0161eg reda i Tejlorova formula
2.5 Optimizacija gradijentnim iterativnim postupkom<\/p>\n\n\n\n

3 Slu\u010dajne promenljive i linearna regresija<\/h4>\n\n\n\n

3.1 Prostor verovatno\u0107e i slu\u010dajne promenljive
3.2 Va\u017ene raspodele i numeri\u010dke karakteristike slu\u010dajnih promenljivih
3.3 Ocene parametara, ta\u010dkaste i intervalne, Metod maksimalne verodostojnosti
3.4 Linearna regresija najmanjih kvadrata i Jednostavni linearni model
3.5 Slu\u010dajni vektori, vi\u0161edimenzionalne slu\u010dajne promenljive
3.6 Op\u0161ti linearni modeli<\/p>\n\n\n\n

Na\u010din polaganja<\/h3>\n\n\n\n

Predmet se sastoji iz zadataka koji se pola\u017eu pismeno i teorije koja se pola\u017ee na usmenom delu.<\/p>\n\n\n\n

Pismeni delovi se pola\u017eu u toku slu\u0161anja nastave preko kolokvijuma i u svakom ispitnom roku u terminu za koji je prijavljen ispit.<\/p>\n\n\n\n

Va\u017eenje pismenog dela polo\u017eenog preko kolokvijuma je do kraja kalendarske godine u kojoj je odslu\u0161an predmet ili do poni\u0161tavanja izlaskom na pismeni ispit i re\u0161avanjem zadataka iz odgovaraju\u0107eg dela.<\/p>\n\n\n\n

Va\u017eenje pismenog dela polo\u017eenog u ispitnom roku je do usmenog ispita u tom roku, najdu\u017ee 7 dana.<\/p>\n\n\n\n

Postoji minimalan broj bodova koji se mora osvojiti da bi se neki deo pismenog ispita ra\u010dunao kao polo\u017een.<\/p>\n\n\n\n

Usmeni ispit se odr\u017eava par dana posle pismenog ispita, u terminu dogovorenom na pismenom ispitu. Na usmeni ispit su pozvani studenti koji su prijavili ispit u tom roku i imaju polo\u017eene pismene delove.<\/p>\n\n\n\n

Ocene se formiraju na osnovu osvojenih bodova, u skladu sa Statutom FTN-a: 51+ -> 6, 61+ -> 7, …<\/p>\n\n\n\n

 <\/td>Deo1<\/td>Deo2<\/td>Deo3<\/td>Usmeni<\/td>suma<\/td><\/tr>
MAX<\/td>25<\/td>20<\/td>25<\/td>10+10+10<\/td>100<\/td><\/tr>
MIN<\/td>15<\/td>10<\/td>10<\/td>0<\/td>51<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Stanje bodova posle 19. II 2026.<\/p>\n\n\n\n

brind<\/strong><\/td>Kol1<\/td>Kol2<\/td>Kol3<\/td><\/tr>
E9-05\/2021<\/td>15<\/td>20<\/td><\/td><\/tr>
E9-01\/2024<\/td>23<\/td>20<\/td><\/td><\/tr>
E9-02\/2024<\/td><\/td><\/td><\/td><\/tr>
E9-03\/2024<\/td>19<\/td><\/td><\/td><\/tr>
E9-04\/2024<\/td><\/td><\/td><\/td><\/tr>
E9-05\/2024<\/td><\/td><\/td><\/td><\/tr>
E9-06\/2024<\/td>10<\/td><\/td><\/td><\/tr>
E9-09\/2024<\/td>15<\/td>20<\/td>25<\/td><\/tr>
E9-10\/2024<\/td><\/td><\/td>23<\/td><\/tr>
E9-12\/2024<\/td>12<\/td><\/td><\/td><\/tr>
E9-13\/2024<\/td>23<\/td><\/td><\/td><\/tr>
E9-14\/2024<\/td><\/td><\/td><\/td><\/tr>
E9-01\/2025<\/td><\/td>20<\/td>22<\/td><\/tr>
E9-02\/2025<\/td>18<\/td><\/td><\/td><\/tr>
E9-03\/2025<\/td><\/td><\/td><\/td><\/tr>
E9-04\/2025<\/td><\/td><\/td><\/td><\/tr>
E9-05\/2025<\/td>24<\/td>20<\/td>25<\/td><\/tr>
E9-06\/2025<\/td><\/td>20<\/td>22<\/td><\/tr>
E9-07\/2025<\/td><\/td><\/td><\/td><\/tr>
E9-08\/2025<\/td>16<\/td>20<\/td>25<\/td><\/tr>
E9-09\/2025<\/td><\/td><\/td><\/td><\/tr>
E9-10\/2025<\/td><\/td><\/td><\/td><\/tr>
E9-11\/2025<\/td>23<\/td>20<\/td>22<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

SEMESTAR 1 ESPB 6 FOND \u010cASOVA 3+1+2 Sadr\u017eaj 1 Linearna algebra 1.1 Vektorski prostori, nezavisnost, baza1.2 Linearne transformacije1.3 Matrice, rang, sistemi linearnih jedna\u010dina1.4 Norme, unutra\u0161nji proizvodi, du\u017eine, uglovi1.5 Ortonormirana baza, ortogonalni komplement1.6 Ortogonalne projekcije, rotacije1.7 Unutra\u0161nji proizvodi funkcija1.7 Determinanta i trag1.8 Karakteristi\u010dni koreni i vektori1.9 Cholesky dekompozicija1.10 Dijagonalizacija1.11 SVD 2 Vektorski ra\u010dun sa funkcijama vi\u0161e […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3119,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-3267","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/pages\/3267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3267"}],"version-history":[{"count":14,"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/pages\/3267\/revisions"}],"predecessor-version":[{"id":3946,"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/pages\/3267\/revisions\/3946"}],"up":[{"embeddable":true,"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=\/wp\/v2\/pages\/3119"}],"wp:attachment":[{"href":"https:\/\/nblok306.ftn.uns.ac.rs\/~zoran\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}