{"id":41,"date":"2017-03-31T08:34:01","date_gmt":"2017-03-31T08:34:01","guid":{"rendered":"https:\/\/cmu-edu.eu\/traian-lalescu\/?page_id=41"},"modified":"2017-04-11T10:17:25","modified_gmt":"2017-04-11T10:17:25","slug":"sectiunea-a","status":"publish","type":"page","link":"https:\/\/cmu-edu.eu\/traian-lalescu\/sectiunea-a\/","title":{"rendered":"Sec\u021biunea A"},"content":{"rendered":"<h2>Anii I \u0219i II, Faculta\u021bi de Matematic\u0103<\/h2>\n<div class=\"clearfix ap-row\"><div class=\"ap_column ap-span3\"><h3>Structuri algebrice<\/h3>\n<p>Legi de compozi\u021bie. Monoizi.\nGrupuri. Ordinul unui element \u00eentr-un grup. Teorema lui Lagrange. Subgrup normal, grup\nfactor, teorema fundamentala de izomorfism pentru grupuri. Grupuri ciclice. Grupuri depermutari.\nInele, ideale, inel factor, teorema fundamentala de izomorfism pentru inele. Inele de matrice.\nCorpuri, caracteristica unui corp. Corpul frac\u021biilor unui domeniu de integritate.<\/p>\n<h3>II. Polinoame<\/h3>\n<p>Inele de polinoame \u00eentr-un numar finit de nedeterminate peste un inel comutativ.\nFuncii polinomiale. Radacini ale polinoamelor. Teorema lui Bezout. Rela\u021biile lui Viete.\nPolinoame simetrice. Teorema fundamentala a polinoamelor simetrice, formulele lui Newton.<\/p>\n<h3>III. Algebra liniara<\/h3>\n<p>Spa\u021bii vectoriale. Subspa\u021bii vectoriale. (In)dependen\u021ba liniara, baza, dimensiune. Aplica\u021bii\nliniare, nucleu, imagine.\nMatrice, rang, determinan\u021bi, sisteme de ecua\u021bii liniare.\nVectori \u0219i valori proprii. Teorie Jordan.\nForme biliniare \u0219i forme patratice. Spa\u021bii vectoriale euclidiene, baze ortogonale \u0219i\nortonormate, aplica\u021bii ortogonale.<\/p><\/div>\n<div class=\"ap_column ap-span3\"><h3>IV. Analiza matematica<\/h3>\n<p>\u0218iruri \u0219i serii de numere complexe.\n\u0218iruri \u0219i serii de func\u021bii, serii de puteri. Convergen\u021ba uniforma.\nTopologie generala: compacitate, conexiune, spa\u021bii metrice, spa\u021bii normate.\nContinuitate \u00een R, continuitate uniforma. Teorema de aproximare a lui Weierstrass.\nCalcul diferen\u021bial \u00een R. Teoremele clasice ale calculului diferen\u021bial.\nIntegrala Riemann-Stieltjes. Teoremele clasice ale calculului integral. Criteriul lui Lebesgue\nde integrabilitate Riemann.\nIntegrale improprii, integrale cu parametru. Func\u021biile Gama \u0219i Beta. Formula lui Stirling.\nSerii Fourier. Teorema de aproximare a lui Weierstrass, varianta trigonometrica.<\/p>\n<h3>V. Geometrie<\/h3>\n<p>Geometrie afina. Spa\u021bii afine. Repere afine \u0219i carteziene. Ecua\u021biile varieta\u021bilor liniare.\nAplica\u021bii afine. Grupul afin. Transla\u021bii, omotetii, simetrii. Conice \u0219i cuadrice \u00een spa\u021bii afine.\nClasificarea afina a hipercuadricelor.\nGeometrie euclidiana. Spa\u021bii euclidiene. Varieta\u021bi liniare perpendiculare. Izometrii. Conice \u0219i\ncuadrice \u00een spa\u021bii euclidiene. Clasificarea metrica a hipercuadricelor.\nGeometrie proiectiva. Spa\u021bii proiective, subspa\u021bii proiective, morfisme proiective. Teorema\nfundamentala a geometriei proiective. Clasificarea proiectiva a hipercuadricelor.<\/p><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Anii I \u0219i II, Faculta\u021bi de Matematic\u0103<\/p>\n","protected":false},"author":4,"featured_media":107,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-41","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/comments?post=41"}],"version-history":[{"count":3,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":127,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/41\/revisions\/127"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/media\/107"}],"wp:attachment":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/media?parent=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}