{"id":8,"date":"2025-11-18T11:39:59","date_gmt":"2025-11-18T09:39:59","guid":{"rendered":"https:\/\/mat.ub.edu\/matematiques\/?page_id=8"},"modified":"2026-01-21T07:48:12","modified_gmt":"2026-01-21T05:48:12","slug":"presentacio","status":"publish","type":"page","link":"https:\/\/mat.ub.edu\/matematiques\/","title":{"rendered":"Presentaci\u00f3"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_single_image image=&#8221;14&#8243; img_size=&#8221;2001&#215;200&#8243; alignment=&#8221;center&#8221; style=&#8221;vc_box_rounded&#8221; css_animation=&#8221;appear&#8221; css=&#8221;&#8221;][vc_column_text css=&#8221;&#8221;]<\/p>\n<h1>Grau en Matem\u00e0tiques<\/h1>\n<p>[\/vc_column_text][vc_column_text css=&#8221;&#8221;]<\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 18pt;\"><strong>PLA ESTUDIS 2026<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<table class=\"responsive\" style=\"border-collapse: collapse; width: 95.8925%; height: 573px;\">\n<tbody>\n<tr class=\"responsive\" style=\"border-style: hidden; background-color: #e8e8e8;\">\n<td class=\"xl21\" style=\"height: 16px; width: 5.15894%;\" height=\"22\"><span style=\"font-size: 12pt;\"><strong>CURS<\/strong><\/span><\/td>\n<td class=\"xl22\" style=\"width: 33.4321%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>SEMESTRE DE TARDOR<\/strong><\/span><\/td>\n<td class=\"xl22\" style=\"width: 4.07633%; height: 16px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>ECTS<\/strong><\/span><\/td>\n<td class=\"xl22\" style=\"width: 5.78756%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>TIPUS<\/strong><\/span><\/td>\n<td class=\"xl22\" style=\"width: 54.1464%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>SEMESTRE DE PRIMAVERA<\/strong><\/span><\/td>\n<td class=\"xl22\" style=\"width: 43.9579%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>ECTS<\/strong><\/span><\/td>\n<td class=\"xl23\" style=\"width: 27.9394%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>TIPUS<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl17\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td class=\"xl30\" style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 54.1464%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><span style=\"font-size: 12pt;\"><strong>PRIMER<\/strong><\/span><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>INTRODUCCI\u00d3 A L&#8217;AN\u00c0LISI MATEM\u00c0TICA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>\u00c0LGEBRA LINEAL I MULTILINEAL<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>INTRODUCCI\u00d3 A L&#8217;ALGEBRA LINEAL<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>C\u00c0LCUL EN UNA VARIABLE<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>INTRODUCCI\u00d3 A LA PROGRAMACI\u00d3<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>ALGOR\u00cdSMICA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>FONAMENTS I ARITM\u00c8TICA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>M\u00c8TODES NUM\u00c8RICS 1<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>FB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl17\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td class=\"xl30\" style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td class=\"xl38\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl38\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl30\" style=\"width: 54.1464%; height: 15px;\"><\/td>\n<td class=\"xl38\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl39\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><span style=\"font-size: 12pt;\"><strong>SEGON<\/strong><\/span><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>ESTRUCTURES ALGEBRAIQUES<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TOPOLOGIA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>C\u00c0LCUL DIFERENCIAL EN DIVERSES VARIABLES<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>C\u00c0LCUL INTEGRAL EN DIVERSES VARIABLES<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>MATEM\u00c0TICA DISCRETA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>M\u00c8TODES NUM\u00c8RICS 2<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>GEOMETRIA LINEAL<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>GEOMETRIA PROJECTIVA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl32\" style=\"height: 16px; width: 5.15894%;\" height=\"22\"><\/td>\n<td class=\"xl27\" style=\"width: 33.4321%; height: 16px;\"><\/td>\n<td class=\"xl36\" style=\"width: 4.07633%; height: 16px; text-align: center;\"><\/td>\n<td class=\"xl36\" style=\"width: 5.78756%; height: 16px; text-align: center;\"><\/td>\n<td class=\"xl27\" style=\"width: 54.1464%; height: 16px;\"><\/td>\n<td class=\"xl36\" style=\"width: 43.9579%; height: 16px; text-align: center;\"><\/td>\n<td class=\"xl37\" style=\"width: 27.9394%; height: 16px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><span style=\"font-size: 12pt;\"><strong>TERCER<\/strong><\/span><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>PROBABILITATS<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>ESTAD\u00cdSTICA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>EQUACIONS DIFERENCIALS<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>GEOMETRIA DIFERENCIAL<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>9<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>AN\u00c0LISI REAL<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>AN\u00c0LISI COMPLEXA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TEORIA DE GALOIS<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>EQUACIONS EN DERIVADES PARCIALS<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><span style=\"font-size: 12pt;\"><strong>QUART<\/strong><\/span><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>F\u00cdSICA MATEM\u00c0TICA<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OB<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 5<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 1<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 2<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 7<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl18\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 3<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TREBALL DE FI DE GRAU<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>12<\/strong><\/span><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>TFG<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl19\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTATIVA 4<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 4.07633%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>6<\/strong><\/span><\/td>\n<td class=\"xl34\" style=\"width: 5.78756%; height: 15px; text-align: center;\"><span style=\"font-size: 12pt;\"><strong>OP<\/strong><\/span><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><\/td>\n<td class=\"xl34\" style=\"width: 43.9579%; height: 15px; text-align: center;\"><\/td>\n<td class=\"xl35\" style=\"width: 27.9394%; height: 15px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl29\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td class=\"xl30\" style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 54.1464%; height: 15px;\"><\/td>\n<td class=\"xl30\" style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl25\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"background-color: #e8e8e8; width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>EN EL MOMENT D&#8217;ESCOLLIR LES ASSIGNATURES OPTATIVES, ES POT OPTAR PER UNA DE LES SEG\u00dcENTS MENCIONS<\/strong><\/span><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px; background-color: #e8e8e8;\"><span style=\"font-size: 12pt;\"><strong>ASSIGNATURES OPTATIVES PR\u00d2PIES DE MATEM\u00c0TIQUES<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl25\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>MENCI\u00d3 EN MATEM\u00c0TIQUES FONAMENTALS<\/strong><\/span><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>GEOMETRIA I TOPOLOGIA DE VARIETATS<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl25\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>MENCI\u00d3 EN CI\u00c8NCIA DE DADES<\/strong><\/span><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>CORBES ALGEBRAIQUES<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl25\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>MENCI\u00d3 EN ECONOMIA<\/strong><\/span><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>LOGICA<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl25\" style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"background-color: #e8e8e8; width: 33.4321%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TAMB\u00c9 ES POT OPTAR PER UN ITINERARI LLIURE<\/strong><\/span><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TEORIA DE CONJUNTS<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td class=\"xl26\" style=\"height: 16px; width: 5.15894%;\" height=\"22\"><\/td>\n<td class=\"xl27\" style=\"width: 33.4321%; height: 16px;\"><\/td>\n<td class=\"xl27\" style=\"width: 4.07633%; height: 16px;\"><\/td>\n<td class=\"xl27\" style=\"width: 5.78756%; height: 16px;\"><\/td>\n<td style=\"width: 54.1464%; height: 16px;\"><span style=\"font-size: 12pt;\"><strong>COMBINAT\u00d2RIA<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 16px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TEORIA ALGEBRAICA DE NOMBRES<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>TEORIA ANAL\u00cdTICA DE NOMBRES<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>\u00c0LGEBRA COMMUTATUVA I COMPUTACIONAL<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>AN\u00c0LISI FUNCIONAL<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>AN\u00c0LISI HARM\u00d2NICA I COMPLEXA<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>OPTIMITZACI\u00d3<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>SISTEMES DIN\u00c0MICS<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; height: 15px;\"><\/td>\n<td style=\"width: 54.1464%; height: 15px;\"><span style=\"font-size: 12pt;\"><strong>MODELITZACI\u00d3 I SIMULACI\u00d3<\/strong><\/span><\/td>\n<td style=\"width: 71.8973%; height: 15px;\" colspan=\"2\" width=\"133\"><\/td>\n<\/tr>\n<tr style=\"border-style: hidden;\">\n<td style=\"height: 15px; width: 5.15894%;\" height=\"21\"><\/td>\n<td style=\"width: 33.4321%; height: 15px;\"><\/td>\n<td style=\"width: 4.07633%; height: 15px;\"><\/td>\n<td style=\"width: 5.78756%; 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