{"id":606,"date":"2022-02-04T22:26:07","date_gmt":"2022-02-04T21:26:07","guid":{"rendered":"https:\/\/www.dm.unipi.it\/didattica\/bachleors-degree\/programmes-of-study\/"},"modified":"2025-11-27T09:53:48","modified_gmt":"2025-11-27T08:53:48","slug":"study-plan","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/didattica\/en\/bachelors-degree\/study-plan\/","title":{"rendered":"Study Plan"},"content":{"rendered":"\n<p class=\"has-text-align-justify\"><p data-start=\"95\" data-end=\"533\"><strong data-start=\"95\" data-end=\"184\">Each student is required to submit their study plan by November 30 of the second year<\/strong> (or within one month of enrollment if transferring into the Bachelor\u2019s Degree Program in Mathematics during the academic year and entering a year above the first).<br data-start=\"348\" data-end=\"351\"\/>To prepare their personal study plan, students must use the <a href=\"https:\/\/caps.dm.unipi.it\/dashboard\" target=\"_blank\" rel=\"noopener\"><strong data-start=\"411\" data-end=\"429\">CAPS interface<\/strong><\/a>, accessible with their university credentials. The plan will then be evaluated by the Career Committee.&#13;\nA study plan may be submitted multiple times during the course of study, but submissions are allowed <strong data-start=\"636\" data-end=\"700\">only within the following three windows of the academic year<\/strong>:<\/p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1 September &#8211; 30 November;<\/strong><\/li>\n\n\n\n<li><strong>1 February &#8211; 31 March<\/strong>;<\/li>\n\n\n\n<li><strong>1 June &#8211; 30 June.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Any study plan submitted outside these periods will remain pending and will be evaluated during the next available submission window. In urgent or exceptional cases, students may request early evaluation from the <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/collegial-bodies-and-minutes\/\">President of the Degree Programme<\/a>.<\/p>\n\n\n\n<p>The Bachelor\u2019s Degree Program in Mathematics offers two curricula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Fundamental Curriculum<\/strong>;<\/li>\n\n\n\n<li><strong>Computational Curriculum<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>The first-year courses are common to both curricula.<\/p>\n\n\n\n<p>Students choose their curriculum when they submit their study plan.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">To modify an already approved study plan, it is sufficient to submit a new one, always respecting the submission windows. Likewise, if a student wishes to change their curriculum, they simply need to submit a new study plan with the updated curriculum.\r\nChanges to the study plan and curriculum take effect immediately once the plan is approved. New plans must, however, be submitted well in advance of the intended graduation date.<\/p>\n\n\n\n<p>The valid study plan is always the latest submitted and approved.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong data-start=\"1874\" data-end=\"1888\">IMPORTANT:<\/strong> It is essential to select the option corresponding to one\u2019s own year of enrolment. For earlier enrolments or for additional details, please refer to the curriculum framework of the Bachelor\u2019s Degree Programme on <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/bachelors-degree\/curriculum-framework\/\">the dedicated webpage<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"false\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-6060\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Students enrolled from A.Y. 2021\/22 onward<\/h4><div id=\"ac-6060\" class=\"c-accordion__content\">\n<table id=\"tablepress-10\" class=\"tablepress tablepress-id-10 tbody-has-connected-cells\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\"><strong>Fundamental Curriculum<\/strong><\/td><td class=\"column-3\"><strong>Computational Curriculum<\/strong><\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td rowspan=\"6\" class=\"column-1\">Year 1<\/td><td colspan=\"2\" class=\"column-2\">Mathematical analysis 1 (15 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td colspan=\"2\" class=\"column-2\">Arithmetic (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td colspan=\"2\" class=\"column-2\">Physics I with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td colspan=\"2\" class=\"column-2\">Fundaments of programming with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-6\">\n\t<td colspan=\"2\" class=\"column-2\">Geometry 1 (15 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-7\">\n\t<td colspan=\"2\" class=\"column-2\">Introductory Computational Mathematics Lab (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-8\">\n\t<td rowspan=\"7\" class=\"column-1\">Year 2<\/td><td colspan=\"2\" class=\"column-2\">Algebra 1 (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-9\">\n\t<td colspan=\"2\" class=\"column-2\">Mathematical analysis 2 (12 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-10\">\n\t<td colspan=\"2\" class=\"column-2\">Numerical analysis with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-11\">\n\t<td colspan=\"2\" class=\"column-2\">Elements of probability and statistics (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-12\">\n\t<td colspan=\"2\" class=\"column-2\">Geometry 2 (12 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-13\">\n\t<td colspan=\"2\" class=\"column-2\">Scientific English (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-14\">\n\t<td class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td><td class=\"column-3\">Algorithms and data structure (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-15\">\n\t<td rowspan=\"9\" class=\"column-1\">Year 3<\/td><td colspan=\"2\" class=\"column-2\">Rational Mechanics (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-16\">\n\t<td class=\"column-2\">Physics II (9 CFU\/ECTS)<\/td><td class=\"column-3\">Scientific Computing (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-17\">\n\t<td class=\"column-2\">Physics III (6 CFU\/ECTS)<\/td><td class=\"column-3\">Computational laboratory (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-18\">\n\t<td class=\"column-2\">Experimental laboratory of computational mathematics (6 CFU\/ECTS)<\/td><td class=\"column-3\">Programming languages with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-19\">\n\t<td class=\"column-2\"><a href=\"https:\/\/www.dm.unipi.it\/didattica\/laurea-triennale\/piano-di-studi\/gruppo-mcma\/\" target=\"_blank\">One exam from the MCMA group (6 CFU\/ECTS)<\/a><\/td><td class=\"column-3\">Operational research (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-20\">\n\t<td class=\"column-2\"><a href=\"https:\/\/www.dm.unipi.it\/didattica\/laurea-triennale\/piano-di-studi\/gruppo-mctf\/\" target=\"_blank\">One exam from the MCTF group (6 CFU\/ECTS)<\/a><\/td><td class=\"column-3\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-21\">\n\t<td colspan=\"2\" class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-22\">\n\t<td colspan=\"2\" class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-23\">\n\t<td colspan=\"2\" class=\"column-2\"><strong>Final Exam (9 CFU\/ECTS)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-10 from cache -->\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"false\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-6061\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Students enrolled from A.Y. 2015\/16 to A.Y. 2020\/21<\/h4><div id=\"ac-6061\" class=\"c-accordion__content\">\n<table id=\"tablepress-11\" class=\"tablepress tablepress-id-11 tbody-has-connected-cells\">\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-1\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\"><strong>Fundamental Curriculum<\/strong><\/td><td class=\"column-3\"><strong>Computational Curriculum<\/strong><\/td>\n<\/tr>\n<tr class=\"row-2\">\n\t<td rowspan=\"6\" class=\"column-1\">Year 1<\/td><td colspan=\"2\" class=\"column-2\">Mathematical analysis 1 (15 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td colspan=\"2\" class=\"column-2\">Arithmetic (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td colspan=\"2\" class=\"column-2\">Physics I with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td colspan=\"2\" class=\"column-2\">Fundaments of programming with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-6\">\n\t<td colspan=\"2\" class=\"column-2\">Geometry 1 (15 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-7\">\n\t<td colspan=\"2\" class=\"column-2\">Laboratory of Communication through computer (3 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-8\">\n\t<td rowspan=\"8\" class=\"column-1\">Year 2<\/td><td colspan=\"2\" class=\"column-2\">Algebra 1 (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-9\">\n\t<td colspan=\"2\" class=\"column-2\">Mathematical analysis 2 (12 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-10\">\n\t<td colspan=\"2\" class=\"column-2\">Numerical analysis with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-11\">\n\t<td colspan=\"2\" class=\"column-2\">Elements of probability and statistics (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-12\">\n\t<td colspan=\"2\" class=\"column-2\">Geometry 2 (12 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-13\">\n\t<td colspan=\"2\" class=\"column-2\">Scientific English (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-14\">\n\t<td colspan=\"2\" class=\"column-2\">Didactics Laboratory of computational mathematics (3 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-15\">\n\t<td class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td><td class=\"column-3\">Algorithms and data structure (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-16\">\n\t<td rowspan=\"9\" class=\"column-1\">Year 3<\/td><td colspan=\"2\" class=\"column-2\">Rational Mechanics (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-17\">\n\t<td class=\"column-2\">Physics II (9 CFU\/ECTS)<\/td><td class=\"column-3\">Scientific Computing (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-18\">\n\t<td class=\"column-2\">Physics III (6 CFU\/ECTS)<\/td><td class=\"column-3\">Computational laboratory (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-19\">\n\t<td class=\"column-2\">Experimental laboratory of computational mathematics (6 CFU\/ECTS)<\/td><td class=\"column-3\">Programming languages with laboratory (9 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-20\">\n\t<td class=\"column-2\"><a href=\"https:\/\/www.dm.unipi.it\/didattica\/laurea-triennale\/piano-di-studi\/gruppo-mcma\/\" target=\"_blank\">One exam from the MCMA group (6 CFU\/ECTS)<\/a><\/td><td class=\"column-3\">Operational research (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-21\">\n\t<td class=\"column-2\"><a href=\"https:\/\/www.dm.unipi.it\/didattica\/laurea-triennale\/piano-di-studi\/gruppo-mctf\/\" target=\"_blank\">One exam from the MCTF group (6 CFU\/ECTS)<\/a><\/td><td class=\"column-3\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-22\">\n\t<td colspan=\"2\" class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-23\">\n\t<td colspan=\"2\" class=\"column-2\">Free-choice course (6 CFU\/ECTS)<\/td>\n<\/tr>\n<tr class=\"row-24\">\n\t<td colspan=\"2\" class=\"column-2\"><strong>Final Exam (9 CFU\/ECTS)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-11 from cache -->\n\n\n\n<p>* \u201cDynamical Systems\u201d for students enrolled up to and including the 2016\/17 academic year<\/p>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Notes<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u201cDynamical Systems\u201d for students enrolled up to and including the 2016\/17 academic year. As \u201cfree-choice activities,\u201d students may select courses from the Degree Programme not already included in the plan, as well as courses offered by other Degree Programmes at the University of Pisa. These courses must have content consistent with the learning objectives of the Bachelor\u2019s Degree in Mathematics. It is also possible to include <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/useful-info\/internships-and-training\/\">an internship<\/a> at private companies or public institutions affiliated with the Department of Mathematics or the University of Pisa.<\/li>\n\n\n\n<li>Not all courses listed in the Regulations and present in the various groups are offered every year; students are advised to consult the <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/lectures-exams\/course-offer\/\"><strong data-start=\"2823\" data-end=\"2844\">course offer<\/strong><\/a>to check which courses are available before selecting them in their study plan.<\/li>\n\n\n\n<li>Before completing the Bachelor\u2019s study plan, it is also recommended to consult the <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/\">Master\u2019s study plan page<\/a> and the related notes, to gain a broader perspective on the full academic pathway.<\/li>\n\n\n\n<li>From the <strong data-start=\"3130\" data-end=\"3157\">2024\/2025 academic year<\/strong>, the course <em data-start=\"3170\" data-end=\"3198\">Scientific English (013ZW)<\/em> is no longer offered.<br data-start=\"3220\" data-end=\"3223\">Starting <strong data-start=\"3232\" data-end=\"3250\">1 October 2024<\/strong>, to obtain the 6 ECTS credits in English, students must pass the <strong data-start=\"3316\" data-end=\"3348\">B2 language proficiency test<\/strong> of the <a href=\"https:\/\/www.cli.unipi.it\/\" target=\"_blank\" rel=\"noopener\">University Language Centre<\/a> (CLI).<br data-start=\"3389\" data-end=\"3392\">Alternatively, students may obtain a <strong data-start=\"3429\" data-end=\"3463\">B2-level or higher certificate<\/strong> from an accredited institution (including CLI) and request formal recognition via <a href=\"https:\/\/caps.dm.unipi.it\/forms\/edit\" target=\"_blank\" rel=\"noopener\">CAPS<\/a> using the form <em data-start=\"3566\" data-end=\"3634\">\u201cRequest for the recording of Scientific English \u2013 013ZW \u2013 6 ECTS\u201d<\/em>.<\/li>\n\n\n\n<li><p data-start=\"3637\" data-end=\"3938\">Changes to the curriculum or study plans submitted and approved through CAPS are <strong data-start=\"3718\" data-end=\"3756\">not automatically updated in Alice<\/strong>.<br data-start=\"3757\" data-end=\"3760\">For the Bachelor\u2019s and Master\u2019s Degree Programs in Mathematics, the valid curriculum and study path are those defined in the <strong data-start=\"3885\" data-end=\"3937\">latest study plan submitted in CAPS and approved<\/strong>.\r\nIn conclusion, students are advised <strong data-start=\"3976\" data-end=\"4021\">not to worry about possible discrepancies<\/strong> recorded in Alice compared to the CAPS study plan; the academic record will be aligned with the latest approved study plan shortly before the graduation session for which the student has registered.\r\nIt is nevertheless possible to request a verification of Alice\u2013CAPS inconsistencies by writing to <em data-start=\"4320\" data-end=\"4345\"><a class=\"decorated-link cursor-pointer\" href=\"mailto:patrizia.lenzi@unipi.it\" rel=\"noopener\" data-start=\"4321\" data-end=\"4344\">patrizia.lenzi@unipi.it<\/a><\/em> (University Student Office, reference for the Bachelor\u2019s and Master\u2019s Degree Programs in Mathematics).<br data-start=\"4448\" data-end=\"4451\"><strong data-start=\"4451\" data-end=\"4460\">Note:<\/strong> attach your CAPS study plan to the email and CC <em data-start=\"4509\" data-end=\"4534\"><a class=\"decorated-link cursor-pointer\" href=\"mailto:chiara.luzzati@unipi.it\" rel=\"noopener\" data-start=\"4510\" data-end=\"4533\">chiara.luzzati@unipi.it<\/a><\/em> (Teaching Office of the Department of Mathematics).\r\nFor the specific case of <strong data-start=\"4613\" data-end=\"4628\">extra exams<\/strong>, please refer to <a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/extra-exams\/\">the following page<\/a>.<\/p><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Each student is required to submit their study plan by November 30 of the second year (or within one month&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/bachelors-degree\/study-plan\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3769,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-606","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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