{"id":756,"date":"2022-02-04T22:26:07","date_gmt":"2022-02-04T21:26:07","guid":{"rendered":"https:\/\/www.dm.unipi.it\/didattica\/?page_id=756"},"modified":"2022-04-14T09:41:41","modified_gmt":"2022-04-14T07:41:41","slug":"modaffint-group","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/","title":{"rendered":"ModAffInt Group"},"content":{"rendered":"\n<p>The&nbsp;<strong>ModAffInt group<\/strong>&nbsp;contains supplementary courses. Each course in this group yields 6 CFU\/ECTS, except the ones marked with (*) which yield 9 CFU\/ECTS. The courses are:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Advanced mechanics<\/li><li>Advanced numerical linear algebra<\/li><li>Advanced probability<\/li><li>Advanced statistics<\/li><li>Algebra 1<\/li><li>Algebra 2<\/li><li>Algebraic geometry A<\/li><li>Algebraic geometry B<\/li><li>Algebraic geometry C<\/li><li>Algebraic geometry D<\/li><li>Algebraic geometry E<\/li><li>Algebraic geometry F<\/li><li>Algebraic geometry G<\/li><li>Algebraic number theory 1<\/li><li>Algebraic number theory 2<\/li><li>Algebraic number theory 3<\/li><li>Algebraic topology A<\/li><li>Algebraic topology B<\/li><li>Algorithms and data structures<\/li><li>Analysis in metric spaces<\/li><li>Analytic number theory A<\/li><li>Analytic number theory B<\/li><li>Applications of differential equations in biomedicine<\/li><li>Applications of fluid dynamics in biomedicine<\/li><li>Approximation methods<\/li><li>Automated control theory<\/li><li>Calculus of variations A<\/li><li>Calculus of variations B<\/li><li>Category theory<\/li><li>Celestial mechanics<\/li><li>Coding theory<\/li><li>Coding theory and cryptography<\/li><li>Combinatorial optimization<\/li><li>Complements of mathematics education<\/li><li>Complex analysis A<\/li><li>Complex analysis B<\/li><li>Complex differential geometry<\/li><li>Computability theory<\/li><li>Computational commutative algebra and algebraic geometry<\/li><li>Computational real geometry<\/li><li>Computer algebra<\/li><li>Computer algebra A<\/li><li>Computer algebra B<\/li><li>Contact geometry<\/li><li>Continuous mechanics<\/li><li>Convex analysis<\/li><li>Coxeter groups<\/li><li>Cyclotomic fields<\/li><li>Data analysis<\/li><li>Descriptive complexity theory<\/li><li>Didactics of mathematics and new technologies<\/li><li>Differential geometry and topology<\/li><li>Differential operators and index theorems<\/li><li>Differential topology<\/li><li>Discrete dynamical systems<\/li><li>Discrete mathematics<\/li><li>Dynamical systems<\/li><li>Dynamics of the solar system<\/li><li>Elementary mathematics from an advanced standpoint: arithmetic<\/li><li>Elementary mathematics from an advanced standpoint: geometry<\/li><li>Elementary number theory<\/li><li>Elements of algebraic geometry<\/li><li>Elements of algebraic topology<\/li><li>Elements of calculus in homogeneous groups<\/li><li>Elements of calculus of variations<\/li><li>Elements of celestial mechanics<\/li><li>Elements of complex analysis<\/li><li>Elements of mathematical logic<\/li><li>Elements of probability and statistics<\/li><li>Elements of set theory<\/li><li>Elliptic curves<\/li><li>Elliptic equations<\/li><li>Equations of fluid mechanics<\/li><li>Ergodic theory<\/li><li>\u00c9tale cohomology<\/li><li>Evolution problems<\/li><li>Fields and Galois theory<\/li><li>Financial mathematics<\/li><li>Foundations of mathematics<\/li><li>Functional analysis<\/li><li>Functional spaces<\/li><li>Game theory<\/li><li>General topology<\/li><li>Geometric analysis<\/li><li>Geometric measure theory<\/li><li>Geometry and topology of surfaces<\/li><li>Geometry of metric spaces<\/li><li>Group theory<\/li><li>Groups and representations<\/li><li>Harmonic analysis<\/li><li>Higher algebra A<\/li><li>Higher algebra B<\/li><li>Higher analysis<\/li><li>History of ancient mathematics and its tradition<\/li><li>History of mathematics<\/li><li>Holomorphic dynamics<\/li><li>Homological algebra<\/li><li>Hyperbolic dynamics<\/li><li>Hyperbolic equations<\/li><li>Hyperbolic geometry<\/li><li>Introduction to geometric measure theory<\/li><li>Introduction to p-adic analysis<\/li><li>Introduction to quantum mechanics<\/li><li>Knot theory A<\/li><li>Knot theory B<\/li><li>Lie algebras and Lie groups<\/li><li>Linear algebraic groups<\/li><li>Linear and multilinear algebra<\/li><li>Linear and nonlinear waves<\/li><li>Low-dimensional topology and geometry<\/li><li>Math physics<\/li><li>Mathematical analysis 3<\/li><li>Mathematical logic<\/li><li>Mathematical methods in cryptography<\/li><li>Mathematical models in biomedicine and mathematical physics<\/li><li>Mathematical statistics<\/li><li>Mathematics and music<\/li><li>Mathematics and society<\/li><li>Mathematics for teaching middle school A<\/li><li>Mathematics for teaching middle school B<\/li><li>Measure theory<\/li><li>Microlocal analysis<\/li><li>Minimal surfaces<\/li><li>Model theory<\/li><li>Modular forms<\/li><li>Noncommutative algebra<\/li><li>Nonlinear analysis<\/li><li>Nonlinear capacity, variational inequalities and applications<\/li><li>Non-standard analysis<\/li><li>Numerical methods for Fourier analysis<\/li><li>Numerical methods for graphics<\/li><li>Numerical methods for Markov chains<\/li><li>Numerical methods for ordinary differential equations<\/li><li>Operational research<\/li><li>Operational research and communication and transport nets<\/li><li>Optimal control theory<\/li><li>Orbital determination<\/li><li>Ordinary differential equations<\/li><li>Origins and development of modern mathematics<\/li><li>p-adic Galois representations<\/li><li>Parabolic equations<\/li><li>Partial differential equations<\/li><li>Partial differential equations 2<\/li><li>Physics complements<\/li><li>Physics II (*)<\/li><li>Physics III<\/li><li>Physics lab for teaching<\/li><li>Post-quantum cryptography<\/li><li>Probability<\/li><li>Problem solving<\/li><li>Problems and methods in history of mathematics<\/li><li>Problems and methods in mathematics education research<\/li><li>Proof theory<\/li><li>Rational mechanics<\/li><li>Real analysis<\/li><li>Real geometry A<\/li><li>Real geometry B<\/li><li>Real geometry C<\/li><li>Relativistic mechanics<\/li><li>Riemannian geometry<\/li><li>Scientific computing<\/li><li>Semigroup theory<\/li><li>Set theory A<\/li><li>Set theory B<\/li><li>Simplectic geometry<\/li><li>Space mechanics<\/li><li>Special functions<\/li><li>Stochastic differential equations and applications<\/li><li>Stochastic processes<\/li><li>Symmetric spaces<\/li><li>Technologies for education<\/li><li>Theory and methods of optimization<\/li><li>Theory of functions<\/li><li>Topological methods for differential equations<\/li><li>Topological methods in the global analysis<\/li><li>Ultrafilters and nonstandard methods<\/li><li>2-manifolds<\/li><li>3-manifolds<\/li><li>4-manifolds<\/li><\/ul>\n\n\n\n<p>Please refer to the\u00a0<a href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/regolamenti-corso-di-laurea-magistrale\/\">Master&#8217;s Course Regulations<\/a>\u00a0to get more information on single courses.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The&nbsp;ModAffInt group&nbsp;contains supplementary courses. Each course in this group yields 6 CFU\/ECTS, except the ones marked with (*) which yield&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":630,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":"","_members_access_role":[],"_members_access_error":""},"class_list":["post-756","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>ModAffInt Group - Education<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ModAffInt Group - Education\" \/>\n<meta property=\"og:description\" content=\"The&nbsp;ModAffInt group&nbsp;contains supplementary courses. Each course in this group yields 6 CFU\/ECTS, except the ones marked with (*) which yield&hellip;Read More...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/\" \/>\n<meta property=\"og:site_name\" content=\"Education\" \/>\n<meta property=\"article:modified_time\" content=\"2022-04-14T07:41:41+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/modaffint-group\\\/\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/modaffint-group\\\/\",\"name\":\"ModAffInt Group - Education\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#website\"},\"datePublished\":\"2022-02-04T21:26:07+00:00\",\"dateModified\":\"2022-04-14T07:41:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/modaffint-group\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/modaffint-group\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/modaffint-group\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Master\u2019s Degree\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Study Plan\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/masters-degree\\\/study-plan\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"ModAffInt Group\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/\",\"name\":\"Education\",\"description\":\"Department of Mathematics - University of Pisa\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#organization\",\"name\":\"Education\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/wp-content\\\/uploads\\\/sites\\\/3\\\/2022\\\/07\\\/matematica_dx_bianco-1.png\",\"contentUrl\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/wp-content\\\/uploads\\\/sites\\\/3\\\/2022\\\/07\\\/matematica_dx_bianco-1.png\",\"width\":1612,\"height\":463,\"caption\":\"Education\"},\"image\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/didattica\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"ModAffInt Group - Education","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/","og_locale":"en_US","og_type":"article","og_title":"ModAffInt Group - Education","og_description":"The&nbsp;ModAffInt group&nbsp;contains supplementary courses. Each course in this group yields 6 CFU\/ECTS, except the ones marked with (*) which yield&hellip;Read More...","og_url":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/","og_site_name":"Education","article_modified_time":"2022-04-14T07:41:41+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/","url":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/","name":"ModAffInt Group - Education","isPartOf":{"@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#website"},"datePublished":"2022-02-04T21:26:07+00:00","dateModified":"2022-04-14T07:41:41+00:00","breadcrumb":{"@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/modaffint-group\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.dm.unipi.it\/didattica\/en\/"},{"@type":"ListItem","position":2,"name":"Master\u2019s Degree","item":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/"},{"@type":"ListItem","position":3,"name":"Study Plan","item":"https:\/\/www.dm.unipi.it\/didattica\/en\/masters-degree\/study-plan\/"},{"@type":"ListItem","position":4,"name":"ModAffInt Group"}]},{"@type":"WebSite","@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#website","url":"https:\/\/www.dm.unipi.it\/didattica\/en\/","name":"Education","description":"Department of Mathematics - University of Pisa","publisher":{"@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.dm.unipi.it\/didattica\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#organization","name":"Education","url":"https:\/\/www.dm.unipi.it\/didattica\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#\/schema\/logo\/image\/","url":"https:\/\/www.dm.unipi.it\/didattica\/wp-content\/uploads\/sites\/3\/2022\/07\/matematica_dx_bianco-1.png","contentUrl":"https:\/\/www.dm.unipi.it\/didattica\/wp-content\/uploads\/sites\/3\/2022\/07\/matematica_dx_bianco-1.png","width":1612,"height":463,"caption":"Education"},"image":{"@id":"https:\/\/www.dm.unipi.it\/didattica\/en\/#\/schema\/logo\/image\/"}}]}},"publishpress_future_action":{"enabled":false,"date":"2026-07-23 08:12:32","action":"change-status","newStatus":"draft","terms":[],"taxonomy":"translation_priority","extraData":[]},"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/pages\/756","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/comments?post=756"}],"version-history":[{"count":1,"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/pages\/756\/revisions"}],"predecessor-version":[{"id":757,"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/pages\/756\/revisions\/757"}],"up":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/pages\/630"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/didattica\/en\/wp-json\/wp\/v2\/media?parent=756"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}