{"id":1324,"date":"2025-08-08T14:58:17","date_gmt":"2025-08-08T14:58:17","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/master\/?p=1324"},"modified":"2026-07-17T10:48:21","modified_gmt":"2026-07-17T10:48:21","slug":"advanced-mathematics-mav","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/advanced-mathematics-mav\/","title":{"rendered":"Advanced Mathematics (MAV)"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;4.27.4&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row _builder_version=&#8221;4.16&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Academic Team<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (42)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; hover_enabled=&#8221;0&#8243; global_colors_info=&#8221;{}&#8221; url=&#8221;https:\/\/members.ift.uam-csic.es\/karllandsteiner\/&#8221; url_new_window=&#8221;on&#8221; sticky_enabled=&#8221;0&#8243;][\/et_pb_image][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (43)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; hover_enabled=&#8221;0&#8243; global_colors_info=&#8221;{}&#8221; url=&#8221;https:\/\/www.uam.es\/ciencias\/fisica-teorica\/jose-del-peso&#8221; url_new_window=&#8221;on&#8221; sticky_enabled=&#8221;0&#8243;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Content<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p><strong>Type: Optional\u2013 PEC Track \u2013 1st Trimester<\/strong><\/p>\n<p>This course provides a solid foundation in the key mathematical tools used in modern theoretical physics, with a focus on<span>\u00a0<\/span><strong>differential geometry<\/strong>,<span>\u00a0<\/span><strong>group theory<\/strong>, and<span>\u00a0<\/span><strong>probability &amp; statistics<\/strong>. Students will not only learn the theory but also apply these methods to real physical problems and data analysis. Emphasis is placed on mathematical reasoning, problem-solving, and collaborative work.<\/p>\n<p><strong>Main Topics<\/strong><\/p>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<ul>\n<li><strong>Differential Geometry<\/strong><span>\u00a0<\/span>\u2013 Manifolds, tensor algebra, vector bundles, connections, curvature, Riemannian geometry, and basics of manifold topology.<\/li>\n<li><strong>Group Theory<\/strong><span>\u00a0<\/span>\u2013 Lie groups and algebras, representation theory, classification of algebras, and applications to symmetries in physics (Poincar\u00e9, Lorentz, internal symmetries).<\/li>\n<li><strong>Probability &amp; Statistics<\/strong><span>\u00a0<\/span>\u2013 Probability distributions, estimators, hypothesis testing, Bayesian statistics, and Monte Carlo simulations.<\/li>\n<\/ul>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Reading List<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p>Group Theory:<br \/>\n1) H. Georgi: \u201cLie Algebras in Particle Physics\u201d,<br \/>\n2) H.F. Jones: \u201cGroups, Representations and Physics\u201d<br \/>\n3) J.F. Cornwell: \u201cGroup Theory in Physcis\u201d, Vols. 1,2<\/p>\n<p class=\"wp-block-paragraph\">Differential Geometry:<br \/>\n1) Nash, Sen: \u201cTopology and Geometry for Physicists\u201d<br \/>\n2) M. Nakahara: \u201cGeometry, Topology and Physics\u201d<\/p>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Teaching Plan Information<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (21)&#8221; url=&#8221;https:\/\/drive.google.com\/file\/d\/1viJ7saw9WobRX3_vHI8eknZgubXvsFd0\/view&#8221; url_new_window=&#8221;on&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; custom_margin=&#8221;50px||||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Schedule<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (20)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic TeamCourse ContentType: Optional\u2013 PEC Track \u2013 1st Trimester This course provides a solid foundation in the key mathematical tools used in modern theoretical physics, with a focus on\u00a0differential geometry,\u00a0group theory, and\u00a0probability &amp; statistics. Students will not only learn the theory but also apply these methods to real physical problems and data analysis. Emphasis is [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Academic Team<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1496,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/members.ift.uam-csic.es\/karllandsteiner\/\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-1024x576.png\" alt=\"\" class=\"wp-image-1496\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1498,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.uam.es\/ciencias\/fisica-teorica\/jose-del-peso\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-1024x576.png\" alt=\"\" class=\"wp-image-1498\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Content<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p><strong>Type: Optional\u2013 PEC Track \u2013 1st Trimeste<\/strong>r<br>This course provides a solid foundation in the key mathematical tools used in modern theoretical physics, with a focus on <strong>differential geometry<\/strong>, <strong>group theory<\/strong>, and <strong>probability &amp; statistics<\/strong>. Students will not only learn the theory but also apply these methods to real physical problems and data analysis. Emphasis is placed on mathematical reasoning, problem-solving, and collaborative work.<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p><strong>Main Topics<\/strong><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li><strong>Differential Geometry<\/strong> \u2013 Manifolds, tensor algebra, vector bundles, connections, curvature, Riemannian geometry, and basics of manifold topology.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Group Theory<\/strong> \u2013 Lie groups and algebras, representation theory, classification of algebras, and applications to symmetries in physics (Poincar\u00e9, Lorentz, internal symmetries).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Probability &amp; Statistics<\/strong> \u2013 Probability distributions, estimators, hypothesis testing, Bayesian statistics, and Monte Carlo simulations.<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Reading List<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>Group Theory:<br>1) H. Georgi: \u201cLie Algebras in Particle Physics\u201d,<br>2) H.F. Jones: \u201cGroups, Representations and Physics\u201d<br>3) J.F. Cornwell: \u201cGroup Theory in Physcis\u201d, Vols. 1,2<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>Differential Geometry:<br>1) Nash, Sen: \u201cTopology and Geometry for Physicists\u201d<br>2) M. Nakahara: \u201cGeometry, Topology and Physics\u201d<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Teaching Plan Information<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1470,\"width\":\"407px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"custom\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><a href=\"https:\/\/drive.google.com\/file\/d\/1viJ7saw9WobRX3_vHI8eknZgubXvsFd0\/view?usp=drive_link\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1024x576.png\" alt=\"\" class=\"wp-image-1470\" style=\"width:407px;height:auto\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Schedule<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"id\":1471,\"width\":\"318px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1024x576.png\" alt=\"\" class=\"wp-image-1471\" style=\"width:318px;height:auto\"\/><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p><\/p>\n<!-- \/wp:paragraph -->","_et_gb_content_width":"1080","footnotes":""},"categories":[26,22],"tags":[],"class_list":["post-1324","post","type-post","status-publish","format-standard","hentry","category-optional-en","category-pec-track"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1324","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/comments?post=1324"}],"version-history":[{"count":9,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1324\/revisions"}],"predecessor-version":[{"id":2371,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1324\/revisions\/2371"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1324"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1324"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}