{"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":"2025-09-03T14:16:54","modified_gmt":"2025-09-03T14:16:54","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":"\n<h2 class=\"wp-block-heading\">Academic Team<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/members.ift.uam-csic.es\/karllandsteiner\/\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-1024x576.png\" alt=\"\" class=\"wp-image-1496\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-42-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.uam.es\/ciencias\/fisica-teorica\/jose-del-peso\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-1024x576.png\" alt=\"\" class=\"wp-image-1498\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-43-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Course Content<\/h2>\n\n\n\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\n\n\n<p><strong>Main Topics<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Differential Geometry<\/strong> \u2013 Manifolds, tensor algebra, vector bundles, connections, curvature, Riemannian geometry, and basics of manifold topology.<\/li>\n\n\n\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\n\n\n<li><strong>Probability &amp; Statistics<\/strong> \u2013 Probability distributions, estimators, hypothesis testing, Bayesian statistics, and Monte Carlo simulations.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Reading List<\/h2>\n\n\n\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\n\n\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\n\n\n<h2 class=\"wp-block-heading\">Teaching Plan Information<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/drive.google.com\/file\/d\/1viJ7saw9WobRX3_vHI8eknZgubXvsFd0\/view?usp=drive_link\"><img decoding=\"async\" width=\"1024\" height=\"576\" 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\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/a><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">Course Schedule<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" 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\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic Team Course Content Type: Optional\u2013 PEC Track \u2013 1st TrimesterThis course provides a solid foundation in the key mathematical tools used in modern theoretical physics, with a focus on differential geometry, group theory, and probability &amp; statistics. Students will not only learn the theory but also apply these methods to real physical problems and &hellip; <a href=\"https:\/\/projects.ift.uam-csic.es\/master\/advanced-mathematics-mav\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Advanced Mathematics (MAV)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1324","post","type-post","status-publish","format-standard","hentry","category-sin-categoria"],"_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":4,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1324\/revisions"}],"predecessor-version":[{"id":1499,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1324\/revisions\/1499"}],"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}]}}