{"id":276,"date":"2019-01-04T14:47:43","date_gmt":"2019-01-04T19:47:43","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/mathguy\/?page_id=276"},"modified":"2026-03-19T08:34:04","modified_gmt":"2026-03-19T12:34:04","slug":"mad-4401","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/mathguy\/courses\/mad-4401\/","title":{"rendered":"MAD 4401"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">MAD 4401<\/h1>\n\n\n\n\n\n\n\n<p>Ever wondered how a calculator really finds square roots, how computers solve<br>\ndifferential equations, or how we can trust numbers that come from messy real-world data?<br>\nMAD 4401 is where analysis meets algorithms: we study how to turn continuous mathematics<br>\ninto computations a computer can actually do \u2014 and how to measure the error when it does.<\/p>\n\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\">What will we study?<\/h2>\n\n\n\n<p>The course focuses on numerical methods that power modern science, engineering,<br>\nand data analysis. Core topics include:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Error analysis and computer arithmetic (floating-point, round-off, and accuracy).<\/li>\n<li>Root-finding methods such as bisection, Newton, and secant methods.<\/li>\n<li>Interpolation and polynomial approximation (Lagrange, Newton forms, splines).<\/li>\n<li>Least-squares ideas and simple linear regression for data fitting.<\/li>\n<li>Numerical differentiation and integration (trapezoidal &amp; Simpson rules, composites).<\/li>\n<li>Numerical methods for initial value ODEs (Euler, Runge\u2013Kutta, step-size and stability).<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">How will we learn?<\/h2>\n\n\n\n<p>MAD 4401 blends mathematical theory with hands-on computation:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Weekly homework to practice analysis and hand calculations.<\/li>\n<li>Group computer labs where you implement algorithms (typically using Python or similar tools) and explore real data sets.<\/li>\n<li>Discussion boards and in-class activities focused on explaining results and error behavior clearly and professionally.<\/li>\n<li>Three midterm exams plus a cumulative final to synthesize the material.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Why might this course be a good fit for you?<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>You enjoy \u201chow does this actually work on a computer?\u201d questions, not just formulas on paper.<\/li>\n<li>You want stronger intuition for error, approximation, and numerical stability \u2014 ideas that show up in modeling, data science, and scientific computing.<\/li>\n<li>You are planning to use mathematics, science, or engineering in a setting where simulations and computation matter.<\/li><\/ul>\n\n\n\n<p>We use open-source numerical analysis texts, so you\u2019ll always have digital access to the<br>\nprimary references for the course.<\/p>\n\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\">Spring 2026 Syllabi<\/h2>\n\n\n\n<p>Full details about grading, policies, weekly schedules, and required materials are<br>\navailable in the syllabi for each section.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/mathguy\/content-removed\/\" rel=\"attachment wp-att-438\">S26syllabus_mad4401_online<\/a><br>\n<!-- Replace #ONLINE_SYLLABUS_URL with the actual link to the uploaded online syllabus PDF --><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/mathguy\/content-removed\/\" rel=\"attachment wp-att-437\">S26syllabus_mad4401<\/a><\/li><\/ul>\n\n\n\n<p>Both sections cover the same core numerical analysis topics and use the same main<br>\nopen-source textbook. Meeting times, exam logistics, and some activities differ, so be<br>\nsure to check the correct syllabus for your registered section.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":634,"featured_media":0,"parent":8,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-276","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/users\/634"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/comments?post=276"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/276\/revisions"}],"predecessor-version":[{"id":468,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/276\/revisions\/468"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/8"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/media?parent=276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}