{"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":"2026-09-14T11:19:14","modified_gmt":"2026-09-14T15:19:14","slug":"mad-4401","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/mathguy\/courses\/mad-4401\/","title":{"rendered":"MAD 4401"},"content":{"rendered":"\n<section class=\"fullwidth-text-block\">\n<div class=\"container px-0\">\n<div class=\"row align-items-start\">\n<div class=\"col-12\">\n\n\n<h1 class=\"wp-block-heading\">MAD 4401 \u2014 Introduction to Numerical Analysis<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Numerical analysis is where mathematical theory meets computation.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\nEver wondered how a calculator finds square roots, how a computer approximates the solution\nof a differential equation, or how much confidence we should place in a numerical answer?\nMAD 4401 studies the algorithms that allow computers to solve mathematical problems\napproximately, efficiently, and reliably.\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\nThe central idea of the course is not simply to obtain a numerical answer, but to understand\n<strong>why an algorithm works, how quickly it converges, how error enters the computation,\nand when a numerical result can be trusted.<\/strong>\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Course Development<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nI have taught MAD 4401 regularly at the University of Florida and have continually redesigned\nthe course as computational tools have changed. Earlier versions of the course used\nMathematica and other proprietary software; I later converted the computational examples\nand projects to <strong>Python<\/strong> so that students could work with a free, open-source\nlanguage widely used in mathematics, scientific computing, and data science.\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\nI also adopted an open-source numerical analysis textbook, expanded the course&#8217;s\nMyOpenMath question bank, developed new Python-based computational projects, and\ncreated assessments that combine mathematical derivation with computation.\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\nDuring <strong>Spring 2025 Professional Development Leave<\/strong>, I worked with the\nUniversity of Florida&#8217;s <strong>Center for Instructional Technology and Training (CITT)<\/strong>\nto redesign MAD 4401 as a fully online course. This work included restructuring the course\nfor online delivery, recording instructional materials, developing online homework and\ncomputer projects, and building a reusable online course structure for future offerings.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What Will We Study?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nThe course focuses on numerical methods that appear throughout mathematics, science,\nengineering, data analysis, and scientific computing. Core topics include:\n<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n\n<li><strong>Error analysis and computer arithmetic<\/strong> \u2014 floating-point representation, round-off error, truncation error, and accuracy.<\/li>\n\n\n\n<li><strong>Root-finding methods<\/strong> \u2014 bisection, fixed-point iteration, Newton&#8217;s method, and related algorithms.<\/li>\n\n\n\n<li><strong>Interpolation and polynomial approximation<\/strong> \u2014 Lagrange interpolation, Newton divided differences, and spline ideas.<\/li>\n\n\n\n<li><strong>Least-squares approximation and regression<\/strong> \u2014 fitting mathematical models to data.<\/li>\n\n\n\n<li><strong>Numerical differentiation and integration<\/strong> \u2014 finite-difference approximations, trapezoidal methods, Simpson&#8217;s rules, and composite methods.<\/li>\n\n\n\n<li><strong>Numerical methods for initial-value differential equations<\/strong> \u2014 Euler methods, Runge-Kutta methods, step size, error, and stability.<\/li>\n\n\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Mathematics First, Computation Second<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nAlthough Python is an important tool in the course, MAD 4401 is not primarily a programming class.\nThe mathematics behind the algorithms remains central. Students are expected to understand\nthe assumptions behind a method, analyze its error, compare competing approaches, and explain\nwhy one numerical method may succeed where another fails.\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\nThe computer then becomes a laboratory: students can test theoretical results, investigate\nconvergence, visualize error, work with problems too large for hand calculation, and compare\nmathematical predictions with actual numerical behavior.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">How Will We Learn?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nMAD 4401 combines mathematical analysis with hands-on computation. Depending on the section\nand mode of delivery, course activities may include:\n<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n\n<li>\n<strong>Homework<\/strong> focused on mathematical derivations, error analysis, and numerical techniques.\n<\/li>\n\n\n\n<li>\n<strong>Python computer projects and labs<\/strong> in which students implement and compare numerical algorithms.\n<\/li>\n\n\n\n<li>\n<strong>MyOpenMath<\/strong> assignments with randomized numerical problems and computational exercises.\n<\/li>\n\n\n\n<li>\n<strong>Discussion and explanation<\/strong> of convergence, stability, approximation, and error rather than simply reporting a numerical answer.\n<\/li>\n\n\n\n<li>\n<strong>Examinations<\/strong> that assess both conceptual understanding and the ability to carry out numerical analysis by hand.\n<\/li>\n\n\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Why Take Numerical Analysis?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n\n\n<li>You want to understand what is happening underneath the numerical tools used by computers.<\/li>\n\n\n\n<li>You are interested in scientific computing, applied mathematics, data science, engineering, or computational modeling.<\/li>\n\n\n\n<li>You want a deeper understanding of approximation, numerical error, convergence, and stability.<\/li>\n\n\n\n<li>You want experience translating mathematical algorithms into working computational methods.<\/li>\n\n\n\n<li>You enjoy courses that combine proofs and analysis with practical computation.<\/li>\n\n\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Open-Source Course Materials<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nA major goal of the course redesign has been to reduce dependence on expensive proprietary\nsoftware and textbooks. Current versions of MAD 4401 use Python and open-source numerical\nanalysis resources whenever possible, giving students access to the same computational tools\nafter the course ends.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Syllabi<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nFull details about grading, course policies, schedules, prerequisites, required materials,\nand section-specific activities are available through Simple Syllabus.\n<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n\n<li>\n<a href=\"https:\/\/ufl.simplesyllabus.com\/en-US\/syllabus-library\">\nMAD 4401 syllabi in the Simple Syllabus Library\n<\/a>\n<\/li>\n\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\nDifferent sections cover the same core numerical-analysis material, but meeting times,\nexam logistics, and some course activities may differ. Students should consult the syllabus\nfor their registered section.\n<\/p>\n\n\n<\/div>\n<\/div>\n<\/div>\n<\/section>\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":479,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/276\/revisions\/479"}],"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}]}}