{"id":7930,"date":"2020-09-08T16:16:19","date_gmt":"2020-09-08T08:16:19","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?page_id=7930"},"modified":"2023-02-20T08:35:02","modified_gmt":"2023-02-20T00:35:02","slug":"degree-programs-en","status":"publish","type":"page","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/en\/degree-programs-en\/","title":{"rendered":"Degree Programs"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"7930\" class=\"elementor elementor-7930\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f5c7333 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f5c7333\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;shape_divider_top&quot;:&quot;opacity-tilt&quot;}\">\n\t\t\t\t\t<div class=\"elementor-shape elementor-shape-top\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 2600 131.1\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0 0L2600 0 2600 69.1 0 0z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.5\" d=\"M0 0L2600 0 2600 69.1 0 69.1z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.25\" d=\"M2600 0L0 0 0 130.1 2600 69.1z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7cd583f\" data-id=\"7cd583f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6657bbd elementor-widget elementor-widget-spacer\" data-id=\"6657bbd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-559a129 animated-fast elementor-widget__width-inherit elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"559a129\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInDown&quot;,&quot;_animation_delay&quot;:0}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span style=\"font-size: 36px\">Undergraduated Program Curriculum Framework<\/span><br><span lang=\"EN-US\" style=\"font-size:15pt\">Department of Mathematics, National Taiwan Normal University\n\n<\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-12f4f64 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"12f4f64\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-652d255 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"652d255\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-35f63ce\" data-id=\"35f63ce\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b74f184 elementor-icon-list--layout-inline elementor-align-start elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"b74f184\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items elementor-inline-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item elementor-inline-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#curriculum\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-circle-o\" aria-hidden=\"true\"><\/i>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Master Program Curriculum Framework<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item elementor-inline-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#phd\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-circle-o\" aria-hidden=\"true\"><\/i>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Ph.D. Program Curriculum Framework<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b0adc7e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b0adc7e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-029ae40\" data-id=\"029ae40\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9fd6556 elementor-widget elementor-widget-spacer\" data-id=\"9fd6556\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e616743 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e616743\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1bcc9e2\" data-id=\"1bcc9e2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-545beb5 elementor-widget elementor-widget-heading\" data-id=\"545beb5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Students in this undergraduated program are required to finish the following courses:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-914a535 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"914a535\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a0656ab\" data-id=\"a0656ab\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b373b61 elementor-widget elementor-widget-text-editor\" data-id=\"b373b61\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>applicable to students accepted since the school year 2021:<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f4e3ace elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f4e3ace\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-44e11b1\" data-id=\"44e11b1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d6e9d9c elementor-widget elementor-widget-Table\" data-id=\"d6e9d9c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-52376ec\"   >course types<\/th><th class=\"elementor-inline-editing elementor-repeater-item-63a469c\"   >required credits<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<td data-label=\"course types\"   class=\"elementor-repeater-item-770ec28 td-content-type-default\" > <p style=\"color:blue\">Compulsory courses<\/p><\/td><td data-label=\"required credits\"   class=\"elementor-repeater-item-224afa6 td-content-type-default\" >on the common ground of the whole university:  <span style=\"color:blue\">32 credits<\/span>\n<br>required by the department of the Mathematics: <span style=\"color:blue\"> 53 credits<\/span>\n<\/td><\/tr><tr><td data-label=\"course types\"   class=\"elementor-repeater-item-51fa68f td-content-type-default\" > <p style=\"color:blue\"> Selective courses<\/p><\/td><td data-label=\"required credits\"   class=\"elementor-repeater-item-71efbe8 td-content-type-default\" >required by the department of the Mathematics : <span style=\"color:blue\">18 credits<\/span>\n<br>according to one's free will: <span style=\"color:blue\">25 credits<\/br>\n<\/td><\/tr><tr><td data-label=\"course types\"   class=\"elementor-repeater-item-4f63a6d td-content-type-default\" > Total<\/td><td data-label=\"required credits\"   class=\"elementor-repeater-item-2dee002 td-content-type-default\" ><span style=\"color:blue\">128 credits<\/span><\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b0882ab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b0882ab\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c1725d4\" data-id=\"c1725d4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ee3b08c elementor-widget elementor-widget-text-editor\" data-id=\"ee3b08c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>For those who apply for the secondary school teacher pareparation program, they have to take additional courses required by MOE (Misinstry Of Education).<br \/>There are <span style=\"color: blue;\">26 credits<\/span> totally.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-546f36c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"546f36c\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;shape_divider_top&quot;:&quot;opacity-tilt&quot;}\">\n\t\t\t\t\t<div class=\"elementor-shape elementor-shape-top\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 2600 131.1\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0 0L2600 0 2600 69.1 0 0z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.5\" d=\"M0 0L2600 0 2600 69.1 0 69.1z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.25\" d=\"M2600 0L0 0 0 130.1 2600 69.1z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0eff3b7\" data-id=\"0eff3b7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1c7eaa8 elementor-widget elementor-widget-spacer\" data-id=\"1c7eaa8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bb15e15 animated-fast elementor-widget__width-inherit elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"bb15e15\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInDown&quot;,&quot;_animation_delay&quot;:0}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span style=\"font-size: 36px\">Curriculum Framework for Postgraduate Programmes of Study<\/span><br><span lang=\"EN-US\" style=\"font-size:15pt\">Department of Mathematics, National Taiwan Normal University\n\n<\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eebcc69 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"eebcc69\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-79d763b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"79d763b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-177a043\" data-id=\"177a043\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1e5449d elementor-widget elementor-widget-spacer\" data-id=\"1e5449d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-758dbb2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"758dbb2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6d1808b\" data-id=\"6d1808b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8d2cdf5 elementor-widget elementor-widget-heading\" data-id=\"8d2cdf5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Courses design<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fc43c27 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fc43c27\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9efaf9d\" data-id=\"9efaf9d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-75540ca elementor-widget elementor-widget-text-editor\" data-id=\"75540ca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>\u00a0 For graduate programs, the aims of the Master and PhD programs of our department are to train researchers in mathematics and mathematics education, and also to train mathematics professors and lectures for universities. Those who graduate from our Master or PhD programs focus their careers in research and teaching. Due to the fact that some graduate students took courses in mathematics education in undergraduate years, they would like to go into the domain of mathematics education research. Therefore, this department was separated into mathematics section and mathematics education section since 1993, so those who want to work in mathematics education may do so. To help students in their future research and occupations, courses in our graduate programs are separated into two groups: mathematics and mathematics education. In mathematics section, courses are divided into four domains: analysis, algebra, geometry and applied mathematrics. With the domain of mathematics education, courses of the whole department are divided into a total of five domains. The domain of applied mathematics is further subdivided into five subdomains, which are differential equations, probability and statistics, computer, combinatorics and discrete mathematics, and finally optimization theory. The courses in mathematics education can also be roughly categorized in two types: mathematrics education and history of mathematics.<\/strong><\/p><p><strong>\u00a0 Besides delving into the research domain for their dissertations, this department also requires students to take at least six credits of courses that belong to another domain. When choosing which courses for professors to teach, we try to provide basic courses in each year, and for other selective course the lectures are provided according students\u2019 needs. The way to do it is to let professors of the graduate programs to fill a form about which courses they want to teach. According the regulations of the university and the department, those students who have exceptional performances can apply to be directly accepted into the PhD program in their first year of the Master\u2019s program.<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c52c060 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c52c060\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ac7f130\" data-id=\"ac7f130\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-42318e4 elementor-widget elementor-widget-menu-anchor\" data-id=\"42318e4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"curriculum\"><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2ee339d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2ee339d\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;shape_divider_top&quot;:&quot;opacity-tilt&quot;}\">\n\t\t\t\t\t<div class=\"elementor-shape elementor-shape-top\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 2600 131.1\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0 0L2600 0 2600 69.1 0 0z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.5\" d=\"M0 0L2600 0 2600 69.1 0 69.1z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.25\" d=\"M2600 0L0 0 0 130.1 2600 69.1z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c27c971\" data-id=\"c27c971\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-99c8c8e elementor-widget elementor-widget-spacer\" data-id=\"99c8c8e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c808432 animated-fast elementor-widget__width-inherit elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"c808432\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInDown&quot;,&quot;_animation_delay&quot;:0}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span style=\"font-size: 36px\">Master Program Curriculum Framework<\/span><br><span lang=\"EN-US\" style=\"font-size:15pt\">Department of Mathematics, National Taiwan Normal University\n\n<\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a2c28de elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"a2c28de\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0e2496c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0e2496c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5f578be\" data-id=\"5f578be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-625f9e5 elementor-widget elementor-widget-spacer\" data-id=\"625f9e5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e0c9299 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e0c9299\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-591cb1a\" data-id=\"591cb1a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-45e232e elementor-widget elementor-widget-heading\" data-id=\"45e232e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Students in this Master program are required to finish the following courses:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-57a9782 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"57a9782\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b05d3f5\" data-id=\"b05d3f5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-04ebc7d elementor-widget elementor-widget-text-editor\" data-id=\"04ebc7d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: red;\">Remark: All of the courses provided by the department would be lectured in whole-English whenever it is beneficial for both international students and local students.<\/span><\/strong><br \/><strong>applicable to students accepted since the academic year 2022<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-db9cc95 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"db9cc95\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-06e7b78\" data-id=\"06e7b78\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8b156aa elementor-widget elementor-widget-Table\" data-id=\"8b156aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-c14cd83\"   >Applicable school year<\/th><th class=\"elementor-inline-editing elementor-repeater-item-4f86707\"   >Necessary credits<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f59daaf\"   >Selective credits<\/th><th class=\"elementor-inline-editing elementor-repeater-item-9b2c3a4\"   >Total credits <br>for graduation<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<\/tr><tr><td data-label=\"Applicable school year\"   class=\"elementor-repeater-item-484dc7f td-content-type-default\" >2022<\/td><td data-label=\"Necessary credits\"   class=\"elementor-repeater-item-2c58474 td-content-type-default\" >Mathematics section <span style=\"color:blue\"> 15 credits<\/span>\n<br>Mathematics education section  <span style=\"color:blue\">7credits<\/span>\n<br>Statistics and Computational Sci. section <span style=\"color:blue\"> 3 credits<\/span>\n<\/td><td data-label=\"Selective credits\"   class=\"elementor-repeater-item-d7321c5 td-content-type-default\" >Selective courses for the Mathematics education section: \n<br>Each student has to take at least <span style=\"color:blue\"> 6 credits<\/span> in any <br>two different course domains before they graduate.<\/td><td data-label=\"Total credits for graduation\"   class=\"elementor-repeater-item-29594fd td-content-type-default\" ><span style=\"color:blue\">27<\/span><\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-66bddd4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66bddd4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-efe12d5\" data-id=\"efe12d5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a3d8e7b elementor-widget elementor-widget-text-editor\" data-id=\"a3d8e7b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #2b667f;\">1. Required curses for the whole department: At least 3 credits before graduation<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-86b9b05 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"86b9b05\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0bf70af\" data-id=\"0bf70af\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-49911b8 elementor-widget elementor-widget-Table\" data-id=\"49911b8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-5b0ed52\"   >Course Code<\/th><th class=\"elementor-inline-editing elementor-repeater-item-9050d78\"   >Course Name<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f744fcc\"   >Credit<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f055848\"   >Note<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<td data-label=\"Course Code\"   class=\"elementor-repeater-item-8a38283 td-content-type-default\" >MAC8028<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-e307ddc td-content-type-default\" >Trend of Mathematics Research<\/td><td data-label=\"Credit\"   class=\"elementor-repeater-item-5ca2902 td-content-type-default\" >1<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-ac0ad37 td-content-type-default\" >This course must be retaken with<br> a passing score for <span style=\"color:blue\">3 times<\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-084b0c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"084b0c0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8766abd\" data-id=\"8766abd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-67d1c91 elementor-widget elementor-widget-text-editor\" data-id=\"67d1c91\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #2b667f;\">2. Required curses for the <span style=\"color: blue;\">Mathematics section<\/span>: At least 12 credits before graduation<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4761cd8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4761cd8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7bf5c3b\" data-id=\"7bf5c3b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7308f98 elementor-widget elementor-widget-Table\" data-id=\"7308f98\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-4227c1f\"   >COURSE CODE<\/th><th class=\"elementor-inline-editing elementor-repeater-item-c927e3f\"   >Course Name<\/th><th class=\"elementor-inline-editing elementor-repeater-item-260e166\"   >Total Credit<\/th><th class=\"elementor-inline-editing elementor-repeater-item-a4db67f\"   >Note<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-e9eeb8c td-content-type-default\" >Real Analysis (I) (II) <\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-451e5ac td-content-type-default\" >MAC0087, MAC0088 <\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-bff1667 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-0f26002 td-content-type-default\" ><\/td><\/tr><tr><td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-07f5d16 td-content-type-default\" >Modern Algebra (I) (II)<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-c4cda98 td-content-type-default\" >MAC0093, MAC0094<\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-51cba52 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-4707d3a td-content-type-default\" ><\/td><\/tr><tr><td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-ea2a93f td-content-type-default\" >Complex Analysis (I) (II) <\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-1e0a036 td-content-type-default\" >MAC0089, MAC0090 <\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-44d3b36 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-a4be79f td-content-type-default\" ><\/td><\/tr><tr><td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-d23fe86 td-content-type-default\" >Introduction to Partial Differential Equations (I) (II)<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-309e1a8 td-content-type-default\" >MAC0132, MAC0133<\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-5cd74f7 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-44bac65 td-content-type-default\" ><\/td><\/tr><tr><td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-09ccb62 td-content-type-default\" >Riemannian Geometry (I) (II)<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-689ae44 td-content-type-default\" >MAC7001, MAC7002<\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-ac77099 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-f2aa946 td-content-type-default\" ><\/td><\/tr><tr><td data-label=\"COURSE CODE\"   class=\"elementor-repeater-item-8c28f9a td-content-type-default\" >Combinatorics (I) (II) <\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-a94b77a td-content-type-default\" >MAC0015, MAC0016<\/td><td data-label=\"Total Credit\"   class=\"elementor-repeater-item-2921b81 td-content-type-default\" >6<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-0001db0 td-content-type-default\" ><\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de5b7f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de5b7f6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b8f0526\" data-id=\"b8f0526\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-61bf27c elementor-widget elementor-widget-text-editor\" data-id=\"61bf27c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>Each student has to take the course Real Analysis (I) (II) or Modern algebra (I) (II)\u00a0<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c6979fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c6979fc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dabd2c9\" data-id=\"dabd2c9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0e1684f elementor-widget elementor-widget-text-editor\" data-id=\"0e1684f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #2b667f;\">3. Required curses for the <span style=\"color: blue;\">Mathematics education section<\/span>: At least 4 credits before graduation<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0ae1951 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0ae1951\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8941626\" data-id=\"8941626\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-158ebc3 elementor-widget elementor-widget-Table\" data-id=\"158ebc3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-5b0ed52\"   >Course Code<\/th><th class=\"elementor-inline-editing elementor-repeater-item-9050d78\"   >Course Name<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f744fcc\"   >Credit<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f055848\"   >Note<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<td data-label=\"Course Code\"   class=\"elementor-repeater-item-8a38283 td-content-type-default\" >MAM0097<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-e307ddc td-content-type-default\" >Topics in Mathematics Education Research (I)<\/td><td data-label=\"Credit\"   class=\"elementor-repeater-item-5ca2902 td-content-type-default\" >2<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-ac0ad37 td-content-type-default\" > <\/td><\/tr><tr><td data-label=\"Course Code\"   class=\"elementor-repeater-item-54a029a td-content-type-default\" >MAM0098<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-d6d4a7a td-content-type-default\" >Topics in Mathematics Education Research (II)<\/td><td data-label=\"Credit\"   class=\"elementor-repeater-item-70d8859 td-content-type-default\" >2<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-6bd223d td-content-type-default\" > <\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d1c28bd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d1c28bd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-484ffca\" data-id=\"484ffca\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cefad78 elementor-widget elementor-widget-text-editor\" data-id=\"cefad78\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #2b667f;\">4. Selective courses for the <span style=\"color: blue;\">Mathematics education section<\/span>:<\/span><\/strong><\/p><p><strong>Each student has to take at least 6 credits in any two different course domains before they graduate (The 6 credits cannot consist of two courses of level (I))<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cc681c2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cc681c2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-767fb80\" data-id=\"767fb80\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6542017 elementor-widget elementor-widget-menu-anchor\" data-id=\"6542017\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"phd\"><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6c1a3b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c1a3b4\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;shape_divider_top&quot;:&quot;opacity-tilt&quot;}\">\n\t\t\t\t\t<div class=\"elementor-shape elementor-shape-top\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 2600 131.1\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M0 0L2600 0 2600 69.1 0 0z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.5\" d=\"M0 0L2600 0 2600 69.1 0 69.1z\"\/>\n\t<path class=\"elementor-shape-fill\" style=\"opacity:0.25\" d=\"M2600 0L0 0 0 130.1 2600 69.1z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9e7b23f\" data-id=\"9e7b23f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e5a1902 elementor-widget elementor-widget-spacer\" data-id=\"e5a1902\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a9ccb7a animated-fast elementor-widget__width-inherit elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"a9ccb7a\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;slideInDown&quot;,&quot;_animation_delay&quot;:0}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span style=\"font-size: 36px\">Ph.D. Program Curriculum Framework<\/span><br><span lang=\"EN-US\" style=\"font-size:15pt\">Department of Mathematics, National Taiwan Normal University\n\n<\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01befa9 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"01befa9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3a0aabc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3a0aabc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-93cc115\" data-id=\"93cc115\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f6d6e6b elementor-widget elementor-widget-spacer\" data-id=\"f6d6e6b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-90d8c88 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90d8c88\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-70f0078\" data-id=\"70f0078\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-93b0ace elementor-widget elementor-widget-heading\" data-id=\"93b0ace\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Students in this PhD program are required to finish the following courses:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c6d77f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c6d77f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-799c5a2\" data-id=\"799c5a2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d0e4a9e elementor-widget elementor-widget-text-editor\" data-id=\"d0e4a9e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: red;\">Remark: All of the courses provided by the department would be lectured in whole-English whenever it is beneficial for both international students and local students.<\/span><\/strong><br \/><strong>applicable to students accepted since the school year 2020<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-28cc391 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28cc391\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ce493cb\" data-id=\"ce493cb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5778ecc elementor-widget elementor-widget-Table\" data-id=\"5778ecc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-c14cd83\"   >Applicable school year<\/th><th class=\"elementor-inline-editing elementor-repeater-item-4f86707\"   >Necessary credits<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f59daaf\"   >Selective credits<\/th><th class=\"elementor-inline-editing elementor-repeater-item-9b2c3a4\"   >Total credits <br>for graduation<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<\/tr><tr><td data-label=\"Applicable school year\"   class=\"elementor-repeater-item-484dc7f td-content-type-default\" >2020<\/td><td data-label=\"Necessary credits\"   class=\"elementor-repeater-item-2c58474 td-content-type-default\" ><span style=\"color:blue\">4<\/span><\/td><td data-label=\"Selective credits\"   class=\"elementor-repeater-item-d7321c5 td-content-type-default\" ><span style=\"color:blue\">18<\/span><\/td><td data-label=\"Total credits for graduation\"   class=\"elementor-repeater-item-29594fd td-content-type-default\" ><span style=\"color:blue\">22<\/span><\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6ad3744 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ad3744\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-158568c\" data-id=\"158568c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-01f808f elementor-widget elementor-widget-Table\" data-id=\"01f808f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"Table.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<table class=\"tafe-table \">\n\t\t\t<thead  class=\"tafe-table-header\">\n\t\t\t\t<tr>\n\t\t\t\t\t<th class=\"elementor-inline-editing elementor-repeater-item-5b0ed52\"   >Course Code<\/th><th class=\"elementor-inline-editing elementor-repeater-item-9050d78\"   >Course Name<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f744fcc\"   >Credit<\/th><th class=\"elementor-inline-editing elementor-repeater-item-f055848\"   >Note<\/th>\t\t\t\t<\/tr>\n\t\t\t<\/thead>\n\t\t\t\t\t\t<tbody class=\"tafe-table-body\">\n\t\t\t\t<tr>\n\t\t\t\t\t<td data-label=\"Course Code\"   class=\"elementor-repeater-item-8a38283 td-content-type-default\" >MAC8028<\/td><td data-label=\"Course Name\"   class=\"elementor-repeater-item-e307ddc td-content-type-default\" >Trend of Mathematics Research<\/td><td data-label=\"Credit\"   class=\"elementor-repeater-item-5ca2902 td-content-type-default\" >1<\/td><td data-label=\"Note\"   class=\"elementor-repeater-item-ac0ad37 td-content-type-default\" >This course must be retaken with<br> a passing score for<span style=\"color:blue\"> 4 times<\/td>\t\t\t\t<\/tr>\n\t\t\t<\/tbody>\n\t\t<\/table>\n\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0a06823 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0a06823\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ceeb938\" data-id=\"ceeb938\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-56dea68 elementor-widget elementor-widget-text-editor\" data-id=\"56dea68\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<strong><span style=\"color: #2b667f;\">2.\tSelective courses for the whole department: 18 credits in total<\/span><\/strong>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Undergraduated Program Curriculum FrameworkDepartment o 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