{"id":29846,"date":"2026-10-19T15:37:56","date_gmt":"2026-10-19T07:37:56","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?page_id=29846"},"modified":"2026-10-21T11:13:15","modified_gmt":"2026-10-21T03:13:15","slug":"ph-d-program","status":"publish","type":"page","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/en\/course-en\/ph-d-program\/","title":{"rendered":"Ph.D. Program"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"29846\" class=\"elementor elementor-29846\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2ea2825 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2ea2825\" 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-132200f\" data-id=\"132200f\" 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-9ec16a1 elementor-widget elementor-widget-spacer\" data-id=\"9ec16a1\" 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-14b0062 animated-fast elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"14b0062\" 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>Ph.D. Program Courses<\/span><br><span>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-87fd759 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"87fd759\" 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-0d06151 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0d06151\" 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-3572d81\" data-id=\"3572d81\" 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-6f2f50c elementor-widget elementor-widget-spacer\" data-id=\"6f2f50c\" 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-181b60b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"181b60b\" 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-06f04d7\" data-id=\"06f04d7\" 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-8f9a085 elementor-widget elementor-widget-heading\" data-id=\"8f9a085\" 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-b8e75db elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b8e75db\" 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-51cc5ef\" data-id=\"51cc5ef\" 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-bc112ec elementor-widget elementor-widget-Table\" data-id=\"bc112ec\" 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-4f86707\"   >Compulsory 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<td data-label=\"Compulsory 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-9a9f147 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9a9f147\" 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-0227d8d\" data-id=\"0227d8d\" 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-41a3ca8 elementor-widget elementor-widget-text-editor\" data-id=\"41a3ca8\" 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. Compulsory courses for the whole department: 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-c2c709e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2c709e\" 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-081df60\" data-id=\"081df60\" 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-3e1a2d5 elementor-widget elementor-widget-Table\" data-id=\"3e1a2d5\" 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-28f1961 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28f1961\" 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-ac15cd5\" data-id=\"ac15cd5\" 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-a1e7c12 elementor-widget elementor-widget-text-editor\" data-id=\"a1e7c12\" 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. Selective courses for the whole department: 18 credits in total<\/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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Ph.D. Program CoursesDepartment of Mathematics, Nationa [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":29823,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"left-sidebar","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"ocs-sidebar-for-course","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-29846","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/pages\/29846","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=29846"}],"version-history":[{"count":11,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/pages\/29846\/revisions"}],"predecessor-version":[{"id":29990,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/pages\/29846\/revisions\/29990"}],"up":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/pages\/29823"}],"wp:attachment":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=29846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}