{"id":84007,"date":"2023-06-02T14:14:32","date_gmt":"2023-06-02T06:14:32","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=84007"},"modified":"2024-05-07T13:39:17","modified_gmt":"2024-05-07T05:39:17","slug":"%e9%9b%a2%e6%95%a3%e6%95%b8%e5%ad%b8-discrete-mathematics-99%e5%ad%b8%e5%b9%b4%e5%ba%a6-%e8%b3%87%e8%a8%8a%e5%b7%a5%e7%a8%8b%e5%ad%b8%e7%b3%bb-%e6%98%93%e5%bf%97%e5%81%89%e8%80%81%e5%b8%ab","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-computer-science\/%e9%9b%a2%e6%95%a3%e6%95%b8%e5%ad%b8-discrete-mathematics-99%e5%ad%b8%e5%b9%b4%e5%ba%a6-%e8%b3%87%e8%a8%8a%e5%b7%a5%e7%a8%8b%e5%ad%b8%e7%b3%bb-%e6%98%93%e5%bf%97%e5%81%89%e8%80%81%e5%b8%ab","title":{"rendered":"\u96e2\u6563\u6578\u5b78 Discrete Mathematics &#8211; 99\u5b78\u5e74\u5ea6 | \u8cc7\u8a0a\u5de5\u7a0b\u5b78\u7cfb \u6613\u5fd7\u5049\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"84007\" class=\"elementor elementor-84007\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" data-element_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=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78bf394\" data-id=\"78bf394\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9a5e0e8 elementor-widget elementor-widget-breadcrumbs\" data-id=\"9a5e0e8\" data-element_type=\"widget\" data-widget_type=\"breadcrumbs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/ocw.nycu.edu.tw\/wp-content\/plugins\/elementor-pro\/assets\/css\/widget-theme-elements.min.css\"><p id=\"breadcrumbs\"><span><span><a href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_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=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_80164\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t<div class=\"penci-ibox-stit\">Discrete Mathematics  - 99 Academic Year<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u96e2\u6563\u6578\u5b78  - 99\u5b78\u5e74\u5ea6<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg 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aria-selected=\"false\" data-tab=\"3\" role=\"tab\" tabindex=\"-1\" aria-controls=\"syllabus-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 48-21.5 48-48V112c0-26.5-21.5-48-48-48zM96 424c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm96-192c13.3 0 24 10.7 24 24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 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                     <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/www.cs.nycu.edu.tw\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u8cc7\u8a0a\u5de5\u7a0b\u5b78\u7cfb<\/a>\u00a0\u63d0\u4f9b\u3002<\/p><p class=\"text\"><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4, serif;\">1. To demonstrate to students how mathematics can be applied to solve nontrivial real-life problems<\/span><\/p><p class=\"text\"><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4, serif;\">2. To gain more experience with mathematical thinking, arguments and proof techniques, which are essential in reasoning about computation<\/span><\/p><p class=\"text\"><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4, serif;\">3. To learn about a number of different discrete structures (e.g., sets, relations, graphs, trees, etc.) that provide the mathematical formalizations for many computational problems<\/span><\/p><p class=\"text\"><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4, serif;\">4. To hope that students will not only learn some powerful mathematical tools but also develop their ability to perceive, to formulate, and to solve mathematical problems<\/span><\/p><p class=\"text\"><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4, serif;\">5. To provide a gateway to more advanced courses in any computer science courses, including data structures, algorithm, database automata theory, computer security, etc.<\/span><\/p><ul><li>\u00a0<\/li><\/ul><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\uff1a<br \/><\/span><\/p><p class=\"text\">Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th ed., McGraw-Hill Inc.<\/p><p style=\"color: #ff00ff; font-size: 14px;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<br \/><br \/><\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u6559\u5e2b<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u8cc7\u8a0a\u5de5\u7a0b\u5b78\u7cfb \u6613\u5fd7\u5049\u8001\u5e2b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u5b78\u5206<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u5b78\u5206<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5e74\u5ea6<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span 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nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u63d0\u4f9b<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a>\u00a0 \u00a0<a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/a> \u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-339\" class=\"tablepress tablepress-id-339\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\">\u7b2c\u4e00\u9031<\/td><td class=\"column-2\">Logic and Proofs (1\/5)<br \/>\n1.1 Proposition Logic<br \/>\n1.2 Proposition Equivalences<br \/>\n1.3 Predicates and Quantifiers<br \/>\n1.4 Nested Quantifiers<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=84033\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e00\u9031<\/td><td class=\"column-2\">Logic and Proofs (2\/5)<br \/>\n1.1 Proposition Logic<br \/>\n1.2 Proposition Equivalences<br \/>\n1.3 Predicates and Quantifiers<br \/>\n1.4 Nested Quantifiers<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87479\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/td><td class=\"column-2\">Logic and Proofs (3\/5)<br \/>\n1.1 Proposition Logic<br \/>\n1.2 Proposition Equivalences<br \/>\n1.3 Predicates and Quantifiers<br \/>\n1.4 Nested Quantifiers<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87485\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/td><td class=\"column-2\">Logic and Proofs (4\/5)<br \/>\n1.5 Rules of Inference<br \/>\n1.6 Introduction to Proofs<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87491\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">\u7b2c\u4e09\u9031<\/td><td class=\"column-2\">Logic and Proofs (5\/5)<br \/>\n1.7 Proof Methods and Strategy<br \/>\nSets, Functions, Sequences, and Sums (1\/3)<br \/>\nPreliminary Test #1<br \/>\n2.1 Sets<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87497\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">\u7b2c\u56db\u9031<\/td><td class=\"column-2\">Sets, Functions, Sequences, and Sums (2\/3)<br \/>\n2.2 Set Operations<br \/>\n2.3 Functions<br \/>\n2.4 Sequences and Summations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87503\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">\u7b2c\u56db\u9031<\/td><td class=\"column-2\">Sets, Functions, Sequences, and Sums (3\/3)<br \/>\n2.2 Set Operations<br \/>\n2.3 Functions<br \/>\n2.4 Sequences and Summations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87509\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e94\u9031<\/td><td class=\"column-2\">Algorithms and the Integers (1\/4)<br \/>\n3.4 The Integers and Division<br \/>\n3.5 Primes and Greatest Common Divisors<br \/>\n3.6 Integers and Algorithms<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87515\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">\u7b2c\u4e94\u9031<\/td><td class=\"column-2\">Algorithms and the Integers (2\/4)<br \/>\n3.4 The Integers and Division<br \/>\n3.5 Primes and Greatest Common Divisors<br \/>\n3.6 Integers and Algorithms<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87521\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e94\u9031<\/td><td class=\"column-2\">Algorithms and the Integers (3\/4)<br \/>\n3.4 The Integers and Division<br \/>\n3.5 Primes and Greatest Common Divisors<br \/>\n3.6 Integers and Algorithms<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87527\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">\u7b2c\u4e03\u9031<\/td><td class=\"column-2\">Algorithms and the Integers (4\/4)<br \/>\n3.7 Applications of Number Theory<br \/>\nInduction and Recur (1\/4)<br \/>\n4.1 Mathematical Induction<br \/>\n4.2 Strong Induction and Well-Ordering<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87533\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e03\u9031<\/td><td class=\"column-2\">Induction and Recur (2\/4)<br \/>\n4.1 Mathematical Induction<br \/>\n4.2 Strong Induction and Well-Ordering<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87539\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">\u7b2c\u516b\u9031<\/td><td class=\"column-2\">Induction and Recur (3\/4)<br \/>\n4.3 Recursive Definitions and Structural Induction<br \/>\n4.4 Recursive Algorithms<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87545\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">\u7b2c\u516b\u9031<\/td><td class=\"column-2\">Induction and Recur (4\/4)<br \/>\n4.3 Recursive Definitions and Structural Induction<br \/>\n4.4 Recursive Algorithms<br \/>\nCounting (1\/2)<br \/>\n5.1 The Basics of Counting<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87551\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">\u7b2c\u4e5d\u9031<\/td><td class=\"column-2\">Counting (2\/2)<br \/>\n5.2 The Pigeonhole Principle<br \/>\n5.3 Permutations and Combinations<br \/>\n5.4 Binomial Coefficients<br \/>\n5.5 Generalized Permutations and Combinations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87557\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e00\u9031<\/td><td class=\"column-2\">Advanced Counting Techniques (1\/4)<br \/>\n7.1 Recurrence Relations<br \/>\n7.2 Solving Linear Recurrence Relations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87563\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Advanced Counting Techniques (2\/4)<br \/>\n7.4 Generating Functions<br \/>\nExample 1-3<br \/>\n7.5 Inclusion-Exclusion<br \/>\n7.6 Applications of Inclusion-Exclusion<br \/>\n8.1 Relations and Their Properties<br \/>\n8.2 n-ary Relations and Their Applications<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87569\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Advanced Counting Techniques (3\/4)<br \/>\n7.4 Generating Functions<br \/>\nExample 1-3<br \/>\n7.5 Inclusion-Exclusion<br \/>\n7.6 Applications of Inclusion-Exclusion<br \/>\n8.1 Relations and Their Properties<br \/>\n8.2 n-ary Relations and Their Applications<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87575\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Advanced Counting Techniques (4\/4)<br \/>\n7.4 Generating Functions<br \/>\nExample 1-3<br \/>\n7.5 Inclusion-Exclusion<br \/>\n7.6 Applications of Inclusion-Exclusion<br \/>\nRelations (1\/4)<br \/>\n8.1 Relations and Their Properties<br \/>\n8.2 n-ary Relations and Their Applications<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87581\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u56db\u9031<\/td><td class=\"column-2\">Relations (2\/4)<br \/>\n8.3 Representing Relations<br \/>\n8.4 Closures of Relations<br \/>\n8.5 Equivalence Relations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87587\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u56db\u9031<\/td><td class=\"column-2\">Relations (3\/4)<br \/>\n8.3 Representing Relations<br \/>\n8.4 Closures of Relations<br \/>\n8.5 Equivalence Relations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87593\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e94\u9031<\/td><td class=\"column-2\">Relations (4\/4)<br \/>\n8.6 Partial Orderings<br \/>\nGraphs(1\/3)<br \/>\n9.1 Graphs and Graph Models<br \/>\n9.2 Graph Terminology and Special Types of Graphs<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87599\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u516d\u9031<\/td><td class=\"column-2\">Graphs (2\/3)<br \/>\n9.3 Representing Graphs and Graph Isomorphism<br \/>\n9.4 Connectivity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87605\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e03\u9031<\/td><td class=\"column-2\">Graphs (3\/3)<br \/>\n9.5 Euler and Hamilton Paths<br \/>\n9.6 Shortest-Path Problems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=87611\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-339 from cache --><\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">1. To demonstrate to students how mathematics can be applied to solve nontrivial real-life problems<\/p><p class=\"text\">2. To gain more experience with mathematical thinking, arguments and proof techniques, which are essential in reasoning about computation<\/p><p class=\"text\">3. To learn about a number of different discrete structures (e.g., sets, relations, graphs, trees, etc.) that provide the mathematical formalizations for many computational problems<\/p><p class=\"text\">4. To hope that students will not only learn some powerful mathematical tools but also develop their ability to perceive, to formulate, and to solve mathematical problems<\/p><p class=\"text\">5. To provide a gateway to more advanced courses in any computer science courses, including data structures, algorithm, database automata theory, computer security, etc.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th ed., McGraw-Hill Inc.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">2 Preliminary Test<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">20%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2 Midterm<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">40%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1 Final<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">35%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Homework, Quizzes and others <\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">10%<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><table style=\"font-style: normal; line-height: 20px; font-size: 15px; text-align: center;\" border=\"1\" cellspacing=\"0\"><tbody><tr><td bgcolor=\"#e4d8b0\" width=\"76\"><div style=\"text-align: center;\"><span style=\"color: #000000; font-weight: bold;\"><strong>\u5b78\u671f\u9031\u6b21<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"135\"><div style=\"text-align: center;\" align=\"center\"><span style=\"font-family: 'Times New Roman'; font-weight: bold;\"><strong>\u4e0a\u8ab2\u65e5\u671f<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"440\"><div style=\"text-align: center; font-size: 15px; font-weight: bold;\"><strong>\u53c3\u8003\u8ab2\u7a0b\u9032\u5ea6<\/strong><\/div><\/td><\/tr><tr><td style=\"text-align: center;\"><p><span class=\"text\">\u7b2c\u4e00\u9031<\/span><\/p><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2011\/02\/22 &amp; 02\/25<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.1 Proposition Logic <br \/>1.2 Proposition Equivalences <br \/>1.3 Predicates and Quantifiers\u3000<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/03\/01 &amp; 03\/04<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.4 Nested Quantifiers <br \/>1.5 Rules of Inference <br \/>1.6 Introduction to Proofs<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/03\/08 &amp; 03\/11<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.7 Proof Methods and Strategy <br \/>Preliminary Test #1 <br \/>2.1 Sets\u3000<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u56db\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/03\/15 &amp; 03\/18<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>2.2 Set Operations <br \/>2.3 Functions <br \/>2.4 Sequences and Summations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e94\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/03\/22 &amp; 03\/25<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.4 The Integers and Division <br \/>3.5 Primes and Greatest Common Divisors <br \/>3.6 Integers and Algorithms<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516d\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/03\/29 &amp; 04\/01<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Preliminary Test #2 <br \/>Break<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e03\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/04\/05 &amp; 04\/08<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.7 Applications of Number Theory <br \/>4.1 Mathematical Induction <br \/>4.2 Strong Induction and Well-Ordering<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516b\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/04\/12 &amp; 04\/15<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>4.3 Recursive Definitions and Structural Induction <br \/>4.4 Recursive Algorithms <br \/>5.1 The Basics of Counting <br \/>4.4 Recursive Algorithms<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e5d\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/04\/19 &amp; 04\/22<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>5.2 The Pigeonhole Principle <br \/>5.3 Permutations and Combinations <br \/>5.4 Binomial Coefficients<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/04\/26 &amp; 04\/29<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#F2F2EC\"><ul><li>5.5 Generalized Permutations and Combinations <br \/>Midterm #1 Ch 3.3~3.7 &amp; Ch.4.1~4.4<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e00\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/05\/03 &amp; 05\/06<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>5.6 Generating Permutations and Combinations <br \/>7.1 Recurrence Relations <br \/>7.2 Solving Linear Recurrence Relations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2011\/05\/10 &amp; 05\/13<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>7.3 Divide-and-Conquer Algorithms and Recurrence Relations <br \/>7.4 Generating Functions <br \/>7.5 Inclusion-Exclusion <br \/>7.6 Applications of Inclusion-Exclusion<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">2011\/05\/17 &amp; 05\/20<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>8.1 Relations and Their Properties <br \/>Midterm #2: Chapter 5,7 (not including 7.3)<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u56db\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">2011\/05\/24 &amp; 05\/27<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>8.3 Representing Relations <br \/>8.4 Closures of Relations <br \/>8.5 Equivalence Relations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e94\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2011\/05\/31 &amp; 06\/03<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>8.6 Partial Orderings<br \/>9.1 Graphs and Graph Models <br \/>9.2 Graph Terminology and Special Types of Graphs<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u516d\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">2011\/06\/07 &amp; 06\/10<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>9.3 Representing Graphs and Graph Isomorphism <br \/>9.4 Connectivity <br \/>9.5 Euler and Hamilton Paths <br \/>9.6 Shortest-Path Problems\u3000<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e03\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2011\/06\/14 &amp; 06\/17<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>10.1 Introduction to Trees <br \/>10.3 Tree Traversal <br \/>10.5 Minimum Spanning Trees<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u516b\u9031<\/span><\/td><td 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