{"id":4045,"date":"2026-05-25T10:24:30","date_gmt":"2026-05-25T10:24:30","guid":{"rendered":"https:\/\/nucs-edu.org\/?p=4045"},"modified":"2026-05-28T18:09:21","modified_gmt":"2026-05-28T18:09:21","slug":"cst-1212","status":"publish","type":"post","link":"https:\/\/nucs-edu.org\/en\/syllabus\/cst-1212\/","title":{"rendered":"Mathematics (CST-1212)"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"4045\" class=\"elementor elementor-4045\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ae03813 e-flex e-con-boxed wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"ae03813\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7a8f1cd elementor-widget elementor-widget-text-editor\" data-id=\"7a8f1cd\" data-element_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<!-- CST-1212 Mathematics Syllabus \u2013 NUCS WordPress Content -->\n<!-- Paste this into the WordPress Text\/HTML tab of the page editor -->\n\n<style>\n  .nucs-math-syllabus {\n    font-family: 'Georgia', serif;\n    max-width: 1080px;\n    margin: 0 auto;\n    color: #1a1a2e;\n    text-align: left;\n  }\n\n  .nucs-math-syllabus * { text-align: left; 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color: #333;\n    margin-bottom: 3px; margin-left: 16px;\n  }\n\n  .nucs-math-syllabus .outline-table tr.assignment-row td {\n    background: #fff3f3; border-left: 4px solid #e53935;\n    color: #c62828; font-family: 'Arial', sans-serif;\n    font-size: 13px; font-weight: 600; padding: 8px 16px;\n    text-align: left !important;\n  }\n\n  .nucs-math-syllabus .outline-table tr.final-row td {\n    background: #1a1a2e; color: #fff; font-weight: 700;\n    font-size: 14px; padding: 14px 16px; letter-spacing: 2px;\n    text-align: left !important;\n  }\n<\/style>\n\n<div class=\"nucs-math-syllabus\">\n\n  <!-- Header -->\n  <div class=\"syllabus-header\">\n    <h1>Mathematics<\/h1>\n    <div class=\"course-code\">Course Code: CST-1212 &nbsp;|&nbsp; Second Semester<\/div>\n    <div class=\"meta-grid\">\n      <div class=\"meta-item\">\n        <strong>Duration<\/strong>\n        <span>15 Weeks<\/span>\n      <\/div>\n      <div class=\"meta-item\">\n        <strong>Lectures<\/strong>\n        <span>3 per week &nbsp;&times;&nbsp; 1 hour<\/span>\n      <\/div>\n    <\/div>\n  <\/div>\n\n  <!-- Textbook -->\n  <div class=\"section-title\">Textbook<\/div>\n  <div class=\"textbook-box\">\n    <div class=\"tb-icon\">&#128218;<\/div>\n    <div>\n      <div class=\"tb-label\">Required Textbook<\/div>\n      <div class=\"tb-title\">Discrete Mathematics and Its Applications, 8<sup>th<\/sup> Edition<\/div>\n      <div class=\"tb-author\">Kenneth H. Rosen &mdash; McGraw-Hill<\/div>\n    <\/div>\n  <\/div>\n\n  <!-- Course Description -->\n  <div class=\"section-title\">Course Description<\/div>\n  <div class=\"description-box\">\n    This course introduces second-semester students to the foundational concepts of discrete mathematics as applied in computer science and related disciplines. Topics span the logical foundations of mathematics, basic algebraic structures, algorithmic thinking, number theory, combinatorics, probability, and graph theory. Students develop the ability to construct rigorous mathematical arguments, analyse algorithms for efficiency, and apply discrete structures to solve computational problems \u2014 building the theoretical backbone required for advanced study in computer science and software engineering.\n  <\/div>\n\n  <!-- Learning Objectives & Outcomes -->\n  <div class=\"olo-grid\">\n    <div class=\"olo-box objectives\">\n      <h3>Learning Objectives<\/h3>\n      <ol>\n        <li>Introduce the foundations of propositional and predicate logic, and develop skills in constructing and evaluating mathematical proofs.<\/li>\n        <li>Build understanding of fundamental discrete structures including sets, functions, sequences, and matrices.<\/li>\n        <li>Develop familiarity with algorithm design and analyse the growth and complexity of algorithms.<\/li>\n        <li>Introduce number theory concepts including divisibility, modular arithmetic, and prime numbers.<\/li>\n        <li>Develop competency in mathematical induction and recursive definitions.<\/li>\n        <li>Build counting and combinatorial reasoning skills, including permutations, combinations, and the Pigeonhole Principle.<\/li>\n        <li>Introduce discrete probability, Bayes&#8217; theorem, and expected value.<\/li>\n        <li>Introduce graph theory, graph models, and graph representations for use in computing applications.<\/li>\n      <\/ol>\n    <\/div>\n    <div class=\"olo-box outcomes\">\n      <h3>Learning Outcomes<\/h3>\n      <ul>\n        <li>Construct and evaluate logical propositions and proofs using propositional and predicate logic.<\/li>\n        <li>Work with sets, functions, sequences, and matrices in mathematical and computational contexts.<\/li>\n        <li>Analyse algorithm efficiency using Big-O notation and complexity measures.<\/li>\n        <li>Apply number theory principles including modular arithmetic and prime factorisation.<\/li>\n        <li>Use mathematical induction and recursive definitions to prove statements and define structures.<\/li>\n        <li>Solve counting problems using permutations, combinations, and the Pigeonhole Principle.<\/li>\n        <li>Apply discrete probability theory including Bayes&#8217; theorem and expected value calculations.<\/li>\n        <li>Model and analyse problems using graph representations and graph terminology.<\/li>\n      <\/ul>\n    <\/div>\n  <\/div>\n\n  <!-- Major Topics -->\n  <div class=\"section-title\">Major Topics Covered<\/div>\n  <div class=\"topics-covered\">\n    <div class=\"pills\">\n      <div class=\"pill\">Logic &amp; Proofs<\/div>\n      <div class=\"pill\">Sets &amp; Functions<\/div>\n      <div class=\"pill\">Algorithms<\/div>\n      <div class=\"pill\">Number Theory<\/div>\n      <div class=\"pill\">Induction &amp; Recursion<\/div>\n      <div class=\"pill\">Counting<\/div>\n      <div class=\"pill\">Discrete Probability<\/div>\n      <div class=\"pill\">Graph Theory<\/div>\n    <\/div>\n  <\/div>\n\n  <!-- Assessment -->\n  <div class=\"section-title\">Assessment Components<\/div>\n  <div class=\"assessment-bar\">\n    <div class=\"assess-block assignment\"><div class=\"lbl\">Assignments<\/div><\/div>\n    <div class=\"assess-block tutorial\"><div class=\"lbl\">Tutorial<\/div><\/div>\n    <div class=\"assess-block exam\"><div class=\"lbl\">Final Exam<\/div><\/div>\n  <\/div>\n\n  <!-- Delivery Note -->\n  <div class=\"delivery-note\">\n    <strong>Lecture Structure:<\/strong> 3 lectures per week, each up to 60 minutes. Assignments are distributed throughout the semester via LMS, with a Tutorial and Final Exam at the end of the term.\n  <\/div>\n\n  <!-- Course Outline -->\n  <div class=\"section-title\">Course Outline<\/div>\n  <table class=\"outline-table\">\n    <thead>\n      <tr>\n        <th style=\"width:110px;\">Week<\/th>\n        <th>Topic<\/th>\n      <\/tr>\n    <\/thead>\n    <tbody>\n\n      <!-- Topic I -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic I<\/span> The Foundations: Logic and Proofs<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 01<\/td>\n        <td class=\"topic-cell\"><li>Propositional Logic<\/li><\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 02<\/td>\n        <td class=\"topic-cell\">\n          <li>Applications of Propositional Logic<\/li>\n          <li>Propositional Equivalences<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 03<\/td>\n        <td class=\"topic-cell\">\n          <li>Predicates and Quantifiers<\/li>\n          <li>Nested Quantifiers<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic II -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic II<\/span> Basic Structures: Sets, Functions, Sequences, Sums, and Matrices<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 04<\/td>\n        <td class=\"topic-cell\">\n          <li>Sets<\/li>\n          <li>Set Operations<\/li>\n          <li>Functions<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 05<\/td>\n        <td class=\"topic-cell\">\n          <li>Sequences and Summations<\/li>\n          <li>Matrices<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic III -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic III<\/span> Algorithms<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 06<\/td>\n        <td class=\"topic-cell\">\n          <li>The Growth of Functions<\/li>\n          <li>Complexity of Algorithms<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic IV -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic IV<\/span> Number Theory<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 07<\/td>\n        <td class=\"topic-cell\">\n          <li>Divisibility and Modular Arithmetic<\/li>\n          <li>Integer Representations and Algorithms<\/li>\n          <li>Primes and Greatest Common Divisors<\/li>\n        <\/td>\n      <\/tr>\n      <tr class=\"assignment-row\"><td><\/td><td>&#128203; Assignment<\/td><\/tr>\n\n      <!-- Topic V -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic V<\/span> Induction and Recursion<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 08<\/td>\n        <td class=\"topic-cell\">\n          <li>Mathematical Induction<\/li>\n          <li>Strong Induction and Well-Ordering<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 09<\/td>\n        <td class=\"topic-cell\">\n          <li>Recursive Definitions and Structural Induction<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic VI -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic VI<\/span> Counting<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 10<\/td>\n        <td class=\"topic-cell\">\n          <li>The Basics of Counting<\/li>\n          <li>The Pigeonhole Principle<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 11<\/td>\n        <td class=\"topic-cell\">\n          <li>Permutations and Combinations<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic VII -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic VII<\/span> Discrete Probability<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 12<\/td>\n        <td class=\"topic-cell\">\n          <li>An Introduction to Discrete Probability<\/li>\n          <li>Probability Theory<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 13<\/td>\n        <td class=\"topic-cell\">\n          <li>Bayes&#8217; Theorem<\/li>\n          <li>Expected Value and Variance<\/li>\n        <\/td>\n      <\/tr>\n\n      <!-- Topic VIII -->\n      <tr class=\"chapter-row\">\n        <td colspan=\"2\"><span class=\"chapter-num\">Topic VIII<\/span> Graphs<\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 14<\/td>\n        <td class=\"topic-cell\">\n          <li>Graphs and Graph Models<\/li>\n          <li>Graph Terminology and Special Types of Graphs<\/li>\n        <\/td>\n      <\/tr>\n      <tr>\n        <td class=\"week-cell\">Week 15<\/td>\n        <td class=\"topic-cell\">\n          <li>Representing Graphs and Graph Isomorphism<\/li>\n        <\/td>\n      <\/tr>\n      <tr class=\"assignment-row\"><td><\/td><td>&#128203; Assignment &nbsp;|&nbsp; &#128221; Tutorial<\/td><\/tr>\n\n      <!-- Final Exam -->\n      <tr class=\"final-row\">\n        <td colspan=\"2\">&#127891; &nbsp; Final Exam<\/td>\n      <\/tr>\n\n    <\/tbody>\n  <\/table>\n\n<\/div>\n<!-- End CST-1212 Mathematics Syllabus -->\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\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Mathematics Course Code: CST-1212 &nbsp;|&nbsp; 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