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Mathematics

Course Code: CST-1212  |  Second Semester
Duration 15 Weeks
Lectures 3 per week  ×  1 hour
Textbook
📚
Required Textbook
Discrete Mathematics and Its Applications, 8th Edition
Kenneth H. Rosen — McGraw-Hill
Course Description
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 β€” building the theoretical backbone required for advanced study in computer science and software engineering.

Learning Objectives

  1. Introduce the foundations of propositional and predicate logic, and develop skills in constructing and evaluating mathematical proofs.
  2. Build understanding of fundamental discrete structures including sets, functions, sequences, and matrices.
  3. Develop familiarity with algorithm design and analyse the growth and complexity of algorithms.
  4. Introduce number theory concepts including divisibility, modular arithmetic, and prime numbers.
  5. Develop competency in mathematical induction and recursive definitions.
  6. Build counting and combinatorial reasoning skills, including permutations, combinations, and the Pigeonhole Principle.
  7. Introduce discrete probability, Bayes’ theorem, and expected value.
  8. Introduce graph theory, graph models, and graph representations for use in computing applications.

Learning Outcomes

  • Construct and evaluate logical propositions and proofs using propositional and predicate logic.
  • Work with sets, functions, sequences, and matrices in mathematical and computational contexts.
  • Analyse algorithm efficiency using Big-O notation and complexity measures.
  • Apply number theory principles including modular arithmetic and prime factorisation.
  • Use mathematical induction and recursive definitions to prove statements and define structures.
  • Solve counting problems using permutations, combinations, and the Pigeonhole Principle.
  • Apply discrete probability theory including Bayes’ theorem and expected value calculations.
  • Model and analyse problems using graph representations and graph terminology.
Major Topics Covered
Logic & Proofs
Sets & Functions
Algorithms
Number Theory
Induction & Recursion
Counting
Discrete Probability
Graph Theory
Assessment Components
Assignments
Tutorial
Final Exam
Lecture Structure: 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.
Course Outline
Week Topic
Topic I The Foundations: Logic and Proofs
Week 01
  • Propositional Logic
    		•
    Week 02
  • Applications of Propositional Logic
  • Propositional Equivalences
    		•
    Week 03
  • Predicates and Quantifiers
  • Nested Quantifiers
    		•
    Topic II Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
    Week 04
  • Sets
  • Set Operations
  • Functions
    		•
    Week 05
  • Sequences and Summations
  • Matrices
    		•
    Topic III Algorithms
    Week 06
  • The Growth of Functions
  • Complexity of Algorithms
    		•
    Topic IV Number Theory
    Week 07
  • Divisibility and Modular Arithmetic
  • Integer Representations and Algorithms
  • Primes and Greatest Common Divisors
    		•
    📋 Assignment
    Topic V Induction and Recursion
    Week 08
  • Mathematical Induction
  • Strong Induction and Well-Ordering
    		•
    Week 09
  • Recursive Definitions and Structural Induction
    		•
    Topic VI Counting
    Week 10
  • The Basics of Counting
  • The Pigeonhole Principle
    		•
    Week 11
  • Permutations and Combinations
    		•
    Topic VII Discrete Probability
    Week 12
  • An Introduction to Discrete Probability
  • Probability Theory
    		•
    Week 13
  • Bayes’ Theorem
  • Expected Value and Variance
    		•
    Topic VIII Graphs
    Week 14
  • Graphs and Graph Models
  • Graph Terminology and Special Types of Graphs
    		•
    Week 15
  • Representing Graphs and Graph Isomorphism
    		•
    📋 Assignment  |  📝 Tutorial
    🎓   Final Exam