CS104

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Mathematical Foundations of Computing

Course (UG/PG)

Undergraduate

Offering Unit/Department

Course Description

This course serves as an introduction to the theory of discrete mathematics, which lays the foundation for computer science courses such as data structures, algorithms, relational database theory and cryptography. The topics covered in this course are mathematical logic, elementary number theory, recursion, set theory, functions, combinatorics and graphs. The course will consist of lectures and tutorials to help students understand the covered topics.

Course Learning Outcomes

1. Express a logic statement in terms of predicates, quantifiers and logical connectives.

2. Prove a statement using direct/indirect approaches.

3. Apply elementary number theory to proof problems on divisibility and prime numbers.

4. Use mathematical inductions to prove sequence expressions.

5. Identify the differences between weak and strong induction.

6. Solve elementary set problems with setalgebraion: Restricted

7. Distinguish functions which are injective and/or surjective.

8. Solve problems which involve composite functions.

9. Employ the principle of inclusion/exclusion rule and pigeonhole principle to solve combinatorial problems.

10. Solve discrete probability problems.

11. Use binomial theorem to solve sequence problems.

12. Understand the basic concepts of trees and graphs.

Discipline-Specific Competencies

Formal Proof Construction, Algorithm Analysis, Combinatorial Decision-making, Computational Modelling, Research

SMU Graduate Learning Outcomes

Disciplinary Knowledge, Critical thinking & problem solving, Self-directed learning

Grading Basis

GRD - Graded