Course code  :  PMAT 11223

Title               :  Discrete Mathematics I

Pre-requisites :  A/L Combined Mathematics

Learning Outcomes:

On successful completion of the course, the student should be able to;

1. apply rules of propositional, predicate logic and methods of proof
2. demonstrate working knowledge of sets
3. demonstrate an understanding of relations and functions and be able to determine their properties
4. define equivalence relations and equivalence classes
5. define composite function
6. explain the conditions for the existence of the inverse function
7. use the Boolean algebra to simplify complex logic expressions.

Course Contents:

Mathematical Logic: Propositional logic, Propositional equivalences, Predicates and quantifiers, Nested
quantifiers, Rules of inference, Arguments, Normal forms, Methods of proof, Mathematical induction, Strong
induction, Well ordering principle.

Sets: Set notations; Sets of numbers and intervals; Subsets and equal sets; Power set; Cartesian product of sets; Set
operations; Algebra of sets.

Boolean Algebra: Boolean expressions and Boolean functions, Identities of Boolean Algebra, Duality, Logic gates,
Combinations of gates, Examples of circuits, Minimization of circuits

Relations: Relations and their properties, Functions as relations, Relations on a set, Properties of Relations,
Combining relations, n-ary relations, Equivalence relations, Equivalence classes and partitions,
Partial Orderings.

Functions: Function notation; One-to-one and onto functions; Composition of functions, Inverse function.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

Recommended Reading:

1. Johnsonbaugh, R. (8th Ed., 2017). Discrete Mathematics, Pearson.
2. Rosen, K.H. (8th Ed., 2018). Discrete Mathematics and Its Applications, McGraw-Hill.