BACHELOR OF SCIENCE IN SOFTWARE ENGINEERING

 PMAT 12102 DISCRETE MATHEMATICS FOR COMPUTING I Status : Core Pre-requisite : G.C.E. (A/L) Co-requisite : None

On completion of this course, the student should be able to:

• Explain logic, sets, relations and functions
• Apply Boolean algebra in simplifying combinatorial circuits.

Propositional Logic: Propositions, Truth values, Logical connectives, Truth table, Tautology and Contradiction, Logical equivalence, Algebra of propositions, Validity of an argument.

Predicate Logic: Quantifiers, Nested quantifiers, Negation of quantified statements, Validity of an argument with quantifiers.

Methods of Proof: Informal idea of a theorem and a proof, Converse, inverse and the contrapositive of a statement, Direct proof, Proof by contradiction, contrapositive, exhaustion and cases, Disproving by counter-examples, Principle of mathematical induction (weak and strong form).

Sets: Set notations, Sets of numbers, Subsets of the real numbers and interval notation, Operations on sets, Algebra of sets, Set identities, Power set, Cartesian product of sets.

Relations: Equivalence relations and equivalence classes, Properties of equivalence classes, Partitioning of sets.

Functions: Function notations, Image and pre-image, One-to-one and onto functions, Composition of functions, Inverse Function, Image and inverse image of subsets under functions.

Boolean algebra: Axioms of Boolean algebra and its properties, Correspondence between Boolean algebra and combinatorial logic circuits, Simplifications of combinatorial logic circuits using Boolean algebra.

Lectures, interactive classroom sessions, and case discussions.

End of course unit examination, group assignments, mid-term examination,class attendance.

1. Johnsonbaugh, R (2009). Discrete Mathematics. MacMillan
2. Lipschutz, S (2009). Discrete Mathematics. McGraw-Hill, New York.