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Course code : PMAT 11212
Title : Mathematics for Computing I
Learning outcomes:
On completion of this course, the student should be able to:
1. apply rules of propositional, predicate logic and methods of proof
2. demonstrate working knowledge of sets, relations, and functions
3. identify the properties of a function
4. find the inverse of function
5. apply Boolean algebra in simplifying combinatorial circuits
Course Content:
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.
Method of Teaching and Learning : Lectures, interactive classroom sessions, and case discussions
Assessment : End of course unit examination, group assignment, mid-term examination, class attendance
Recommended Reading:
1. Johnsonbaugh, R. (8th Ed., 2017). Discrete Mathematics, Pearson.
2. Rosen, K.H. & Krithivasan, K. (7th Ed., 2011). Discrete Mathematics and Its Applications, McGraw-hill.
3. Kreyzig, E. (8th Ed., 2006). Advanced Engineering Mathematics, Wiley Student Edition
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