DISCRETE MATHEMATICS

Brief Course Description

This course introduces the foundations of discrete mathematics as they apply to computer science. It focuses on providing a solid theoretical foundation for further work. Topics covered include functions, relations, sets, simple proof techniques, Boolean algebra, propositional logic, digital logic, elementary number theory, and the fundamentals of counting.

Course Objectives

The course aims to provide students with:

i) Knowledge about operations associated with sets, functions, and relations with examples

ii) Understanding of the basic counting principles, including uses of diagonalization and the pigeonhole principle

iii) Understanding of which proof is best for a given problem and the basic structure of each proof technique giving examples

iv) The ability to compute permutations and combinations of a set, and interpret the meaning in context of particular applications

v) The knowledge require to Analyze a problem to create relevant recurrence equations or to identify important counting questions

vi) An appreciation of the effect of AND, OR, NOT and EOR operations on binary data.

Learning Outcomes

Upon successful completion of the course, students shall be able to:

i) Explain the basic concepts of discrete structures and appreciate their importance as they apply to computing

ii) Manipulate formulae involving sets, integers, reals and functions of such quantities

iii) Solve simple problems involving sets, functions, graphs and trees

iv) Construct sound logical arguments, including use of induction

v) Appreciate the way that discrete mathematics can assist problem solving