# Module Overview

### Discrete Mathematics I

This module introduces the learner to areas in discrete mathematics such as Number Systems, Boolean Algebra and Set Theory.

MATH 1803

##### ECTS Credits

5

*Curricular information is subject to change

Number Systems

Binary, octal, denary and hexadecimal number systems. Conversion from denary to any number system and from any number system to denary. Horner’s method of conversion. Conversion from octal to hexadecimal via binary and vice versa. Binary arithmetic. One’s (1’s) complement method for subtracting binary numbers.

Boolean Algebra

Basic laws of Boolean Algebra- AND, OR, NOT operators. Truth tables. Proof by perfect induction. Algebraic simplification of Boolean expressions. De Morgan’s theorem for complements. Use of Karnaugh maps for simplification of Boolean expressions.  Applications to switching circuits.

Set Theory

Algebra of sets, power sets, cardinality. Representation using Venn diagrams. Cartesian product of sets. Relations. Properties of relations – transitive, reflexive and symmetric. Definition of functions as subsets of relations. Composition of functions. Properties of functions – injective, surjective and bijective.

2 hours  lectures and 1 hour tutorial session per week supplemented by notes and problem sheets.

Module Content & Assessment
Assessment Breakdown %
Formal Examination70
Other Assessment(s)30