Discrete mathematics is concerned with quantities which vary discretely, and because of that has an important role in Computer Science, in which discrete structures such as sets, graphs, lists, and trees play a fundamental role, and the underlying forms of reasoning are based on propositional and predicate logic rather than on calculus and mathematical analysis, with an emphasis on counting rather than measuring, e.g. enumerating permutations and combinations of objects satisfying specified conditions. This module will provide a thorough grounding in the fundamental structures and methods of discrete mathematics that are required for computer science.

The aim of this module is to provide you with the basic concepts and tools developed in discrete mathematics disciplines but needed for the study of computer science. As such, it forms an essential part of a rounded education of a computer scientist or computer expert whose work includes computer-based data manipulations.

On successful completion of this module, you should be able to:
 

Module Specific Skills and Knowledge:
1 demonstrate a sound understanding of selected essential topics in discrete mathematics and their importance in computer science disciplines.
Discipline Specific Skills and Knowledge:
2 reveal sufficient knowledge of fundamental discrete mathematics concepts.
Personal and Key Transferable / Employment Skills and Knowledge:
3 show independent learning skills;
4 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;
5 use learning resources appropriately.

number systems: natural numbers, integers, rationals, reals, complex numbers;

number representation: positional notation (decimal, binary, hexadecimal), twos complement, fixed-point, floating point;

computer arithmetic: addition and subtraction, multiplication and division

set theory and standard notation: Intersection, union, complement, power set, Cartesian product;

functions and relations;

methods of proof;

propositional and first-order logic;

sums of standard finite and infinite series;

counting principles: the addition principle, the multiplication principle, permutations, combinations; some counting problems;

graph theory: basic concepts, definitions and results. Trees, balanced trees.

Reading list for this module: