MA28010 - MATHEMATICS FOR SOFTWARE ENGINEERING

Module Identifier	MA28010
Module Title	MATHEMATICS FOR SOFTWARE ENGINEERING
Academic Year	2001/2002
Co-ordinator	Dr T McDonough
Semester	Semester 1
Other staff	Dr J Lane, Mr David Jones, Dr Edel Sherratt
Mutually Exclusive	Only available as part of a degree course in the Computer Science Department
Course delivery	Lecture	22 x 1 hour lectures
	Workshop	10 x 1 hour workshops
Assessment	Exam	2 Hours	100%
	Resit assessment	2 Hours	100%

General description

Like other branches of science and engineering, Software engineering and Computer Science rely on mathematics for techniques to model the real world both in its physical, and in its more abstract, aspects. The mathematics taught in this module provides the basis for understanding how numbers are stored and manipulated, explains basic coordinate geometry, statistical techniques and the solution of recurrence relations. Practical applications of the material covered will be found in modules on graphics, robotics, programming languages and quantitative aspects of software engineering.

Aims

The aim of this module is to give students the mathematical skills needed to handle the quantitative aspects of software engineering.

Learning outcomes

On completion of this module, a student should be able to:

explain the nature of floating point number representations and the problems that can arise in floating point computation;
perform computations with numbers given in floating point form;
explain the concepts of 2- and 3-dimensional coordinate geometry necessary to implement elementary algorithms used in computer graphics and robotics;
perform computations in 2- and 3-dimensional coordinate geometry;
describe the concept of variability and its manifestation in statistical diagrams;
describe the concepts involved in the statistical modelling of randomness;
solve recurrence relations of first and second order and deduce information about the time complexity of an algorithm.

Syllabus

The presentation of the mathematical ideas will be directed to their use in computing.
1. Numbers; rational and irrational. Computer representation of numbers and floating point operations.
2. Coordinate geometry; lines, planes, conics; translation, rotation, shearing, scaling.
3. Summarising data. Histograms. Five number summaries. Box and whisker plots. Shapes of distributions. Graphical test for symmetry (normality). Binomial experiments and large sample behaviour. The Poisson distribution as a model for randomness. Quick and graphical tests for the Poisson distribution. Waiting times and the exponential distribution.
4. Solution of first and second order linear recurrence relations; some examples of non-linear equations. Application to the assessment of time complexity of algorithms.

Reading Lists

Books
** Recommended Text
K H Rosen. (1999) Discrete Mathematics and its Applications. McGraw-Hill
A Croft & R Davison. (1997) Foundation Maths. 2/e. Addison-Wesley 0201178044
** Supplementary Text
G James. (2001) Modern Engineering Mathematics. 3/e. Prentice Hall/Pearson Education 0130183199