Module Identifier CS20410  
Academic Year 2006/2007  
Co-ordinator Dr Edel M Sherratt  
Semester Semester 1  
Other staff Dr Frederick W Long, Dr Edel M Sherratt  
Pre-Requisite CS10410 or equivalent.  
Course delivery Lecture   22 Hours.  
  Seminars / Tutorials   11 workshops  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours CONVENTIONAL WRITTEN EXAM  100%
Supplementary Assessment2 Hours SUPPLEMENTARY WRITTEN EXAM  100%
Further details  

Learning outcomes

On successful completion of this module students should be able to:
1. Number Representation
a) Carry out calculations in 2's complement and excess-n representations
b) Calculate precision and accuracy of floating point representations
c) Give examples of unexpected results of comparison that occur with floating point representations, and suggest programming alternatives.

2. Geometry
a) relate concepts from 2 and 3-dimensional coordinate geometry to vector algebra
b) perform computations using vectors and matrices to implement elementary algorithms used in computer graphics and robotics

3. Counting Techniques
Use sum and product rules, inclusion exclusion and the pigeonhole principle to answer questions about data and communications resources.

4. Probability and Statistics
a) describe the concept of variability and its manifestation in statistical diagrams;
b) describe the concepts involved in the statistical modelling of randomness.

5. Induction
Carry out proof by induction and complete induction over N.

6. Calculus
a) calculate the gradient of a curve and locate maxima, minima and turning points of a function;
b) calculate indefinite and definite integrals and find the area under a curve;


Brief description

The module will provide a range of skills needed for successful study in graphics, communications, algorithm analysis, artificial intelligence, robotics and formal methods.


This module aims to provide students with the skills needed for successful completion of Part II courses on: Graphics (geometry), Communications (information theory and coding, network planning, network management), Robotics (kinematics), Formal Methods, Artificial Intelligence (learning) and Quantitative Methods (metrics).

1.Number representation: (4 lectures)

calculations in 2's complement and excess-n representations ; precision and accuracy of floating point representations; examples of zero-divisions and unexpected results of comparison that occur because a floating point representation comprises a finite set of representatives of real intervals; programming alternatives; cancellation and guard digits.

2.Geometry: (6 lectures)

2 and 3-dimensional coordinate geometry; basic trigonometrical functions and identities, relating angles in different quadrants; vector and matrix algebra; elementary algorithms in computer graphics and robotics.

3.Counting Techniques: (2 lectures)

sum and product rules, inclusion exclusion and the pigeonhole principle; application of counting techniques to problems in data structures and communications.

4.Probability and Statistics: (4 lectures)

Summarising data. Shapes of distributions. 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. Basic ideas of significance and goodness of fit.

5.Induction: (3 lectures)

What is induction? Proof by induction over N; the Principle of Complete Induction.

6.Calculus: (3 lectures)

gradient of a curve; maxima, minima and turning points of a function; indefinite and definite integrals; area under a curve.

Module Skills

Problem_solving 1. Problem Solving: by completing set worksheets  
Improving own Learning and Performance by mastering Mathematical skills which facilitate learning in many other areas of Computer Science and Software Engineering  
Application of Number a principal focus of the module ¿ along with application of symbols  
Subject Specific Skills Numeracy, symbol manipulation, abstraction  

Reading Lists

** Supplementary Text
Anthony Croft, Robert Davison. (1997) Foundation maths Addison Wesley, 0201178044
James, Glyn. (2001) Modern engineering mathematics Prentice Hall, 0130183199
Rosen, Kenneth H. (1999) Discrete Mathematics and Its Applications McGraw-Hill Publishing Company 0071167560


This module is at CQFW Level 5