# Module Information

#### Course Delivery

Delivery Type | Delivery length / details |
---|---|

Lecture | 20 Hours. |

Practical | 6 x 1 hour workshops |

#### Assessment

Assessment Type | Assessment length / details | Proportion |
---|---|---|

Semester Exam | 2 Hours CONVENTIONAL WRITTEN EXAM | 100% |

Supplementary Exam | 2 Hours SUPPLEMENTARY WRITTEN EXAM | 100% |

### 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.

### Content

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: (4 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: (4 lectures)

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

4.Induction: (4 lectures)

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

5.Calculus: (4 lectures)

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

### Module Skills

Skills Type | Skills details |
---|---|

Application of Number | a principal focus of the module, along with application of symbols |

Improving own Learning and Performance | by mastering Mathematical skills which facilitate learning in many other areas of Computer Science and Software Engineering |

Problem solving | by completing set worksheets |

Subject Specific Skills | Numeracy, symbol manipulation, abstraction |

### Reading List

**Recommended Text**

Croft, Tony (1997.) Foundation maths /Anthony Croft, Robert Davison. 2nd ed. Addison Wesley Primo search James, Glyn. (2001.) Modern engineering mathematics /Glyn James ... [et al.]. 3rd ed. Prentice Hall Primo search Rosen, Kenneth H. (1999.) Discrete mathematics and its applications /Kenneth H. Rosen. 4th ed. WCB/McGraw-Hill Primo search

### Notes

This module is at CQFW Level 5