Title:  Mathematics for Computing 3 
Long Title:  Mathematics for Computing 3 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2009/10 ( September 2009 ) 
Module Delivered in 
no programmes

Module Coordinator: 
AINE NI SHE 
Module Author: 
MICHAEL BRENNAN 
Module Description: 
This module covers an introduction to queueing theory and elementary number theory. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Recognise the basic types of queueing model. 
LO2 
Derive steady state system performance characteristics for finite queues. 
LO3 
Derive steady state balance equations. 
LO4 
Apply various proof techniques, including direct, indirect, contradiction to problems on divisibility, primes, and modular arithmetic. 
LO5 
State and apply basic theorems relating to elementary number theory including Bezout’s Theorem, the Euclidean Algorithm, and the Chinese Remainder Theorem. 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 
No recommendations listed 
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section. 
No requirements listed 
Corequisites

No Co Requisites listed 
Module Content & Assessment
Indicative Content 
Queueing theory
Review of convergent series formulae. Axiomatic development of the Poisson arrival process. Steady state analysis of single server and multiserver queues. The steady state balance method. Finite queues, state dependant arrival, and service rates. Derivation of various measures of performance. Little’s Formula.

Number Theory
Division algorithm, divisibility, prime numbers, fundamental theorem of arithmetic, greatest common divisors, Euclid’s Lemma, Euclidean Algorithm, Bezout’s Theorem, Diophantine equations. Congruences and modular arithmetic, Fermat’s Little Theorem, Euler phifunction, primality tests, the Chinese Remainder theorem.

Assessment Breakdown  % 
Course Work  100.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Other 
One hour written exam 
1,2,3 
40.0 
Week 6 
Other 
One and a half hour written exam 
4,5 
60.0 
Sem End 
No End of Module Formal Examination 
Reassessment Requirement 
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
No Description 
3.0 
Every Week 
3.00 
Tutorial 
No Description 
1.0 
Every Week 
1.00 
Independent & Directed Learning (Noncontact) 
No Description 
3.0 
Every Week 
3.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
This module has no Part Time workload. 
Module Resources
Recommended Book Resources 

 Bunday B. D. 1986, Basic Queueing Theory, Ed. Arnold [ISBN: 0713135700]
 Burton, D.M. 1989, Elementary Number Theory, WCB [ISBN: 013801812X]
 Supplementary Book Resources 

 Rosen, K. 1999, Discrete Mathematics and its Applications, 4th Edition Ed., McGrawHill [ISBN: 0072899050]
 Kreyzig, E. 1999, Advanced Engineering Mathematics, 8th Edition Ed., Wiley [ISBN: 0471154962]
 This module does not have any article/paper resources 

Other Resources 

 Website: Maplesoft Applications Website
 Website: Rosen textbook website
 Website: Wolfram's Mathworld website
 