2008/09 Undergraduate Module Catalogue

MATH1610 Discrete Systems

10 creditsClass Size: 250

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

Pre-requisites

MATH1400

Modelling with Differential Equations

This module is mutually exclusive with

MATH1410

Modelling Force and Motion

This module is approved as an Elective

Module summary

Economics, finance, biology and other subjects appear distinct and each has its own language. However, each treats a process changing in time with the same general mathematical description. This module introduces a general approach to such discrete systems and illustrates its utility with examples from economics, population growth, medicine etc.

Objectives

To develop vector methods and iterative methods for modelling non-mechanical systems. On completion of this module, students should be able to: (a) use vector algebra to solve three dimensional geometric problems such as finding where a given line cuts a given plane; (b) find if one given line intersects another and if so, find the point of meeting; (c) determine fixed points of difference equations and decide if they are attracting or repelling; (d) determine periodic orbits and their stability.

Syllabus

Vector algebra: parallelogram law, components, unit vectors and direction cosines, scalar and vector products, triple products. Application to 3D geometry of lines and planes. Iteration and its limits : iteration in general, static and dynamic outcomes of repeated iteration. Linear one dimensional model, Fixed points, stability. Linear high-dimension system. Fixed points, uniqueness and stability. Invariant sets. Node, saddle, focus, centre. Non-linear systems, equilibrium points and stability. The one-dimensional logistic system, period doubling and chaos.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	22	1.00	22.00
Tutorial	11	1.00	11.00
Private study hours			67.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			100.00

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 08/07/2008

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