Units

---

Sample subject outline - Semester 2 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

An essential skill for a practising applied mathematician, is that of constructing and solving mathematical representations or models of problems that may be encountered, and developing an appreciation of the value of applied mathematics as a theoretical tool in non-mathematical disciplines.

Aims

Through the investigation of case studies and the development and practice of techniques and skills related to the formulation of mathematical models and their numerical solution, this unit provides you with the opportunity to employ these skills you have developed in your studies in mathematics, combining them in a coherent manner for solving topical and relevant problems. You will become familiar with methodologies for developing mathematically based theoretical tools for the solution of problems that may well be outside your core discipline area and in communicating the results of your theoretical study to a diverse audience.

Objectives

After successfully completing this unit you should be able to:

1. Formulate and develop an appropriate mathematical model for a problem under investigation.
2. Analyse and solve a given mathematical model and those of your own construction.
3. Collaborate with your peers in formulating and solving mathematical models.
4. Produce both technical and non-technical reports on the findings of your investigations.

Content

This unit is designed to allow you to develop and practice mathematical modelling skills by considering topical problems. In order for you to develop some expertise in developing modelling strategies for a variety of problems you will be required to consider some or all of the following topics:

1. An overview of the modelling procedure, including assumptions, scaling and dimensional analysis.
2. An overview of reaction kinetics.
3. A review of the role of diffusion in a number of physical processes.
4. Constructing reaction-diffusion models.
5. The Fisher equation and biological waves. Modelling the spread of organisms using non-linear, single species, reaction-diffusion equations in one-spatial dimension.
6. Turing mechanisms and the generation of spatial patterns in population distributions. Modelling multi species reaction-diffusion coupled systems with partial differential equations.
7. Complex systems modelling approaches.

The above list of topics is not exclusive, and will be supplemented as required and where possible to meet your needs and interests.

Approaches to Teaching and Learning

Lectures: 3hrs/wk
Essential background material as outlined above will be delivered to you by way of lecture presentations and group discussions along with supporting documentation where appropriate.

In order for you to develop and practice the skills and modelling methodologies identified in the lecture material, you will be expected to participate in open workshop or problem solving sessions which will include, where appropriate, the use of computing facilities and packages such as MATLAB. It is envisaged that these sessions will help you develop both your critical thinking, technical and communication skills.

Participation in a small group problem solving activity, while allowing you to put into practice mathematical modelling methodologies and solution techniques, will require you to collaborate with the other students in your group in order for you to develop an appropriate mathematical model for the problem under investigation.

Assessment

The assessment items in this unit are designed to determine your level of competency, measured against criteria, in meeting the unit outcomes while providing you with a range of tasks with increasing levels of skill development and difficulty.Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results via Blackboard.

Assessment name: Case Study
Description: You will be required to complete this assessment item to demonstrate proficiency at the technical and modelling skills covered in the lecture activities.
Relates to objectives: 1, 2 & 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Mid Semester

Assessment name: Problem Solving Task
Description: Working in a group of not more than three students, you will be required to:

(i) Conduct a brief review and develop concise definition of a problem outside of the mathematics discipline submitting a draft for feedback and guidance from your lecturer.

(ii) Construct, in collaboration with your group members, an appropriate mathematical model of the problem under investigation submitting a draft for feedback and guidance from your lecturer.

(iii) Analyse and solve your problem, producing a short technical report on your findings.

(iv) Produce and present as a seminar, a short non-technical report on your problem and the findings of your theoretical study.
Relates to objectives: 1, 2, 3, & 4.
Weight: 40%
Internal or external: Internal
Group or individual: Group with Individual Component
Due date: End of Semester

Assessment name: Examination (Theory)
Description: Summative. You will be required to sit an end-of-semester examination on procedural and technical aspects of mathematical modelling and the case studies covered in this unit.
Relates to objectives: 1,2 & 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: End of Semester

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

Texts:
There are no set texts for this unit.

References:
Many references are available in the library and online. You will be directed to these throughout the semester.

Risk assessment statement

There are no out of the ordinary risks associated with this unit since lectures and workshops are held in ordinary lecture theatres or computer laboratories. Basic safety procedures in computer laboratories will be given to you when entering the computer laboratory for the first time. In addition, emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the university's health and safety website for further information.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 10-May-2012