Honours Projects
A list of possible honours
project being offered by staff at the School of Mathematics and Statistics
is given below. Additional projects can also be arranged with other
staff members from the school.
For more information on Honours degrees and projects at the School, contact the Honours Co-ordinator Professor Vladimir Gaitsgory.
Solution methods for elliptic boundary value problems in non-simple domains
Supervisor: Professor Stanley J. Miklavcic
Start Time and Location: January-February 2008; Mawson Lakes Campus, UniSA
Elliptic partial differential equations such as Poisson’s equation, Helmholtz’s equation and the Stokes system of equations are used to describe a wide variety of static and dynamic systems in many areas in science and engineering. These governing equations, while well-known, are not so easily solved in boundary value problems involving non-ideal geometries. The aim of the proposed project is to investigate a novel abstract solution method to circumvent the inherent difficulties of such boundary value problems. Both analytical and numerical work will be involved in this project.
Mapping and Clustering: Climate Impact Modelling on Natural Systems and Disease
Supervisor: Assoc Professor Irene Hudson
Start Time and Location: March 2008; City West Campus (or Mawson Lakes Campus), UniSA
Description: The project aims to link Kohonen maps and clustering methods with a view to map spatial or temporal similarities onto differing scales. The Honours student will be supervised by A. Prof Hudson and liaise also with other PhD students and Postdocs (Susan Kim, Julie Sleep, Manju Agrawal) with similar projects through the Advice Research Consulting Collaborative Statistics (ARCCS) centre. The mathematics will be tested on flowering and climate change data from Australia and disease and climate data from NZ.
Physical and Mathematical Modelling of Sound Source Generation for Synthesis and Multichannel Sound Reproduction
Supervisor: Professor Stanley J. Miklavcic
Start Time and Location: January-February 2008; Mawson Lakes Campus, UniSA
Description: The project centres on physical and mathematical modelling of musical sound source generation, with the aim of deriving accurate mathematical expressions and/or fast numerical algorithms for implementation in real-time, interactive software. The goal is to produce a synthesis and sound reproduction program that includes a user-friendly, graphics interface for potential commercial application.
Combinatorial Optimisation
Supervisor: Kevin White
Start Time and Location: Any starting date, Mawson Lakes Campus or City West Campus, UniSA
Description: Optimisation problems in which the feasible solutions are naturally integer valued or come from some other discrete set are referred to as combinatorial. Some of them, like the minimal spanning tree, are very easy to solve and some, like the celebrated travelling salesperson, are quite difficult. The problems give rise to many interesting solution techniques involving combinatorics, linear programming and primal-dual methods, and lean on properties like complexity of algorithms and unimodularity of matrices. According to the student’s interest, this project could focus on a particular problem or class of problems, or on a particular solution technique. There are many reference works in the area, including Cook et al.[1]
[1] Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A. Combinatorial Optimization Wiley-Interscience 1998.
Indigenous Mathematics
Supervisor: Kevin White
Start Time and Location: Any starting date, Mawson Lakes Campus or City West Campus, UniSA
Description: “The rich and interesting field of Australian Aboriginal and Torres Strait Islander mathematical concepts has been generally ignored by anthropologists, linguists and other researchers.”[2] There is a widespread belief that most Australian Aboriginal languages do not contain words for numbers larger than about four. However, there is much evidence of more extensive and practical counting systems, uses of pattern and order[3], and “ways of dealing with space, time, position [and] shape”[2]. How much does the average Australian mathematics graduate know about the indigenous mathematics of their country and how much should they know? This project involves an investigation of the literature on indigenous Australian mathematical concepts, and the preparation of teaching materials to be included as about 1 unit of an undergraduate course. There could be some interaction with the University’s Unaipon School or with other researchers in anthropology.
[2] Harris, J.
Australian Aboriginal and Islander Mathematics (.pdf), Australian
Aboriginal Studies 1987 no 2 pp. 29-37
[3] Cooke, M.
Seeing Yolngu, seeing mathematics