Recently-completed research projects
Recently-completed research projects that were undertaken in the Department of Mathematics and Statistics on the Bendigo campus of La Trobe University are described below. For further details, please contact the researchers directly (contact details are on the Staff page).
Descriptions of current projects are available on a separate page.
An Application of Queueing Theory to Aged Care – Prof Terry Mills
A few years ago, the Australian government introduced a "transition care" program for hospitals. Some elderly patients may have completed their treatment in a hospital, but for some reason or other, they cannot return home just yet. Perhaps their home needs modification as a result of their illness, or perhaps they are waiting for a bed in an aged care hostel or nursing home. Transition care provides appropriate treatment for patients in this situation. Hospitals were invited to apply for funding for a number of beds under this new scheme. The question facing hospital managers is "How many beds should we request?". Terry Mills collaborated with colleagues from Bendigo Health (A. Crombie, J. Ham, K. Masman) to develop an approach to answering this question based on queueing theory.
History of Mathematics – Dr Christopher Lenard, Prof Terry Mills and Ms Lex Milne
Cathrine Yaneff (BEd(Hons) candidate), Diane Itter (School of Education, LTU), Christopher Lenard and Terry Mills examined Fibonacci's approach to multiplication in "Liber Abaci" (1202) and assessed its potential for adaptation in the classroom in the 21st century. A paper on this project was presented at the annual conference of the Mathematical Association of Victoria in 2007 and appeared in the proceedings. The project was the basis of the thesis: Yaneff, C. (2007) Fibonacci and multiplication, BEd(Hons) thesis, La Trobe University.
Diane Itter, Christopher Lenard, and Terry Mills investigated Fibonacci's approach to fractions in "Liber Abaci". A paper on this project was presented at the annual conference of the Mathematical Association of Victoria in 2008 and appeared in the proceedings.
Charles Fahey (Faculty of Humanities and Social Sciences, LTU), Christopher Lenard, Terry Mills and Lex Milne have completed an appraisal of the mathematical manuscripts of Karl Marx.
Marketing Research for Bendigo Easter Festival 2004 – Prof Terry Mills and Ms Lex Milne
A team consisting of Wenbin Guo (Business, La Trobe, Bendigo), Terry Mills, Lex Milne and Rhett Walker (Business, La Trobe, Bendigo) conducted a marketing research project for the Bendigo Easter Festival 2004.
The Festival dates back to 1869 and is a major event in Bendigo's calendar. Further details can be found here.
The Bendigo Easter Festival Committee of Management asked the team to construct and administer a suitable quality assurance questionnaire. The aims of the project included:
- Determine the level of satisfaction of attendees at the Festival.
- Find out how people react to the major events associated with the Festival.
- Develop a broad demographic profile of people who attend the Festival.
- Examine the effectiveness of the various methods used to promote the Festival.
- Solicit suggestions from attendees for improving the Festival.
The project involved interviewing over 260 attendees of the Festival and was faciliated by a team of students who collected the data. A final report was submitted to the Committee of Management of the Festival in June 2004.
Modelling Regional Migration – Ms Angela Pezic (PhD student), Dr Graeme Byrne (Principal Supervisor), Prof Terry Mills (Associate Supervisor)
In many parts of regional Australia, internal migration is an important aspect of population change. Policy makers, especially in local government, should appreciate the complexity of migration patterns and the underlying factors. The purpose of this thesis is to develop mathematical models that describe internal migration in Victoria. Special attention is paid to the cities of Bendigo and Warrnambool.
Earlier quantitative models for internal migration in Australia tended to have a national perspective. These contributed to a broad view of internal migration, especially interstate migration. They are not particularly helpful at a regional level.
There is a need for more localised models of internal migration. The task of developing such models poses statistical problems. How do we define geographic regions that are appropriate for the model and the sources of data? How do we deal with very small migration flows (even zero flows) between regions? How should the model be specified in light of the previous questions?
This thesis is a contribution to the study of models of internal migration in the context of regional Victoria, and addresses these statistical problems.
The thesis was completed successfully in 2008.
Predicting Emergency Department Demand – Dr Robert Champion and Prof Terry Mills
A team of researchers demonstrated how statistical forecasting methods can be used to make short-term predictions for monthly attendances at the emergency department of one hospital in regional Victoria using data from 2000 to 2005. The ability to predict the demand for attendance at an emergency department of a hospital is valuable – at micro level for such things as planning rosters for staff, and at a macro level for financial and strategic planning for the hospital. Improved resource allocation and strategic planning are potential outcomes of the study. The research team consisted of Robert Champion, Leigh Kinsman, Geraldine Lee, Kevin Masman, Elizabeth May, Terry Mills, Michael Taylor, Paulett Thomas and Ruth Williams.
Further information about the project is given in this media release from the Australian Healthcare Association.
Random Walks – Prof Terry Mills and Dr Simon Smith
Len Champion, Terry Mills and Simon Smith developed an elementary approach to a classical result of Georg Pólya in the theory of random walks.
Socio-economic Evaluation of Community Banking – Dr Graeme Byrne
Graeme was part of a research team (with Mr Ian Pinge and Dr Jill Francis from LTU, Bendigo, and Mr Jason McGovern from Bendigo Bank) that was awarded a La Trobe University Industry Collaborative Grant for the project "A socio-economic evaluation of community banking". The grant was matched dollar for dollar by an industry partner (in this case, Bendigo Bank).
The purpose of the project was to conduct a socio-economic evaluation of the effects of the initial phase of the development of Community Banking on those communities that had established their own Community Bank branch of Bendigo Bank. The project was significant because, while there is no shortage of communities wishing to establish their own Community Bank branches, there had been no research undertaken into the longer-term impact of such action on the socio-economic foundation of these communities. This research provided useful information for policy makers and stakeholders.
Variational Splines – Dr Robert Champion, Dr Christopher Lenard and Prof Terry Mills
Spline functions were introduced to the mathematical literature in the 1940s by I. J. Schoenberg (1903-1990).
The basic idea of a spline function is to use simple functions to construct a smooth piecewise function. For example, cubic splines are smooth, piecewise cubic polynomial functions.
Splines have proved to be very useful tools in applied mathematics, as well as having deep theoretical interest. The study of splines is now a rich mixture of mathematical problems with applications in engineering, the physical sciences, and social sciences.
Our research has been focussed on variational splines. Although splines were introduced as piecewise functions, they often exhibit certain optimal properties. In such cases, they are solutions of variational (or optimisation) problems. Roughly speaking, these splines minimize some sort of "energy" functional. We call such splines "variational splines".
This variational point of view leads to a totally different approach to splines – and a corresponding beautiful theory. Our two survey papers below give an introduction to variational splines.
Champion, R., Lenard, C. T. and Mills, T. M., A variational approach to splines, The ANZIAM Journal, 42(1) (2000), 119-135
Champion, R., Lenard, C. T. and Mills, T. M., An introduction to abstract splines, The Mathematical Scientist, 21(1) (1996), 8-26
VCE Mathematics: Teachers' Responses to Changes in School-based Assessment – Ms Lex Milne
Lex was part of a research team (with Steve Tobias and Dr Chris Brew, both from the Institute for Education at La Trobe University) that was awarded a La Trobe University Intercampus Research Incentive Scheme (IRIS) Grant for 2000.
The team investigated the views of secondary school mathematics teachers on the implementation of the recent assessment changes to the Victorian Certificate of Education (VCE). Over 300 VCE mathematics teachers from across the school sectors (State, Catholic, Independent and TAFE) were surveyed during July–September 2000. The focus of the project was on:
- student and teacher workloads,
- issues of authentication,
- quality of learning outcomes,
- choice of assessment tasks and procedures, and
- the impact on teaching and assessment in Years 7 to 11.
Results from the project appeared in three papers in 2001 – for references, see the list of publications of the Department of Mathematics and Statistics at Bendigo. A complete version of one of the papers, From CATs to coursework: Teacher feedback on the VCE Mathematics 2000, is available here.