I have the following projects and topics available for 2009.
Specific Projects
Using an automated inequality prover for optimisation
Lu Yang (Guangzhou University) has developed an automated prover for a class of algebraic inequalities. Being able to prove inequalities means that you are able to use a simple binary search to find optimal values of an expression subject to constraints, an interesting combination of pure algebra and applied optimisation. This project would suit someone with a good background in algebra and an interest in symbolic computing and optimisation.
Rewriting historical papers
There are a number of classic papers, such as Fisher's "The use of multiple measurements in taxonomic problems" from 1936 and Stigler's "The cost of subsistance" analysis from 1945, which could be updated for more modern times, using methods which were not available to the authors. This project would suit someone with an interest in a broad range of mathematics and in history.
Fractal patterns in music
This project would involve exploring fractal methods for describing and generating time series. These could then be applied to a range of areas (music is my particular interest). This would suit someone with a background in statistics and numerical computation.
General Topics
I have a range of other topics in areas such as
- automated theorem proving
- applications of symbolic compution in algebra
- computational methods in statistics and data mining
- stochastic optimisation techniques
- mathematics and statistics education
Come and have a chat if you are interested in any of these.
Past Projects
These are the project titles from some recent honours students.
Susan Worsley, Threshold Concepts and Troublesome Knowledge, 2008.
Kelly Fleetwood, Advances in Differential Evoluation, 2004.
James McGree, The Traveling Salesman Problem, 2004.
Karyn Hamaty, Reliability: analytic models and simulation methods, 2001.
Mika Nakagoshi, Optimization models for electricity investment, 2001.
Joanne Peulen, A study of value-at-risk estimation methods, 2000 (with Mark Thompson).
Keshena Richardson, Comparisons of data mining techniques used to find factors associated with heart disease, 2000 (with Geoff McLachlan).
Stephen Long, The use of decision trees for discretisation in machine learning, 1999.
Jamie Alcock, Recent advances in error reduction for classification methods, 1999 (with Geoff McLachlan).
Irmgard Kaefer, Evolutionary methods for constrained optimization, 1998.