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Below you can find some specific information about Applied Mathematics Honours.

For other information about doing Honours in Applied Mathematics, see theÌýHonours Page.

Honours Coordinator - Applied

If you have any questions about the Honours year, don't hesitate to contact the Honours Coordinator listed below. In particular, if you are just starting third year and vaguely thinking ahead to Honours, then it is important to choose a sufficiently wide variety of third year courses. Please see the Honours Coordinator to discuss your choice of courses.

Suggested Honours TopicsÌý

The following are suggestions for possible supervisors and Honours projects in Applied Mathematics. Other projects are possible, and you should contact any potential supervisors to discuss your options. You can find a full list of our Applied Mathematics staff via our Staff Directory. Please feel welcome to contact any staff member whose research is of interest.Ìý

You can get in touch with the potential supervisors below via their details on our Staff Directory.Ìý

2025 Honours Projects in Applied Mathematics

This info below contains descriptions of thesis projects offered for Honours year students in Applied Mathematics. Please note that the list is not exhaustive, and feel free to contact supervisors for other projects in their field.

Honours candidates are strongly encouraged to contact their preferred supervisor as early as possible to discuss potential projects and to make sure they have any requisite background knowledge. More information about the Honours year is available by emailing the Applied Mathematics Honours Coordinator, or via our Honours Year webpage.

Mathematical Modelling

Christopher Angstmann

• Modelling with fractional differential equations

Fractional derivatives are a type of nonlocal operator that generalise the concept of a derivative away from integer order. Whilst they are rather esoteric in their initial definition, they have had an increasing place in modelling a wide variety of physical phenomena. By exploring a connection between random walks and fractional derivatives it is possible to derive a wide range of models. This project will develop fractional order PDE models with applications to biomathematics.Ìý

• Semi-Markov compartment models

Compartment models are a widely used class of models that are useful when considering the flow of objects or people or energy between different labelled states, referred to as compartments. Recently we have constructed a general framework for fractional order compartment models, where the governing equations involve fractional order derivatives, via the consideration of a semi-Markov stochastic process. This project will explore the generalisation of the framework to incorporate a wider range of nonlocal operators.

Daniel Han

• Point set registration of the heart

Every person has a beating heart that is essential for human life. In Australia, cardiovascular diseases are the leading cause of death accounting for 24% of all deaths. In collaboration with Royal North Shore Hospital, the project aims to understand if the shape of specific heart chambers and valves can predict patient outcomes and the need for medical intervention. The project will begin with exploring methods (such as coherent point drift) of how one set of points that create a mesh for three dimensional reconstructions of the heart chambers can be matched to another set of points. Then, we will recreate and analyse the average shape of a healthy heart and a diseased heart.

Computational Mathematics

Gary Froyland

• Operator-theoretic and differential-geometric kernel methods for Machine Learning

This project will develop new mathematical and computational approaches to analyse high-dimensional data. Operator-theoretic methods will be explored, including the use of transfer operators, dynamic Laplace operators, and Laplace-Beltrami operators, which extract dominant dynamic and geometric modes from the data. In the theoretical direction, this project will tackle the mathematisation of aspects of machine learning. In a combined theoretical and numerical direction, this project will investigate the construction of these operators from high-dimensional data using dynamic and geometric kernel methods. A possible application is to analysing global scalar fields obtained from satellite imagery such as sea-surface temperature to extract climate oscillations such as the El Nino Southern Oscillation and the Madden-Julian Oscillation. This project will use ideas from dynamical systems, functional analysis, and Riemannian geometry.

Fluid Dynamics, Oceanography and Meteorology

Chris Tisdell

• Exploring the theory of Navier-Stokes equations and their applications to fluid flow

Navier-Stokes equations are of immense theoretical and physical interest. These partial differential equations have been used to better understand the weather, ocean currents, water flow in a pipe and air flow around a wing. However, the theory of the equations has not yet been fully formed. For example, it has not yet been proven whether solutions always exist in three dimensions and, if they do exist, whether they are smooth - i.e. they are infinitely differentiable all points in the domain. The Clay Mathematics Institute has identified this as one of the seven most important open problems in mathematics and has offered a US$1 million prize for a solution or a counter example.

In this project we will examine existence and smoothness of solutions to problems derived from the Navier-Stokes equations that arise in laminar fluid flow in porous tubes and channels. Channel flows - liquid flows confined within a closed conduit with no free surfaces - are everywhere. In plants and animals, they serve as the basic ingredient of vascular systems, distributing energy t