If you are an Advanced Mathematics or Advanced Science student then Honours is build into your program. For all other students, if you are keen on Mathematics and have achieved good results in years 1 to 3, you should consider embarking on an honours year.

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

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

### Honours Coordinator - Applied

Dr Chris Angstmann

Email: c.angstmann@unsw.edu.au

Phone: 9385 1354

Office: Room 4076, Red Centre (Centre Wing), UNSW

If you have any questions about the Honours year, don't hesitate to contact the Honours Coordinator. 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 Topics

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.

#### Biomathematics

- Models of cell division in bacteria and archaea.

- The Insulin Signalling Pathway in Adipocytes - A Mathematical Investigation
- Do glucose transporters queue to get to the cell surface?
- Dynamics and stability of cardiac pacemaker cells
- The interaction of actin and tropomyosin
- Modelling Myelinated Nerve Function

- Pattern Formation with Anomalous Diffusion: How did the leopard get its spots?
- Mathematical Modelling of Plaque Build Up in Alzheimer's Disease

- Mathematical modeling of the persistence of HIV infection
- Within-host dynamics of emerging drug resistant hepatitis B virus
- Estimating the impact of HIV gene therapy

Infection Analytics Program at the Kirby Institute

- Modelling parasite maturation and synchrony
- Modelling drug efficiency when treatment is given at different stages before rupture
- Fitting data of patients with antimalarials to understand population level trends

#### Computational Mathematics

- High-dimensional numerical integration with applications to Bayesian statistics
- Monte Carlo splitting method for integrals with quasi-monotone integrands

Frances Kuo

- The unreasonable effectiveness of quasi-Monte Carlo
- QMC for quantum field problems
- QMC for air pollution modelling

- Approximate cloaking simulation
- Analysis of changing data and applications

- Hierarchical Matrices.
- Approximating the fractional powers of an elliptical differential operator
- Localization of eigenfunctions

- The role of the Landau-Lifschitz equation in micromagnetism
- Stochastic partial differential equations
- Problems in random domains
- Boundary element methods

#### Mathematics Education

- Digital resources in Mathematics: What makes them effective for learning?
- Mathematical learning communities
- Peer to peer support for Mathematics students
- Learning Mathematics on the move via mobile devices

#### Nonlinear Phenomena

- Random walks and fractional calculus

- Topics in dynamical systems and ergodic theory
- Transfer operator analysis with applications to fluid mixing
- Extreme value statistics for chaotic systems
- Lagrangian coherent structures in haemodynamics (blood flow)

- Fractional calculus for fractals
- Random walks on discrete lattices
- Statistical mechanics of small particle systems

- Algebraic dynamics
- Discrete integrable systems

- Topics in Soliton Theory

- Advanced Studies in differential equations
- A Deeper Understanding of Discrete and Continuous Systems Through Analysis on Time Scales
- Advanced Studies in Nonlinear Difference Equations

#### Optimisation

- Topics in Integer Programming and Combinatorial Optimisation
- Stochastic Integer Programming
- Nonlinear and mixed integer optimization with application to radiotherapy
- Optimising fluid mixing

- Multo-objective optimization under data uncertainty
- Robust optimisation and data mining
- Semi-algebraic geometry and polynomial optimisation
- Semi-algebraic optimization and diffusion tensor imaging

- Rank optimisation problem
- Optimisation approaches for tensor eigenvalue problems: modern techniques for multi-relational data analysis
- Nonconvex polynomial optimisation

- Multipoint Voronoi cells

#### Fluid Dynamics, Oceanography and Meteorology

- Lagrangian Coherent Structures in Ocean and Atmosphere Models

- New constraints on large-scale tropospheric transport from global trace-gas measurements
- Ocean biogeochemistry
- Construction of matrix models for geophysical flows
- Turbulence modelling

- Simulating fractal curves in turbulent fluid flows
- Investigating transport pathways in the ocean with Lagrangian Coherent Structures
- Submesoscale ocean dynamics

- Ocean mixing and the absolute velocity in the ocean
- Forming the integrating factor for neutral density in the ocean

- Distilling the ocean's role in climate using thermodynamic diagrams
- Linking the seasonal cycle of ocean water masses to transient climate change
- Asymmetry of the ocean's thermohaline circulation