Honours Year in Mathematics

The Fourth Year Honours Program in mathematics is offered in collaboration between the Department of Mathematics and the Centre for Mathematics and Its Applications, both in the Mathematical Sciences Institute.

The fourth (or honours) year in mathematics normally consists of coursework (50%) and a thesis (50%). Students take four courses, and also present two seminars on suitable topics of their own choice. Ideas and techniques for giving a good seminar can be found in Some Points on Seminar Technique, Seminar on Seminars and How to Give a Good Talk. The program is spread over 10 months from the beginning of February to the end of November. It is also possible to begin in the middle of the year and to enrol in the program on a part-time basis. External students should apply through the ANU Admissions Office.

Detailed information concerning admission requirements and organisation and assessment can be found in the document Honours in Mathematics (see also this link and this link to Study@ANU). More specific information for students entering the program in 2009 can be found in the documents Mathematics Fourth Year Honours, 2009 and Submission Guidelines for Honours Students. For further information contact the coordinator of the honours program, Assoc. Prof. Alexander Isaev, at Alexander.Isaev@anu.edu.au.

A number of ANU Honours Year Scholarships are available for Honours students.

Some useful TeX resources are available on-line for current students. Another excellent link to TeX resourses is here. Information on the thesis format can be found in the document Mathematics Fourth Year Honours, 2009. Past theses can be accessed in the electronic format from within the MSI by clicking here.

Courses

For a list of standard courses please click here and look for Honours Pathway Courses (HPC) and courses having an Honours Pathway Option (HPO). All these courses are suitable for Fourth Year Honours students. In addition, a number of Fourth Year/Graduate courses are offered every year by members of the relevant Research Programs within the MSI. The actual courses will to some extent depend on the students' interests and background. Links to the individual Research Programs are also available from the MSI Homepage under the heading Research.

Thesis Topics

The following is a list of possible fourth year honours topics. It is neither definitive nor exhaustive, and will be modified from time to time. But it should give you an idea of the wide range of possibilities. Contact the relevant people for further discussion and ideas.

It is often possible to undertake your honours project with a supervisor in areas such as Computer Science, Physics, Statistics, or elsewhere, provided there is sufficient mathematical content. Students have the choice of studying mathematics and statistics in their own right and/or applying them in disciplines such as bioinformatics, financial mathematics, computational science, theoretical astrophysics, environmental science. Joint supervision with various Research Institutes is often available to students when relevant. For further information contact the fourth year honours coordinator.

• Andrews, Ben: The Yau and Lawson conjectures for minimal tori, Ricci flow: four-manifolds with positive isotropic curvature, deforming diffeomorphisms of the sphere to rotations, isospectral metrics, inequalities for fundamental frequencies
• Ball, Rowena: Topics in dynamical systems
• Borger, James: Arithmetic algebraic geometry, lambda rings, Witt vectors
• Burden, Conrad: Adsorption models of microarrays
• Carey, Alan: Topics in the general areas of mathematical physics (quantum theory), noncommutative geometry and applications, geometry and quantum field theory, geometric analysis
• Daley, Daryl: Applied probability modelling in telecommunications, epidemiology, stochastic geometry
• Ferrario, Lilia: Co-ordinates projects in the area of Astronomy and Astrophysics
• Hassell, Andrew: eigenfunction concentration; wave diffraction; scattering theory; wavelets; computational problems; nonlinear heat equation
• Hegland, Markus: Stochastic models in molecular biology; learning conditional probability distributions; analysing plasma data
• Hutchinson, John: Analysis on fractals and more generally a range of topics in fractal geometry and related areas
• Hyde, Steve & Robins, Vanessa: Department of Applied Mathematics projects
• Isaev, Alexander: Group actions in complex geometry
• Jakeman, Tony & The Centre for Resource and Environmental Studies: Topics in environmental modelling
• James, Matt: Simulators for quantum information/computation
• Kovacs, Laci: The (abstract) classification of soluble Frobenius complements
• Loy, Rick: Finitely additive measures and all that; spectral continuity; rich and narrow operators; abstract characterisations of analytic functions, operators preserving the spectrum
• McIntosh, Alan: Harmonic analysis, operator theory and partial differential equations
• Maindonald, John: Analysis of microarray data; algorithms for linear and generalised linear models; aspects of multi-level models, including any or all of: (a) multi-level modelling interpretations of anova tables, (b) computational issues, (c) history; topics in the use of R for statistical analysis; data mining from a statistical perspective; "model-free" analysis, etc.
• Neeman, Amnon: K-theory via simplicial sets; homological algebra and derived categories; the algebraic geometry of the chiral Potts model
• Ormerod, Elizabeth: Finite p-groups where many subgroups are 2-subnormal; matrix-product codes over  GF(q)
• Osborne, Michael: ODE estimation, polyhedral optimization
• Rennie, Adam: Analytic index theory, non-commutative topology
• Roberts, Steve: Environmental modelling: methods and algorithms for complicated physical flows; estimation of high dimensional probability density functions (see also the Advanced Computation Program possible research projects)
• Sambridge, Malcolm: Projects in Physics of the Earth, which although couched in terms of graduate students are also applicable to honours year students; (scholarships are also available)
• Stals, Linda: Thin plate splines, adaptive optics, domain decomposition, turbulent transport models (see also Advanced Computation Program)
• Trudinger, Neil: Viscosity solutions to partial differential equations
• Urbas, John: Monge-Ampere and related equations and their applications; surfaces of prescribed Gauss curvature; isometric embedding of two-dimensional Riemannian manifolds; mass transport problems
• Wang, Bai-Ling: Geometry of gerbes and D-branes; K-theory and index theory; topological invariants via gauge theory and string theory
• Welsh, Alan: Mixed models, model selection, sampling ecological populations, model-based analysis of surveys, inference
• Wickramasinghe, Dayal: The formation and detection of black holes (see Astronomy and Astrophysics)
• Wilson, Sue: Bioinformatics, mathematical genetics - epistasis
• In addition, the Department of Theoretical Physics projects can be found here
  

Computational Science Honours Program

The Department of Mathematics and Department of Computer Science offer an honours program in computational science. This program is for people who are particularly interested in using computational modelling to simulate real world phenomena. Interested students should contact Dr Stephen Roberts at Stephen.Roberts@anu.edu.au or look at the BComptlSci honours page for more details.

Honours in Astronomy and Astrophysics

The Department of Mathematics and the Department of Physics together with the Research School of Astronomy and Astrophysics also offer a joint Honours Program in Astrophysics which is particularly suited for students interested in pursuing a post-graduate career in astronomy or astrophysics. It also provides excellent training in the general areas of mathematical modelling, computing and modern instrument development. Interested students should contact Dr Lilia Ferrario at Lilia.Ferrario@maths.anu.edu.au for more details.