Honours Level Courses in Mathematics

The Mathematics Department is almost unique in beginning Honours courses from the first year of study. These units are open to anyone with the appropriate prerequisites, not only those intending to undertake a fourth (Honours) year in mathematics. They are strongly recommended for students needing to apply mathematics in other disciplines. They will be found particularly useful for students in the physical and biological sciences, engineering, computer science and mathematical economics.

INFORMATION SESSIONS: 30/10/00, 17/8/01 see below.

First Year

See the Department of Mathematics for links to the Mathematics Handbook and to the Homepages for first year courses.

Which Course? Students who have done the equivalent of Four Unit Mathematics in New South Wales, or Double Major Extended Mathematics in the Australian Capital Territory, and who feel relatively comfortable with this level of mathematics, should normally enroll in MATH1115 (Mathematics and Applications Honours) rather than MATH1013 (Mathematics and Applications). Students who have done very well in Three Unit Mathematics or Major Minor Mathematics, may also be permitted to enroll in MATH1115, but should discuss this either with an adviser during enrolment week or with a member of the Mathematics Department.

What is the difference? MATH1115 covers the same Calculus and Linear Algebra material as does MATH1013, but there is an additional Foundations component which covers more theoretical material and which is basic for a deeper conceptual understanding and is important for many applications of mathematics in other fields.

Second and Third Years

It is anticipated at this stage that the courses listed below will be available in 2003. Courses marked with * are honours level versions of courses offered at the pass level. For more detail see the online handbook.

	1st Semester	2nd Semester
Second Year	MATH2320: Analysis 1 Honours MATH2405: Calculus and Differential Equations Honours	MATH2322: Algebra 1 Honours MATH2406: Partial Differential Equations and Complex Calculus Honours
Third Year	MATH3401: Number Theory and Cryptography Honours
Third/Fourth Year	MATH3320: Analysis 2 Honours MATH3321: Algebra 2 Honours MATH3322: Mathematical Methods Honours MATH3342: Differential Geometry (probably semester one) ASTR3001: Stars and Astrophysical Fluid Dynamics MATH3501 Scientific and Industrial Modelling	MATH3325: Analysis 3 Honours MATH3228: Complex Analysis Honours MATH3134: Environmental Mathematics Honours MATH3343: Foundations of Mathematics MATH3029: Probability Honours ASTR3002: Galaxies and Cosmology MATH3502 Large Scale Matrix Computations
Fourth Year/Graduate	Harmonic Analysis Probabilistic Modelling by Example Data Mining	Partial Differential Equations Algebra (topic to be decided) Topics in Statistical Science

Suitably qualified second year students may be permitted to take third year courses, and suitably qualified third year students may be permitted to take fourth year/graduate courses (see the honours year in mathematics).

Fourth Year

For full details, including scholarships, see Honours Year in Mathematics.

Mathematical Connections

The opportunities for combining mathematics with other quantitative subjects are much broader than most students realise. If you enjoy doing and/or applying mathematics, the following should help in thinking about further directions of study and about future career possibilities. In the past, students have frequently commented after 3 or 4 years of study that they were unaware of the possibilities that were available to them. The information session was an attempt to address this issue.

The ANU is unique in having associated with the Faculties (undergraduate and graduate students), the Institute for Advanced Studies (IAS). The IAS concentrates on post graduate and graduate students, but increasingly is becoming involved in honours (fourth year) teaching and supervision. This leads to a significantly increased range of possibilities for students. In the past few years we have had students either jointly supervised for an honours degree, or have had students proceed from an honours degree in mathematics to further studies, in almost every Research Institute in the IAS. This indicates the breadth of possibilities for combining high level maths courses with other fields, whether or not you continue to a fourth year in mathematics.  For more information on the IAS begin with the ANU Academic Structure page.

The Mathematical Sciences Institute (MSI) is unique within the ANU in that it spans the IAS (Centre for Mathematics and Its Applications) and the Faculties (Department of Mathematics). MSI consists of Research Groups in Algebra, Abstract Analysis and Geometry, Applied and Nonlinear Analysis, Astronomy and Astrophysics, Stochastic Analysis, Statistical Science, Advanced Computation and Modelling, Mathematical Physics; and the Centres for Bioinformation Science and for Financial Mathematics.

Information Session 30/10/00

The material below consists of overheads presented by Research Groups from MSI, and by Research Groups from elsewhere within the IAS and the ANU. If you want more details, please follow the links or contact the people indicated!

• Algebra and Cryptography, Giuseppe Jurman,
• Partial Differential Equations & Differential Geometry, Ben Andrews, overhead,
• Astrophysics (MSI, Dept Physics, & Research Institute of Astronomy and Astrophysics), Lilia Ferrario
• Modelling Time Dependent Processes, Daryl Daley
• Data Mining & Computational Mathematics (MSI & Research Institute of Information Sciences and Engineering), Markus Hegland and Steve Roberts, overheads, and more overheads,
• Analysis and Geometry, Andrew Hassell, overhead
• Automated Reasoning, Systems and Telecommunications Engineering (Research Institute of Information Sciences and Engineering), Jen Davoren,
• Geophysics: geophysical fluid dynamics, seismology, geodynamics (Research Institute of Earth Sciences), Ross Kerr, overhead and links,
• Porous Media Group (Research Institute of Physical Sciences), Vanessa Robins,
• Environmental Modelling (Centre for Resources and Environmental Sciences), Tony Jakeman and Rebecca Lecher,
• Mathematical Economics (Faulty of Economics and Commerce), Simon Grant
• Mathematical Biology (Botany and Zoology), John Trueman,

Here is information on bioinformatics and statistics:

• Bioinformatics (MSI & John Curtin Institute of Medical Research), Sue Wilson,
• Statistical Science Program, Christian Rau (some notes), Melissa Dobbie  (notes), CSIRO Mathematical and Information Sciences, also Department of Statistics and Econometrics

Information Session 17/8/01

Here is an excellent site giving an overview of mathematics.

The following material was presented at the information session:

• Economics, John Quiggin
• New Bioinformatics Program, Statistics, Bioinformation Science, Sue Wilson, Alexander Isaev, overheads
• Research Institute of Information Science and Engineering, Jen Davoren, Richard Hartley, overheads
• Porous Media Group (Research Institute of Physical Sciences), Vanessa Robins, overhead
• Research Institute of Earth Sciences, Jean Braun, overhead
• Environmental Modelling (Centre for Resources and Environmental Sciences), Rebecca Lecher
• Computational Science Degree, Steve Roberts
• Pure Mathematics Programs, Andrew Hassell, overhead and another

Recent Honours Thesis Areas

Whether or not you do an honours degree in mathematics, the following list of thesis areas for students in the past 5 years also indicates connections between mathematics and other subjects.

• astrophysics
• functional analysis
• partial differential equations
• differential geometry
• chaos
• K-theory
• fluid flow
• gene sequences and evolutionary trees
• data mining
• numerical analysis, finite elements
• environmental mathematics
• image & pattern analysis
• group theory and other algebra
• minimal surfaces
• seismic tomography
• fractals and wavelets
• automated reasoning
• stochastic processes