A synthesis of calculus and linear algebra, this is a fundamental course in the mathematics of curves, surfaces and volumes in three-dimensional space. Extending differentiation, integration and Taylor series to space leads to the important concepts of divergence, gradient and curl and culminates in the classical theorems of Green, Stokes and Gauss. This material is crucial to much of engineering and physics, with applications to mechanics, fluid dynamics and electromagnetism.

This course deals with professional, ethical and social responsibility issues related to employment in mathematics. It considers general principles and relates them to case studies which involve ethical issues in the use of mathematics. It also looks at the place of mathematics in the wider sphere of knowledge and helps you to develop the skills which are necessary to communicate mathematics effectively.

As for MATH2011, but in greater depth.

Differential equations are essential for the study of any continuous phenomenon, whether it be the time evolution of a fish population or a thundercloud, the flow of gas in a pipe, or the ascent of a rocket after ignition. In this course, some of the basic methods for differential equations (both ordinary and partial) are developed, especially for what are called boundary value problems; for example, what are the natural frequencies of a guitar or drum? Methods of this kind play a vital role in acoustics, in problems of temperature distribution, in quantum physics, in chemistry and in many other places. You will also meet the remarkable Fourier series, which play a vital role in modern communications, data analysis, and elsewhere.

As for MATH2120, but in greater depth.

Operations Research, commonly abbreviated as OR, tries to find the "best" course of action subject to restrictions on what you are allowed to do or limited availability of resources. Here "best" might mean maximizing your profit or minimizing your production costs. The constraints may arise from meeting customer demands, limited availability of a resource, or the fact that you must make a whole number of a product (you can't sell half a car). Such problems have wide applicability to business and industry.

A critical part is the development of mathematical models of the decision problem, and this can be of as much benefit to a company as the precise determination of the "best" action. This course concentrates on problems where the objective and constraints are linear functions of the decision variables. This includes linear programming, integer programming, assignment and transportation problems and network flows. The problems can be large, for example running an oil refinery or scheduling an airline's crews, so efficient solution methods are required and the models have to be solved by computer.

An introduction to mathematical models for the circulation of the atmosphere and oceans. The equations of motion are exploited so as to provide simplified models for phenomena including: waves, the effects of the Earth's rotation, the geostrophic wind, upwelling, storm surges. Feedback mechanisms are also modelled: the land/sea breeze, tornadoes, tropical cyclones. Models for large-scale phenomena including El Nino and the East Australian Current will be discussed as well as the role of the atmosphere-ocean system in climate change.

This course is not run every year.

Dynamical systems are ubiquitous mathematical models of systems which evolve in time. These models may be derived from differential equations, where time is continuous or difference equations (discrete time maps), where time moves in distinct steps. In this course, we are interested in dynamical systems which model processes in the real word. These could be fluid flows, nonlinear electrical circuits, dynamics of the heartbeat, development of `relationships', trade cycles in economics or harvesting strategies.

It is usually impossible to `solve' dynamical systems in the sense of obtaining explicit formulae. Accordingly, we will develop geometric methods to obtain qualitative information about the (long-term) behaviour of a dynamical system: Does the system reach an equilibrium state? Is the motion periodic or irregular? Is the motion stable?

The aim of this course is to give a gentle introduction to dynamical systems with the main focus on examples and applications in environmental, physical, biological, social and economic contexts.

As the means by which we can extract detailed information on biological systems have grown, so too has the demand to analyse this information. Repeated assays allow the dynamical nature of a biological system to be developed and this can lead to understanding of how the system can be kept healthy or altered. Mathematical modelling is ideally suited to this task and has played important roles in understanding how HIV overwhelms the immune system, whether a disease will spread through a community, or what the 3-dimensional structure will be for a bacterial population.

This course provides the basic tools for these types of investigations. It applies them to problems such as the interaction of HIV with the immune system, the spread of diseases through the community, pharmacodynamics, and management of renewable and non-renewable resources.

This course is essential for mathematics students contemplating a career related to computing. It gives a solid grounding in the basics of writing mathematical computer programs. The language used to illustrate these principles is MATLAB and no previous knowledge of the language is assumed. The course is a prerequisite for the third year course Advanced Mathematical Computing.

This course, with several applications to algebraic coding, is useful to all students of computer science and communication theory.
Starting from the Euclidean algorithm, we discuss continued fractions and congruences, and consider applications to the construction of secret codes in current use in commerce and industry. The techniques are then extended to polynomials, permitting the construction of the finite fields which are widely used in ``error correcting codes'' - these enable a digitised message to be restored after distortion due to ``noise''.

Linear algebra is a key tool in all of mathematics and its application. For example, the output of many electrical circuits depends linearly on the input (over moderate ranges of input), and successfully correcting the trajectory of a space probe involves repeatedly solving systems of linear equations in hundreds of variables. Linear methods are vital in ecological population models, and in mathematics itself.

You have met systems of linear equations and matrices, vector spaces and linear transformations in first year Mathematics courses, without necessarily understanding all the subtleties involved. In MATH2501, you will review the material from first year, so that vector spaces and linear transformations become familiar friends rather than uneasy acquaintances. You will learn about geometric transformations - projections (which can also be viewed as least squares approximations), rotations and reflections. You will see how to view many linear transformations as being made up of ``stretches'' in various directions, (the diagonalisation process), and the more general Jordan form. This will allow you to calculate functions of matrices (such as the exponential of a matrix) and hence to solve systems of linear differential equations.

Complex analysis is the study of functions f :C --> C where C is the complex plane. Surprisingly, the theory of these functions is very different from that of real-valued functions of a real variable. The theory is also simpler. Assume that f is analytic at the point a in C. By this we mean that f is (complex) differentiable at all points in a some disc D centered at a. Then we can prove that f is differentiable any number of times at all points in D, and that, moreover, the Taylor series for f converges to f(z) for all z in D.

Analytic functions possess many other unexpected properties and one that we exploit frequently is a dramatic result of Cauchy. This result states that if f is analytic on a domain D without ``holes'' then the integral of f along a path in D depends only on the end-points of the path. This result implies, for example, that the integral of f around any closed path in D is 0. After a minimal amount of practice we can use this to evaluate some important improper integrals of real-valued functions of a real variable.

This course covers much the same material as MATH2501, but with important additions, and an emphasis on the concepts rather than the mechanics of linear algebra. Part of the extra material involves complex vector spaces, resulting eventually in a more elegant and useful theory.

But the exciting new ingredient is a brief introduction to groups. Groups are the mathematical heart of symmetry, whether it arises from Escher's art, a differential equation, Rubik's cube or quantum mechanics. You will study groups both as concrete groups of symmetries, and as abstract objects, providing the basic tools for subsequent development, and a fascinating pathway into modern algebra.

As for MATH2520, but in greater depth.

Probabilistic methods are nowadays universally used in all fields of technology and science, whether physical, biological or social. Statistical analysis and presentation of data has become the rule, particularly with the advent of the computer revolution. Nevertheless, probability and statistics retain an aura of mystery for most people, because probabilistic reasoning is so different from day-to-day experience.

This course is the only one in the university which provides a detailed, step-by-step training in the foundations of probabilistic thinking, along with the basic mathematical tools required for its understanding and for further study. It introduces probability distributions and random variables, univariate and multivariate, leading to the derivation of the standard sampling distributions.

It is a must for all those who want to apply the multitude of available statistical computer packages with some understanding of what they are doing and of the limitations of the various models and tests. It is also the only available comprehensive introduction to mathematical probability theory for those engineers and scientists who do not wish to proceed to a detailed study of statistics.

The course is offered at two levels. MATH2801 is the ordinary level, while MATH2901 is the higher level, which offers a more detailed and refined treatment of the mathematics of the course. Students who intend to proceed to the Honours year in Statistics must take the course at the higher level.

Statistics is about using probability models to make decisions from data in the face of uncertainty. This course gives an introduction to the process of building statistical models using an important class of models (linear models). In a linear model we try to predict or explain variation in a response variable in terms of related quantities (predictors). The relationship between the expected response and predictors is linear in unknown model parameters.
Topics covered in the course include how to estimate parameters in linear models, how to compare models using hypothesis testing, how to select a good model or models when prediction of the response is the goal, and how to detect violations of model assumptions and observations which have an undue influence on decisions of interest. Concepts are illustrated with applications from finance, economics, medicine, environmental science and engineering.

Run in association with SAS, this course is expected to be offered for the first time in S2 2005. The use of large datasets in finance, marketing, bioinformatics etc has created a need for skills in querying, manipulating, cleaning, graphing and reporting on complex data, in preparation for its statistical analysis. The course will use industry standard packages (Access, Excel and SAS) and offer the first stages in SAS certification and a work experience placement program.

Description coming shortly

As for MATH2801 but in greater depth.

As for MATH2831 but in greater depth.