Offered By	ANU Joint Colleges of Science
Academic Contact	Dr Linda Stals and Dr Barry Croke
Areas of Interest	Economics, Engineering, Environmental Studies, Mathematics, and Science

Description:

Models are becoming an increasingly important tool in many branches of modern society due to advances in science and technology. As our understanding of these models improves, the complexity of the types of questions being asked increases. The objective of this major is to train students in techniques of model development, use and assessment.

A key requirement for future scientists, industry leaders, resource managers, and policy makers is an ability to build and evaluate models and/or interpret model outputs. Career opportunities for graduates extend into every part of society, including: research (e.g. CSIRO, Universities); public sector (e.g. Bureau of Meteorology, Murray Darling Basin Authority, state government agencies); and private sector (e.g. engineering, finance).

Students are advised to take this major in conjunction with a major or minor from an application area. For example, students may choose to complement this major with a quantitative applications major or minor consisting of courses from areas such as: physics; earth and environmental science; global change science; climate science and policy; environmental geoscience; geophysics; quantitative finance; or mathematical finance.

Coupled with a detailed disciplinary base, this major will provide students with the necessary skills to tackle the problems facing tomorrow's society.

Learning Goals:

Students who complete the major in Mathematical Modelling will be able to:

1. Apply mathematical concepts, including Calculus, Linear Algebra and Differential Equations to analyse specific problems and identify the appropriate mathematics to realise a solution.
2. Use computer programming and statistical analysis skills to efficiently model systems.
3. Recognise the connections between mathematics and other disciplines, and how mathematical ideas are embedded in other contexts.
4. Represent real-world systems from science and technology in a mathematical framework.
5. Employ appropriate methods to analyse, solve and evaluate the performance of mathematical models.
6. Identify relevant disciplinary material and sources to pursue independent mathematical learning and deepen understanding of the behaviour of a system reasoning.
7. Relate the behaviour of the output of the mathematical model to the underlying physical or conceptual model of interest.
8. Extend their experiences of working both independently and collaboratively within the discipline to other contexts.
9. Relate professional and disciplinary information and ideas to varied audiences in effective and appropriate ways.
10. Reflect the professional standards of the discipline and of science in their own work and practice.

Requirements

Requirements:

This major requires the completion of 48 units, which must include:

A total of 12 units from the following compulsory courses:

MATH3501 Scientific and Industrial Modelling

MATH3511 Scientific Computing

A total of 36 units to be chosen from the following courses including:

• 12 units of 1000 level courses including:

- 6 units of courses chosen from:

COMP1100: Introduction to Programming and Algorithms

COMP1130: Data Structures and Algorithms

COMP1730:Programming for Scientists

- 6 units of courses chosen from:

STAT1003: Statistical Techniques

STAT1008 Quantitative Research Methods

• 12 units of 2000 level courses including:

- 6 units of courses chosen from:

MATH2305: Differential Equations and Applications

MATH2405: Maths Methods 1 Honours: Ordinary Differential Equations and Advanced Vector Calculus

- 6 units of courses chosen from:

MATH2306: Partial Differential Equations and Applications

MATH2406: Maths Methods 2 Honours: Partial Differential Equations, Fourier Analysis and Complex Analysis

• A maximum of 6 units chosen from the following 2000 level courses:

MATH2307  Bioinformatics and Biological Modelling

MATH2320  Analysis 1 Honours: Metric Spaces and Applications

COMP2130 Software Analysis and Design

STAT2001  Introductory Mathematical Statistics

STAT2008  Regression Modelling

• A minimum of 6 units chosen from the following 3000 level courses:

MATH3029  Probability Modelling with Applications.

MATH3062  Fractal Geometry and Chaotic Dynamics

MATH3116  Applied Analysis 1 Honours: Metric Spaces and Applications.

MATH3133  Environmental Mathematics

MATH3320  Analysis 2 Honours: Topology, Lebesgue Integration and Hilbert Spaces

MATH3501  Scientific and Industrial Modelling.

MATH3511  Scientific Computing.

MATH3512  Matrix Computations.

MATH3514  Numerical Optimisation.

COMP3320  High Performance Scientific Computing

COMP3600  Algorithms.

STAT3008  Applied Statistics.

STAT3004  Stochastic Modelling

STAT3015  Generalised Linear Modelling

Advice to Students:

What 1st year courses should you enrol in?  COMP1100 or COMP1130 or COMP1730; and either STAT1003 or STAT1008

By its nature, mathematical modelling is a general topic. For the non-compulsory courses in the major, we recommend that students choose two courses that fit into one of the groups listed below. The three different groupings allow students to emphasis different aspects depending on their interests.

Analytical Mathematical Modelling

MATH3116: Applied Analysis 1 Honours: Metric Spaces and Applications or MATH2320: Analysis 1 Honours: Metric Spaces and Applications, plus one of the following courses

MATH3512: Matrix Computations  or MATH3514: Numerical Optimisation

MATH3320: Analysis 2 Honours: Topology, Lebesgue Integration and Hilbert Spaces

Computational Mathematical Modelling

MATH3512: Matrix Computations  or  MATH3514: Numerical Optimisation , plus one of the following courses

COMP3320: High Performance Scientific Computing.

COMP2130: Software Analysis and Design.

COMP3420: Advanced Databases and Data Mining.

COMP3600: Algorithms.

Applied Mathematical Modelling

Any two of the following courses (one of which must be a third year course)

MATH3133: Environmental Mathematics.

MATH3512: Matrix Computations.

MATH3514: Numerical Optimization.

MATH3062: Fractal Geometry and Chaotic Dynamics.

MATH2307: Bioinformatics and Biological Modelling.

MATH3029: Probability Modelling with Applications.

STAT3015: Generalised Linear Modelling.

STAT3008: Applied Statistics.

STAT2008: Regression Modelling.

STAT2001: Introductory Mathematical Statistics.

STAT3004: Stochastic Modelling

The courses in Analytical Mathematical Modelling focus more on the theoretical aspects of modelling. Students considering honours in mathematics with a major in Mathematical Modelling should take the courses in Analytical Mathematical Modelling, along with any other mathematics HPC courses of interest. Students interested in further research in a quantitative discipline may also benefit from  the analytical skills developed in this major.

The courses in Computational Mathematical Modelling focus more on scientific computing. They are intended for students with both a strong interest in mathematics and computing. Students interested in doing honours in Computational Science should take the courses in Computational Mathematical Modelling. Students interested in further research in a discipline with a strong computational component, such as astronomy, can benefit from the technical skills developed in this major.

The courses in Applied Mathematical Modelling are aimed at students interested in developing their skills in building and interpreting models. This includes students whose primary interest is in an application area, such as physics or economics, but wants a better understanding of the models used in their discipline. It also includes students who have more of a professional or vocational focus. Students may be interested in taking this particular grouping of courses with more qualitative courses that better help them communicate their analysis to a wider audience.

Students should be aware of the need to complete the pre-requisites for the level 2000 and 3000 courses. In particular, note that some of the courses are HPC courses. Also, to undertake later year computer science courses it is generally required to undertake 12 units of 2000-level COMP courses.

Students should seek further course advice from the academic convener of this Mathematical Modelling major.

The information published on the Study at ANU 2012 website applies to the 2012 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2011 website.