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 Outcomes

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

## Other Information

**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.

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## Requirements

12 units from completion of the following course(s):

Code | Title | Units |
---|---|---|

MATH3501 | Scientific and Industrial Modelling | 6 |

MATH3511 | Scientific Computing | 6 |

6 units from completion of the following course(s):

Code | Title | Units |
---|---|---|

COMP1100 | Introduction to Programming and Algorithms | 6 |

COMP1130 | Introduction to Programming and Algorithms (Advanced) | 6 |

COMP1730 | Programming for Scientists | 6 |

6 units from completion of the following course(s):

Code | Title | Units |
---|---|---|

STAT1003 | Statistical Techniques | 6 |

STAT1008 | Quantitative Research Methods | 6 |

6 units from completion of the following course(s):

Code | Title | Units |
---|---|---|

MATH2305 | Differential Equations and Applications | 6 |

MATH2405 | Maths Methods 1 Honours: Ordinary Differential Equations and Advanced Vector Calculus | 6 |

6 units from completion of the following course(s):

Code | Title | Units |
---|---|---|

MATH2306 | Partial Differential Equations and Applications | 6 |

MATH2406 | Maths Methods 2 Honours: Partial Differential Equations, Fourier Analysis and Complex Analysis | 6 |

A maximum of 6 units may come from completion of courses from the following list:

Code | Title | Units |
---|---|---|

MATH2307 | Bioinformatics and Biological Modelling | 6 |

MATH2320 | Advanced Analysis 1: Metric Spaces and Applications | 6 |

COMP2130 | Software Analysis and Design | 6 |

STAT2001 | Introductory Mathematical Statistics | 6 |

STAT2008 | Regression Modelling | 6 |

A minimum of 6 units must come from completion of courses from the following list:

Code | Title | Units |
---|---|---|

MATH3029 | Probability Modelling with Applications | 6 |

MATH3062 | Fractal Geometry & Applications to Digital Imaging | 6 |

MATH3116 | Advanced Analysis 1: Metric Spaces and Applications | 6 |

MATH3133 | Environmental Mathematics | 6 |

MATH3320 | Advanced Analysis 2: Topology, Lebesgue Integration and Hilbert Spaces | 6 |

MATH3512 | Matrix Computations | 6 |

MATH3514 | Numerical Optimisation | 6 |

COMP3320 | High Performance Scientific Computation | 6 |

COMP3600 | Algorithms | 6 |

STAT3008 | Applied Statistics | 6 |

STAT3004 | Stochastic Modelling | 6 |

STAT3015 | Generalised Linear Modelling | 6 |