S6003 Master of Mathematics

The course is structured in three parts: Part A. Foundation studies, Part B. Intermediate studies, Part C. Advanced studies.

Part A. Foundation studies
These studies strengthen your foundations in the field of mathematics. You will choose studies that complement your current knowledge of mathematics, in one or more of the areas of Statistics, or Pure, Applied and Computational mathematics.

Part B. Intermediate studies
These studies consolidate your knowledge in one or more fields in mathematics.

Part C. Advanced studies
These studies provide you with advanced knowledge in modern theories and applications of mathematics which will enable you to bring innovative solutions to problems within or outside mathematics. Through a research project you will develop project management and independent research skills. There is a wide range of units to choose from across Pure mathematics, Applied and Computational mathematics and statistics. You can complement your discipline studies with professional development learning.

Master's entry points

Depending on prior qualifications you may receive entry level credit (a form of block credit) which determines your point of entry to the course:

• If you are admitted at entry level 1 you complete 96 credit points, comprising Part A, Part B and Part C.
• If you are admitted at entry level 2 you complete 72 credit points, comprising Part B and Part C.
• If you are admitted at entry level 3 you complete 48 credit points, comprising Part C.

Note: If you are eligible for credit for prior studies you may elect not to receive the credit and complete one of the higher credit-point options.

Course progression map

The course progression map provides guidance on unit enrolment for each semester of study.

The course is structured in three parts: Part A. Foundation studies (24 points), Part B. Intermediate studies (24 points), Part C. Advanced studies (48 points).

Units are 6 points unless otherwise stated.

Part A. Foundation studies (24 points)

You complete four units (24 points) in mathematics not previously completed in your undergraduate studies:

• MTH3011 Partial differential equations
• MTH3020 Complex analysis and integral transforms
• MTH3051 Introduction to computational mathematics
• MTH3060 Advanced ordinary differential equations
• MTH3110 Differential geometry
• MTH3141 Algebra 1: Group theory
• MTH3130 Topology: The mathematics of shape
• MTH3137 Number theory and cryptography (Advanced)
• MTH3140 Real analysis
• MTH3150 Algebra 2: rings and fields
• MTH3160 Functional analysis
• MTH3170 Network mathematics or MTH3175 Network mathematics (advanced)
• MTH3230 Time series and random processes in linear systems
• MTH3241 Random processes in the sciences and engineering
• MTH3251 Financial mathematics
• MTH3260 Statistics of stochastic processes
• MTH3310 Applied mathematical modelling
• MTH3320 Computational linear algebra
• MTH3330 Optimisation
• MTH3340 Numerical methods for partial differential equations
• MTH3360 Fluid dynamics
• MTH3401 Special topics in mathematics 1
• MTH3402 Special topics in mathematics 2

Part B. Intermediate studies (24 points)

You complete four units (24 points) from any of the following:

Pure mathematics

• MTH4099 Measure theory
• MTH4111 Differential geometry
• MTH4113 Low-dimensional topology
• MTH4115 Algebraic topology
• MTH4123 Partial differential equations
• MTH4141 Computational group theory
• MTH4143 Representation Theory
• MTH4151 Advanced graph theory
• MTH4153 Combinatorics

Applied and computational mathematics

• MTH4089 Computational statistical inference
• MTH4311 Methods of applied mathematics
• MTH4321 Methods of computational mathematics
• MTH4323 Numerical analysis and control of differential equations
• MTH4331 Optimisation for data analytics
• MTH4333 Discrete optimisation
• MTH4341 Fluid dynamics and turbulence
• MTH4343 Magnetohydrodynamics and visualisation of scientific data
• MTH4351 Mathematical biology
• MTH4361 Advanced topics in applied mathematics
• MTH4363 Advanced topics in computational mathematics

Statistics

• MTH4240 Mixing of finite Markov chains
• MTH5210 Stochastic calculus and mathematical finance
• MTH5510 Quantitative risk management
• MTH5520 Interest rate modelling
• MTH5530 Computational methods in finance
• MTH5220 The theory of martingales in discrete time
• MTH5230 Markov chains and random walks
• MTH5540 Statistical learning in finance
• MTH5550 Quantitative trading and market microstructure

Part C. Advanced studies (48 points)

You complete:

a. MTH5000 Mathematics master project (24 points)
b. Four units (24 points) from any of the following:

Pure mathematics

• MTH5099 Measure theory
• MTH5111 Differential geometry
• MTH5113 Low-dimensional topology
• MTH5115 Algebraic topology
• MTH5121 Analysis on manifolds
• MTH5123 Partial differential equations
• MTH5141 Computational group theory
• MTH5143 Representation Theory
• MTH5151 Advanced graph theory
• MTH5153 Combinatorics

Applied and computational mathematics

• MTH5311 Methods of applied mathematics
• MTH5323 Numerical analysis and control of differential equations
• MTH5331 Optimisation for data analytics
• MTH5333 Discrete optimisation
• MTH5341 Fluid dynamics and turbulence
• MTH5343 Magnetohydrodynamics and visualisation of scientific data
• MTH5351 Mathematical biology
• MTH5361 Advanced topics in applied mathematics
• MTH5363 Advanced topics in computational mathematics

Statistics

• MTH5210 Stochastic calculus and mathematical finance
• MTH5240 Mixing of finite Markov chains
• MTH5510 Quantitative risk management
• MTH5520 Interest rate modelling
• MTH5530 Computational methods in finance
• MTH5220 The theory of martingales in discrete time
• MTH5230 Markov chains and random walks
• MTH5540 Statistical learning in finance
• MTH5550 Quantitative trading and market microstructure

Special topics

• MTH5010 Special topics in advanced mathematics 1
• MTH5020 Special topics in advanced mathematics 2

Professional units
No more than one unit can be taken from the following:

• FIT5147 Data exploration and visualisation
• FIT5205 Data in society
• Other relevant professional development units approved by the course coordinator

You should note that units successfully completed at level 4 in Part B cannot be taken at level 5 in Part C.