Master of Mathematics - 2019

Mathematics underpins our way of life and our prosperity. Its importance ranges from fundamental developments enabling new technologies, to theories backing up scientific research, to analyses of our physical and societal environments.

The program is designed for graduates with a bachelor degree and a strong foundation in mathematics. Students will acquire advanced knowledge and skills in mathematics, and the capacity to use them to tackle complex problems in a variety of situations. The flexible coursework offering ensures that students can compose a program to suit their interests, from pure mathematics that develops the core theory, to statistics and applied and computational mathematics that extend this theory to bring practical solutions to real-world problems. All these fields contribute to a far-reaching and comprehensive master's program. The combination of coursework and project equips graduates of the program with advanced knowledge and skills that make them employable in industry, or prepare them for doctoral studies.

This master's course caters to various backgrounds, and allows for three entry points and programs (96 points over 2 years, 72 points over 18 months and 48 points over one year), depending on the applicant's previous studies.

These course outcomes are aligned with the Australian Qualifications Framework level 9 and Monash Graduate AttributesAustralian Qualifications Framework level 9 and Monash Graduate Attributes (http://monash.edu.au/pubs/handbooks/alignmentofoutcomes.html).

Upon successful completion of this course it is expected that you will be able to:

1. demonstrate advanced knowledge and critical understanding of principal themes in modern mathematics, including Statistics and Pure, Applied and Computational mathematics
2. apply critical thinking, high-level problem solving, research skills and advanced mathematical techniques within quantitative contexts and in complex problem solving
3. convey ideas and results effectively to technical and non-technical audiences alike and in a variety of formats in a professional context
4. work competently, independently and collaborate effectively in an interdisciplinary, academic and/or professional context.

The course is structured in three parts: Part A. Foundation studies, Part B. Intermediate studies, Part C. Advanced studies. All students complete Part C. Depending upon prior qualifications, you may receive credit for Part A or Part B or a combination of the two.

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.

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). All students complete Part C. Depending upon prior qualifications, you may receive credit for Part A or Part B or a combination of the two.

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

The course progression mapcourse progression map (http://www.monash.edu.au/pubs/2019handbooks/maps/map-s6003.pdf) provides guidance on unit enrolment for each semester of study.

Units are 6 points unless otherwise stated.

Part A. Foundation studies (24 points)

You must complete four units (24 points) in mathematics not previously completed in their 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
• MTH3121 Algebra and number theory
• MTH3130 Topology: The mathematics of shape
• MTH3140 Real analysis
• MTH3150 Algebra and number theory 2
• MTH3160 Functional analysis
• MTH3170 Network mathematics
• 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
• MTH3360 Fluid dynamics
• MTH3401 Special topics in mathematics 1
• MTH3402 Special topics in mathematics 2

Part B. Intermediate studies (24 points)

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

Pure mathematics

• MTH4099 Measure theory
• MTH4111 Differential geometry
• MTH4113Not offered in 2019 Low-dimensional topology
• MTH4115 Algebraic topology
• MTH4121Not offered in 2019 Analysis on manifolds
• MTH4123 Partial differential equations
• MTH4141 Computational group theory
• MTH4151 Advanced graph theory
• MTH4153Not offered in 2019 Combinatorics

Applied and computational mathematics

• MTH4089 Computational statistical inference
• MTH4311 Methods of applied mathematics
• MTH4321 Methods of computational mathematics
• MTH4323Not offered in 2019 Numerical analysis and control of differential equations
• MTH4331 Optimisation for data analytics
• MTH4333Not offered in 2019 Discrete optimisation
• MTH4341 Fluid dynamics and turbulence
• MTH4343Not offered in 2019 Magnetohydrodynamics and visualisation of scientific data
• MTH4351 Mathematical biology
• MTH43XX Advanced topics in applied mathematics
• MTH43XX Advanced topics in computational mathematics

Statistics

• MTH5210 Stochastic calculus and mathematical finance
• MTH5510 Quantitative risk management
• MTH5520 Interest rate modelling
• MTH5530 Computational methods in finance
• MTH5112 Partial differential equations 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 must 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
• MTH5113Not offered in 2019 Low-dimensional topology
• MTH5115 Algebraic topology
• MTH5121Not offered in 2019 Analysis on manifolds
• MTH5123 Partial differential equations
• MTH5141 Computational group theory
• MTH5151 Advanced graph theory
• MTH5153Not offered in 2019 Combinatorics

Applied and computational mathematics

• MTH5089 Computational statistical inference
• MTH5311 Methods of applied mathematics
• MTH5321 Methods of computational mathematics
• MTH5323Not offered in 2019 Numerical analysis and control of differential equations
• MTH5331 Optimisation for data analytics
• MTH5333Not offered in 2019 Discrete optimisation
• MTH5341 Fluid dynamics and turbulence
• MTH5343Not offered in 2019 Magnetohydrodynamics and visualisation of scientific data
• MTH5351 Mathematical biology
• MTH53XX Advanced topics in applied mathematics
• MTH53XX Advanced topics in computational mathematics

Statistics

• MTH5210 Stochastic calculus and mathematical finance
• MTH5510 Quantitative risk management
• MTH5520 Interest rate modelling
• MTH5530 Computational methods in finance
• MTH5112 Partial differential equations 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 exploation 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.

You may exit this course early and apply to graduate with the following awards, provided you have satisfied the requirements for that award during your enrolment in the master's course:

• Graduate Diploma of Mathematics after successful completion of Part A and Part B

Successful completion of this course may provide a pathway to a higher degree by research.