## Course Structure

This course is available for entry:

- Semester 1 (February)
- Semester 2 (July)

### 200 credit points taken over 2 years full-time.

This course is available as full or part-time for domestic students.

The Master of Science (Mathematics & Statistics) offers four streams:

- Applied Mathematics and Mathematical Physics
- Discrete Mathematics and Operations Research
- Pure Mathematics
- Statistics and Stochastic Processes

Your course will comprise of:

- Discipline subjects (137.5 points)
- Professional skills subjects (12.5 points)
- Research project (50 points) OR in special cases, with approval of the Master of Science (Mathematics & Statistics) Program Coordinator, 25 points with an additional 25 points of masters level mathematics and statistics discipline subjects. The Research project commences in the second semester of study in three consecutive semesters.

View Generic Sample Course Plan

## Master of Science - Mathematics & Statistics

### Sample course plan

#### Year 1

#### Year 2

### Key

Core subject Elective subject Professional Skills subject Project subject

## Sample Course Plan

Year 1 - Semester 1 | |
---|---|

Core Subjects | Points |

Advanced Methods: Differential EquationsCore | 12.5 |

## Advanced Methods: Differential EquationsThis subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on ordinary differential equations. Both analytical and approximate techniques are used to determine solutions of ordinary differential equations. Exact solutions by localised series expansion techniques of second-order linear ordinary differential equations and Sturm-Liouville boundary value problems are explored. Special functions are introduced here. Regular and singular perturbation expansion techniques, asymptotic series solutions, dominant balance, and WKB theory are used to determine approximate solutions of linear and nonlinear differential equations. Throughout, the the... Detailed Information MAST90064Type Core | |

Further Discipline Subjects | Points |

Stochastic Calculus with ApplicationsCore | 12.5 |

## Stochastic Calculus with ApplicationsThis subject provides an introduction to stochastic calculus and mathematics of financial derivatives. Stochastic calculus is essentially a theory of integration of a stochastic process with respect to another stochastic process, created for situations where conventional integration will not be possible. Apart from being an interesting and deep mathematical theory, stochastic calculus has been used with great success in numerous application areas, from engineering and control theory to mathematical biology, theory of cognition and financial mathematics. Detailed Information MAST90059Type Core | |

Elective Subjects | Points |

Mathematical Statistical MechanicsElective | 12.5 |

## Mathematical Statistical MechanicsThe goal of statistical mechanics is to describe the behaviour of bulk matter starting from a physical description of the interactions between its microscopic constituents. This subject introduces the Gibbs probability distributions of classical statistical mechanics, the relations to thermodynamics and the modern theory of phase transitions and critical phenomena. The central concepts of critical exponents, universality and scaling are emphasized throughout. Applications include the ideal gases, magnets, fluids, one-dimensional Ising and Potts lattice spin models, random walks and percolation as well as approximate methods of solution. Detailed Information MAST90060Type Elective | |

Random Matrix TheoryElective | 12.5 |

## Random Matrix TheoryRandom matrix theory is a diverse topic in mathematics. It draws together ideas from linear algebra, multivariate calculus, analysis, probability theory and mathematical physics, amongst other topics. It also enjoys a wide number of applications, ranging from wireless communication in engineering, to quantum chaos in physics, to the Reimann zeta function zeros in pure mathematics. A self contained development of random matrix theory will be undertaken in this course from a mathematical physics viewpoint. Topics to be covered include Jacobians for matrix transformation, matrix ensembles and their eigenvalue probability density functions, equilibrium measures, global and local statistical q... Detailed Information MAST90103Type Elective |

Year 1 - Semester 2 | |
---|---|

Elective Subjects | Points |

Advanced Modelling: Case StudiesElective | 12.5 |

## Advanced Modelling: Case StudiesMathematical modelling can give deep insight into many complex systems that arise in nature and technology. It is also used to describe and predict new phenomena, test hypotheses and investigate novel avenues for experiments. This subject presents a series of advanced case studies that demonstrate the utility of mathematical modelling and develop the student's ability to tackle real-world problems arising in scientific, medical or industrial contexts. Mathematical approaches will include discrete, computational and asymptotic methods. The use of appropriate approximations and the interpretation of solutions in the context of the original problem will be emphasised. Detailed Information MAST90080Type Elective | |

Exactly Solvable ModelsElective | 12.5 |

## Exactly Solvable ModelsIn mathematical physics, a wealth of information comes from the exact, non-perturbative, solution of quantum models in one-dimension and classical models in two-dimensions. This subject is an introduction to this beautiful and deep subject. Yang-Baxter equations, Bethe ansatz and matrix product techniques are developed in the context of the critical two-dimensional Ising model, dimers, free fermions, the 6-vertex model, percolation, quantum spin chains and the stochastic asymmetric simple exclusion model. The algebraic setting incorporates the quantum groups, and the Temperley-Lieb and braid-monoid algebras. Detailed Information MAST90065Type Elective | |

Network OptimisationElective | 12.5 |

## Network OptimisationMany practical problems in management, operations research, telecommunication and computer networking can be modelled as optimisation problems on networks. Here the underlying structure is a graph. This subject is an introduction to optimisation problems on networks with a focus on theoretical results and efficient algorithms. It covers classical problems that can be solved in polynomial time, such as shortest paths, maximum matchings, maximum flows, and minimum cost flows. Other topics include complexity and NP-completeness, matroids and greedy algorithms, approximation algorithms, multicommodity flows, and network design. This course is beneficial for all students of discrete mathematic... Detailed Information MAST90013Type Elective | |

Research Project | Points |

Research Project Part ACore | 12.5 |

## Research Project Part AIn this subject, students undertake a substantial research program in the area of Mathematics and Statistics. The research will be conducted under the supervision of a member of the Department's academic staff. A list of the research interests of the Department of Mathematics and Statistics is outlined on the website of the Department. The results will be reported in the form of a thesis and an oral presentation. Detailed Information MAST90075Type Core |

Year 2 - Semester 1 | |
---|---|

Core Subjects | Points |

Advanced Methods: TransformsCore | 12.5 |

## Advanced Methods: TransformsThis subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on integral transform and related techniques. An introduction is given to the calculus of variations and the Euler-Lagrange equation. Advanced complex contour integration techniques are used to evaluate and invert Fourier and Laplace transforms. The general theory includes convolutions, Green’s functions and generalized functions. The methods of Laplace, stationary phase, steepest descents and Watson’s lemma are used to asymptotically approximate integrals. Throughout, the theory is set in the context of examples from applied mathematics and mathematical physics such as the brac... Detailed Information MAST90067Type Core | |

Elective Subjects | Points |

Elements of BioinformaticsElective | 12.5 |

## Elements of BioinformaticsBioinformatics is a key research tool in modern agriculture, medicine, and the life sciences in general. It forms a bridge between complex experimental and clinical data and the elucidation of biological knowledge. This subject presents bioinformatics in the context of its role in science, using examples from a variety of fields to illustrate the history, current status, and future directions of bioinformatics research and practice. Detailed Information BINF90002Type Elective | |

Professional Skills Subjects | Points |

Systems Modelling and SimulationOther | 12.5 |

## Systems Modelling and SimulationModern science and business makes extensive use of computers for simulation, because complex real-world systems often cannot be analysed exactly, but can be simulated. Using simulation we can perform virtual experiments with the system, to see how it responds when we change parameters, which thus allows us to optimise its performance. We use the language R, which is one of the most popular modern languages for data analysis. Detailed Information MAST90045Type Other | |

Research Project | Points |

Research Project Part BCore | 12.5 |

## Research Project Part BIn this subject, students undertake a substantial research program in the area of Mathematics and Statistics. The research will be conducted under the supervision of a member of the Department's academic staff. A list of the research interests of the Department of Mathematics and Statistics is outlined on the website of the Department. The results will be reported in the form of a thesis and an oral presentation. Detailed Information MAST90076Type Core |

Year 2 - Semester 2 | |
---|---|

Elective Subjects | Points |

Riemann Surfaces and Complex AnalysisElective | 12.5 |

## Riemann Surfaces and Complex AnalysisRiemann surfaces arise from complex analysis. They are central in mathematics, appearing in seemingly diverse areas such as differential and algebraic geometry, number theory, integrable systems, statistical mechanics and string theory. The first part of the subject studies complex analysis. It assumes students have completed a first course in complex analysis so begins with a quick review of analytic functions and Cauchy's theorem, emphasising topological aspects such as the argument principle and Rouche's theorem. Topics also include: Schwarz's lemma; limits of analytic functions, normal families, Riemann mapping theorem; multiple-valued functions, differential equations and Riemann sur... Detailed Information MAST90056Type Elective | |

Modelling: Mathematical BiologyElective | 12.5 |

## Modelling: Mathematical BiologyModern techniques have revolutionised biology and medicine, but interpretative and predictive tools are needed. Mathematical modelling is such a tool, providing explanations for counter-intuitive results and predictions leading to new experimental directions. The broad flavour of the area and the modelling process will be discussed. Applications will be drawn from many areas including population growth, epidemic modelling, biological invasion, pattern formation, tumour modelling, developmental biology and tissue engineering. A large range of mathematical techniques will be discussed, for example discrete time models, ordinary differential equations, partial differential equations, stochas... Detailed Information MAST90011Type Elective | |

Research Project | Points |

Research Project Part CCore | 25 |

## Research Project Part CIn this subject, students undertake a substantial research program in the area of Mathematics and Statistics. The research will be conducted under the supervision of a member of the Department's academic staff. A list of the research interests of the Department of Mathematics and Statistics is outlined on the website of the Department. The results will be reported in the form of a thesis and an oral presentation. Detailed Information MAST90077Type Core |

## Subject Options

Applied Mathematics & Mathematical Physics Specialisation - Students complete: | |
---|---|

Core Subjects | Points |

Advanced Methods: TransformsCore | 12.5 |

## Advanced Methods: TransformsThis subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on integral transform and related techniques. An introduction is given to the calculus of variations and the Euler-Lagrange equation. Advanced complex contour integration techniques are used to evaluate and invert Fourier and Laplace transforms. The general theory includes convolutions, Green’s functions and generalized functions. The methods of Laplace, stationary phase, steepest descents and Watson’s lemma are used to asymptotically approximate integrals. Throughout, the theory is set in the context of examples from applied mathematics and mathematical physics such as the brac... Detailed Information MAST90067Type Core | |

Advanced Methods: Differential EquationsCore | 12.5 |

## Advanced Methods: Differential EquationsThis subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on ordinary differential equations. Both analytical and approximate techniques are used to determine solutions of ordinary differential equations. Exact solutions by localised series expansion techniques of second-order linear ordinary differential equations and Sturm-Liouville boundary value problems are explored. Special functions are introduced here. Regular and singular perturbation expansion techniques, asymptotic series solutions, dominant balance, and WKB theory are used to determine approximate solutions of linear and nonlinear differential equations. Throughout, the the... Detailed Information MAST90064Type Core |

37.5 credit points selected from: | |
---|---|

Elective Subjects | Points |

Random Matrix TheoryElective | 12.5 |

## Random Matrix TheoryRandom matrix theory is a diverse topic in mathematics. It draws together ideas from linear algebra, multivariate calculus, analysis, probability theory and mathematical physics, amongst other topics. It also enjoys a wide number of applications, ranging from wireless communication in engineering, to quantum chaos in physics, to the Reimann zeta function zeros in pure mathematics. A self contained development of random matrix theory will be undertaken in this course from a mathematical physics viewpoint. Topics to be covered include Jacobians for matrix transformation, matrix ensembles and their eigenvalue probability density functions, equilibrium measures, global and local statistical q... Detailed Information MAST90103Type Elective | |

Computational Differential EquationsElective | 12.5 |

## Computational Differential EquationsMany processes in the natural sciences, engineering and finance are described mathematically using ordinary or partial differential equations. Only the simplest or those with special structure can be solved exactly. This subject discusses common techniques for computing numerical solutions to differential equations and introduces the major themes of accuracy, stability and efficiency. Understanding these basic properties of scientific computing algorithms should prevent the unwary from using software packages inappropriately or uncritically, and provide a foundation for devising methods for nonstandard problems. We cover both time-independent problems, in one and higher space dimensions, ... Detailed Information MAST90026Type Elective | |

Mathematical BiologyElective | 12.5 |

## Mathematical BiologyModern techniques have revolutionised biology and medicine, but interpretative and predictive tools are needed. Mathematical modelling is such a tool, providing explanations for counter-intuitive results and predictions leading to new experimental directions. The broad flavour of the area and the modelling process will be discussed. Applications will be drawn from many areas including population growth, epidemic modelling, biological invasion, pattern formation, tumour modelling, developmental biology and tissue engineering. A large range of mathematical techniques will be discussed, for example discrete time models, ordinary differential equations, partial differential equations, stochas... Detailed Information MAST90011Type Elective | |

Introduction to String TheoryElective | 12.5 |

## Introduction to String TheoryThe first half of this subject is an introduction to two-dimensional conformal field theory with emphasis on the operator formalism and explicit calculations. The second half is an introduction to string theory based on the first half. For concreteness, the representation theory of Virasoro algebra and bosonic strings will be emphasized. Detailed Information MAST90069Type Elective | |

Mathematical Statistical MechanicsElective | 12.5 |

## Mathematical Statistical MechanicsThe goal of statistical mechanics is to describe the behaviour of bulk matter starting from a physical description of the interactions between its microscopic constituents. This subject introduces the Gibbs probability distributions of classical statistical mechanics, the relations to thermodynamics and the modern theory of phase transitions and critical phenomena. The central concepts of critical exponents, universality and scaling are emphasized throughout. Applications include the ideal gases, magnets, fluids, one-dimensional Ising and Potts lattice spin models, random walks and percolation as well as approximate methods of solution. Detailed Information MAST90060Type Elective | |

Exactly Solvable ModelsElective | 12.5 |

## Exactly Solvable ModelsIn mathematical physics, a wealth of information comes from the exact, non-perturbative, solution of quantum models in one-dimension and classical models in two-dimensions. This subject is an introduction to this beautiful and deep subject. Yang-Baxter equations, Bethe ansatz and matrix product techniques are developed in the context of the critical two-dimensional Ising model, dimers, free fermions, the 6-vertex model, percolation, quantum spin chains and the stochastic asymmetric simple exclusion model. The algebraic setting incorporates the quantum groups, and the Temperley-Lieb and braid-monoid algebras. Detailed Information MAST90065Type Elective | |

Advanced Modelling: Case StudiesElective | 12.5 |

## Advanced Modelling: Case StudiesMathematical modelling can give deep insight into many complex systems that arise in nature and technology. It is also used to describe and predict new phenomena, test hypotheses and investigate novel avenues for experiments. This subject presents a series of advanced case studies that demonstrate the utility of mathematical modelling and develop the student's ability to tackle real-world problems arising in scientific, medical or industrial contexts. Mathematical approaches will include discrete, computational and asymptotic methods. The use of appropriate approximations and the interpretation of solutions in the context of the original problem will be emphasised. Detailed Information MAST90080Type Elective |

Discrete Mathematics & Operations Research specialisation - Students complete: | |
---|---|

Core Subjects | Points |

Advanced Discrete MathematicsCore | 12.5 |

## Advanced Discrete MathematicsThe subject consists of three main topics. The bijective principle with applications to maps, permutations, lattice paths, trees and partitions. Algebraic combinatorics with applications rings, symmetric functions and tableaux. Ordered sets with applications to generating functions and the structure of combinatorial objects. Detailed Information MAST90030Type Core | |

Optimisation for IndustryCore | 12.5 |

## Optimisation for IndustryThe use of mathematical optimisation is widespread in business, where it is a key analytical tool for managing and planning business operations. It is also required in many industrial processes and is useful to government and community organizations. This subject will expose students to operations research techniques as used in industry. A heavy emphasis will be placed on the modelling process that turns an industrial problem into a mathematical formulation. The focus will then be on how to solve the resulting mathematical problem. Mathematical programming and (meta)-heuristic techniques will be reviewed and applied to selected problems. Detailed Information MAST90014Type Core |

37.5 credit points selected from: | |
---|---|

Elective Subjects | Points |

Approximation Algorithms and HeuristicsElective | 12.5 |

## Approximation Algorithms and HeuristicsMany discrete optimisation problems encountered in practice are too difficult to solve exactly in a reasonable time frame. Approximation algorithms and heuristics are the most widely used approaches for obtaining reasonably accurate solutions to such hard problems. This subject introduces the basic concepts and techniques underlying these “inexact” approaches. We will address the following fundamental questions in the subject: How difficult is the problem under consideration? How closely can an optimal solution be approximated? And how can we go about finding near-optimal solutions in an efficient way? We will discuss methodologies for analysing the complexity and approximability of some ... Detailed Information MAST90098Type Elective | |

Scheduling and OptimisationElective | 12.5 |

## Scheduling and OptimisationScheduling is critical to manufacturing, mining, and logistics, and is of increasing importance in healthcare and service industries. Most automated systems, ranging from elevators to industrial robots, embed some kind of scheduling algorithms. Building on the Optimisation background provided in Optimisation for Industry, this subject teaches students how to solve more advanced problems. A particular focus will be scheduling problems, but other more general assignment problems will be discussed. Detailed Information MAST90050Type Elective | |

Network OptimisationElective | 12.5 |

## Network OptimisationMany practical problems in management, operations research, telecommunication and computer networking can be modelled as optimisation problems on networks. Here the underlying structure is a graph. This subject is an introduction to optimisation problems on networks with a focus on theoretical results and efficient algorithms. It covers classical problems that can be solved in polynomial time, such as shortest paths, maximum matchings, maximum flows, and minimum cost flows. Other topics include complexity and NP-completeness, matroids and greedy algorithms, approximation algorithms, multicommodity flows, and network design. This course is beneficial for all students of discrete mathematic... Detailed Information MAST90013Type Elective | |

Enumerative CombinatoricsElective | 12.5 |

## Enumerative CombinatoricsThe subject is about the use of generating functions for enumeration of combinatorial structures, including partitions of numbers, partitions of sets, permutations with restricted cycle structure, connected graphs, and other types of graph. The subject covers the solution of recurrence relations, methods of asymptotic enumeration, and some applications in statistical mechanics. The methods covered have widespread applicability, including in areas of pure and applied mathematics and computer science. Detailed Information MAST90031Type Elective | |

Experimental MathematicsElective | 12.5 |

## Experimental MathematicsModern computers have developed far beyond being great devices for numerical simulations or tedious but straightforward algebra; and in 1990 the first mathematical research paper was published whose sole author was a thinking machine known as Shalosh B Ekhad. This course will discuss some of the great advances made in using computers to purely algorithmically discover (and prove!) nontrivial mathematical theorems in for example Number Theory and Algebraic Combinatorics. Topics include: Automated hypergeometric summation, Groebner basis, Chaos theory, Number guessing, Recurrence relations, BBP formulas. Detailed Information MAST90053Type Elective |

Pure Mathematics specialisation - students complete: | |
---|---|

Core Subjects | Points |

Measure TheoryCore | 12.5 |

## Measure TheoryMeasure Theory formalises and generalises the notion of integration. It is fundamental to many areas of mathematics and probability and has applications in other fields such as physics and economics. Students will be introduced to Lebesgue measure and integration, signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative, conditional expectation, Borel sets and standard Borel spaces, product measures, and the Riesz representation theorem. Detailed Information MAST90012Type Core | |

Algebraic TopologyCore | 12.5 |

## Algebraic TopologyThis subject studies topological spaces and continuous maps between them. It demonstrates the power of topological methods in dealing with problems involving shape and position of objects and continuous mappings, and shows how topology can be applied to many areas, including geometry, analysis, group theory and physics. The aim is to reduce questions in topology to problems in algebra by introducing algebraic invariants associated to spaces and continuous maps. Important classes of spaces studied are manifolds (locally Euclidean spaces) and CW complexes (built by gluing together cells of various dimensions). Topics include: homotopy of maps and homotopy equivalence of spaces, homotopy gro... Detailed Information MAST90023Type Core |

37.5 credit points selected from: | |
---|---|

Elective Subjects | Points |

Algebraic GeometryElective | 12.5 |

## Algebraic GeometryThis course is an introduction to algebraic geometry. Algebraic geometry is the study of zero sets of polynomials. It exploits the interplay between rings of functions and the underlying geometric objects on which they are defined. It is a fundamental tool in may areas of mathematics, including number theory, physics and differential geometry. The syllabus includes affine and projective varieties, coordinate ring of functions, the Nullstellensatz, Zariski topology, regular morphisms, dimension, smoothness and singularities, sheaves, schemes. Detailed Information MAST90097Type Elective | |

Commutative and Multilinear AlgebraElective | 12.5 |

## Commutative and Multilinear AlgebraThe subject covers aspects of multilinear and commutative algebra as well as two substantial applications. Within multilinear algebra this includes bilinear forms and `multilinear products’ of vector spaces, such as tensor products. Commutative algebra concerns itself with properties of commutative rings, such as polynomial rings and their quotients and to modules over such rings. Both topics have wide application, both to other parts of mathematics and to physics. Much of this theory was developed for applications in geometry and in number theory, and the theorems can be used to cast substantial light on problems from geometry and number theory. Detailed Information MAST90025Type Elective | |

Groups, Categories & Homological AlgebraElective | 12.5 |

## Groups, Categories & Homological AlgebraAs well as being beautiful in its own right, algebra is used in many areas of mathematics, computer science and physics. This subject provides a grounding in several fundamental areas of modern advanced algebra including Lie groups, combinatorial group theory, category theory and homological algebra.The material complements that covered in the subject Commutative and Mutlilinear Algebra without assuming it as prerequisite. Detailed Information MAST90068Type Elective | |

Functional AnalysisElective | 12.5 |

## Functional AnalysisFunctional analysis is a fundamental area of pure mathematics, with countless applications to the theory of differential equations, engineering, and physics. The students will be exposed to the theory of Banach spaces, the concept of dual spaces, the weak-star topology, the Hahn-Banach theorem, the axiom of choice and Zorn's lemma, Krein-Milman, operators on Hilbert space, the Peter-Weyl theorem for compact topological groups, the spectral theorem for infinite dimensional normal operators, and connections with harmonic analysis. Detailed Information MAST90020Type Elective | |

Representation TheoryElective | 12.5 |

## Representation TheorySymmetries arise in mathematics as groups and Representation Theory is the study of groups via their actions on vector spaces. It has important applications in many fields: physics, chemistry, economics, biology and others. This subject will provide the basic tools for studying actions on vector spaces. The course will focus on teaching the basics of representation theory via favourite examples: symmetric groups, diagram algebras, matrix groups, reflection groups. In each case the irreducible characters and irreducible modules for the group (or algebra) will be analysed, developing more and more powerful tools as the course proceeds. Examples that will form the core of the material for ... Detailed Information MAST90017Type Elective | |

Differential Topology and GeometryElective | 12.5 |

## Differential Topology and GeometryThis subject extends the methods of calculus and linear algebra to study the geometry and topology of higher dimensional spaces. The ideas introduced are of great importance throughout mathematics, physics and engineering. This subject will cover basic material on the differential topology of manifolds including integration on manifolds, and give an introduction to Riemannian geometry. Topics include: Differential Topology: smooth manifolds, tangent spaces, inverse and implicit function theorems, differential forms, bundles, transversality, integration on manifolds, de Rham cohomology; Riemanian Geometry: connections, geodesics, and curvature of Riemannian metrics; examples coming from Li... Detailed Information MAST90029Type Elective | |

Riemann Surfaces and Complex AnalysisElective | 12.5 |

## Riemann Surfaces and Complex AnalysisRiemann surfaces arise from complex analysis. They are central in mathematics, appearing in seemingly diverse areas such as differential and algebraic geometry, number theory, integrable systems, statistical mechanics and string theory. The first part of the subject studies complex analysis. It assumes students have completed a first course in complex analysis so begins with a quick review of analytic functions and Cauchy's theorem, emphasising topological aspects such as the argument principle and Rouche's theorem. Topics also include: Schwarz's lemma; limits of analytic functions, normal families, Riemann mapping theorem; multiple-valued functions, differential equations and Riemann sur... Detailed Information MAST90056Type Elective |

Statistics & Stochastic Processes specialisation - Students complete: | |
---|---|

Core Subjects | Points |

Mathematical StatisticsCore | 12.5 |

## Mathematical StatisticsThe theory of statistical inference is important for applied statistics and as a discipline in its own right. After reviewing random samples and related probability techniques including inequalities and convergence concepts the theory of statistical inference is developed. The principles of data reduction are discussed and related to model development. Methods of finding estimators are given, with an emphasis on multi-parameter models, along with the theory of hypothesis testing and interval estimation. Both finite and large sample properties of estimators are considered. Applications may include robust and distribution free methods, quasi-likelihood and generalized estimating equations. ... Detailed Information MAST90082Type Core | |

Random ProcessesCore | 12.5 |

## Random ProcessesThe subject covers the key aspects of the theory of stochastic processes that plays the central role in modern probability and has numerous applications in natural sciences and industry. We discuss the following topics: ways to construct and specify random processes, discrete time martingales, Levy processes and more general continuous time Markov processes, point processes. Applications to modelling random phenomena evolving in time are discussed throughout the course. Detailed Information MAST90019Type Core |

37.5 credit points selected from: | |
---|---|

Elective Subjects | Points |

Stochastic Calculus with ApplicationsElective | 12.5 |

## Stochastic Calculus with ApplicationsThis subject provides an introduction to stochastic calculus and mathematics of financial derivatives. Stochastic calculus is essentially a theory of integration of a stochastic process with respect to another stochastic process, created for situations where conventional integration will not be possible. Apart from being an interesting and deep mathematical theory, stochastic calculus has been used with great success in numerous application areas, from engineering and control theory to mathematical biology, theory of cognition and financial mathematics. Detailed Information MAST90059Type Elective | |

Mathematics of RiskElective | 12.5 |

## Mathematics of RiskMathematical modelling of various types of risk has become an important component of the modern financial industry. The subject discusses the key aspects of the mathematics of market risk. Main concepts include loss distributions, risk and dependence measures, copulas, risk aggregation and allocation principles, elements of extreme value theory. The main theme is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Detailed Information MAST90051Type Elective | |

The Practice of StatisticsElective | 12.5 |

## The Practice of StatisticsThis subject builds on methods and techniques learned in theoretical subjects by studying the application of statistics in real contexts. Emphasis is on the skills needed for a practising statistician, including the development of mature statistical thinking, organizing the structure of a statistical problem, the contribution to the design of research from a statistical point of view, measurement issues and data processing. The subject deals with thinking about data in a broad context, and skills required in statistical consulting. Detailed Information MAST90027Type Elective | |

Statistical ModellingElective | 12.5 |

## Statistical ModellingStatistical models are central to applications of statistics and their development motivates new statistical theories and methodologies. Commencing with a review of linear and generalized linear models, analysis of variance and experimental design, the theory of linear mixed models is developed and model selection techniques are introduced. Approaches to non and semiparametric inference, including generalized additive models, are considered. Specific applications may include longitudinal data, survival analysis and time series modelling. Detailed Information MAST90084Type Elective | |

Advanced ProbabilityElective | 12.5 |

## Advanced ProbabilityThis subject mostly explores the key concept from Probability Theory: convergence of probability distributions, which is fundamental for Mathematical Statistics and is widely used in other applications. We study in depth the classical method of characteristic functions and discuss alternative approaches to proving limit theorems of Probability Theory. Detailed Information MAST90081Type Elective | |

Computational Statistics and Data MiningElective | 12.5 |

## Computational Statistics and Data MiningComputing techniques and data mining methods are indispensible in modern statistical research and applications, where “Big Data” problems are often involved. This subject will introduce a number of recently developed statistical data mining methods that are scalable to large datasets and high-performance computing. These include regularized regression such as the Lasso; tree based methods such as bagging, boosting and random forests; and support vector machines. Important statistical computing algorithms and techniques used in data mining will be explained in detail. These include the bootstrap, cross-validation, the EM algorithm, and Markov chain Monte Carlo methods including the Gibbs s... Detailed Information MAST90083Type Elective | |

Multivariate Statistical TechniquesElective | 12.5 |

## Multivariate Statistical TechniquesMultivariate statistics concerns the analysis of collections of random variables that has general applications across the sciences and more recently in bioinformatics. It overlaps machine learning and data mining, and leads into functional data analysis. Here random vectors and matrices are introduced along with common multivariate distributions. Multivariate techniques for clustering, classification and data reduction are given. These include discriminant analysis and principal components. Classical multi-variate regression and analysis of variance methods are considered. These approaches are then extended to high dimensional data, such as that commonly encountered in bioinformatics, mot... Detailed Information MAST90085Type Elective |

All students complete 25 credit points selected from a single specialisation other than their own, and: | |
---|---|

Professional Skills Subjects | Points |

Systems Modelling and SimulationOther | 12.5 |

## Systems Modelling and SimulationModern science and business makes extensive use of computers for simulation, because complex real-world systems often cannot be analysed exactly, but can be simulated. Using simulation we can perform virtual experiments with the system, to see how it responds when we change parameters, which thus allows us to optimise its performance. We use the language R, which is one of the most popular modern languages for data analysis. Detailed Information MAST90045Type Other |

A 50 credit point Research Project (25 credit points in special circumstances) comprising of: | |
---|---|

Research Project | Points |

Research Project Part ACore | 12.5 |

## Research Project Part AIn this subject, students undertake a substantial research program in the area of Mathematics and Statistics. The research will be conducted under the supervision of a member of the School's academic staff. A list of the research interests of the Department of Mathematics and Statistics is outlined on the website of the Department. The results will be reported in the form of a thesis and an oral presentation. Detailed Information MAST90075Type Core | |

Research Project Part BCore | 12.5 |

## Research Project Part BDetailed Information MAST90076Type Core | |

Research Project Part CCore | 25 |

## Research Project Part CDetailed Information MAST90077Type Core |

And 50 credit points selected from any of the specialisations, including up to 25 credit points selected from: | |
---|---|

Elective Subjects | Points |

Constraint ProgrammingElective | 12.5 |

## Constraint ProgrammingAIMS The aims for this subject is for students to develop an understanding of approaches to solving combinatorial optimization problems with computers, and to be able to demonstrate proficiency in modelling and solving programs using a high-level modelling language, and understanding of different solving technologies. The modelling language used is MiniZinc. INDICATIVE CONTENT Topics covered will include: Modelling with Constraints Global constraints Multiple Modelling Model Debugging Scheduling and Packing Finite domain constraint solving Mixed Integer Programming Detailed Information COMP90046Type Elective | |

Statistical Machine LearningElective | 12.5 |

## Statistical Machine LearningAIMS With exponential increases in the amount of data becoming available in fields such as finance and biology, and on the web, there is an ever-greater need for methods to detect interesting patterns in that data, and classify novel data points based on curated data sets. Learning techniques provide the means to perform this analysis automatically, and in doing so to enhance understanding of general processes or to predict future events. Topics covered will include: supervised learning, semi-supervised and active learning, unsupervised learning, kernel methods, probabilistic graphical models, classifier combination, neural networks. This subject is intended to introduce graduate students... Detailed Information COMP90051Type Elective | |

Cryptography and SecurityElective | 12.5 |

## Cryptography and SecurityAIMS The subject will explore foundational knowledge in the area of cryptography and information security. The overall aim is to gain an understanding of fundamental cryptographic concepts like encryption and signatures and use it to build and analyse security in computers, communications and networks. This subject covers fundamental concepts in information security on the basis of methods of modern cryptography, including encryption, signatures and hash functions. This subject is an elective subject in the Master of Engineering (Software). It can also be taken as an advanced elective in Master of Information Technology. INDICATIVE CONTENT The subject will be made up of three parts: Cry... Detailed Information COMP90043Type Elective | |

Declarative ProgrammingElective | 12.5 |

## Declarative ProgrammingAIMS Declarative programming languages provide elegant and powerful programming paradigms which every programmer should know. This subject presents declarative programming languages and techniques. INDICATIVE CONTENT The dangers of destructive update Functional programming Recursion Strong type systems Parametric polymorphism Algebraic types Type classes Defensive programming practice Higher order programming Currying and partial application Lazy evaluation Monads Logic programming Unification and resolution Nondeterminism, search, and backtracking. Detailed Information COMP90048Type Elective | |

Algorithms and ComplexityElective | 12.5 |

## Algorithms and ComplexityAIMS The aim of this subject is for students to develop familiarity and competence in assessing and designing computer programs for computational efficiency. Although computers manipulate data very quickly, to solve large-scale problems, we must design strategies so that the calculations combine effectively. Over the latter half of the 20th century, an elegant theory of computational efficiency developed. This subject introduces students to the fundamentals of this theory and to many of the classical algorithms and data structures that solve key computational questions. These questions include distance computations in networks, searching items in large collections, and sorting them in ord... Detailed Information COMP90038Type Elective | |

Particle PhysicsElective | 12.5 |

## Particle PhysicsParticle Physics is the study of the elementary constituents of matter, and the fundamental forces of nature. The subject introduces modern elementary particle physics, with an emphasis on the theoretical description of the Standard Model of Particle Physics and its experimental basis. Specific topics may include basic group theory; parity and CP violation; global and local symmetries; non-abelian gauge theory; QCD and the quark model; running coupling constants and asymptotic freedom; spontaneous symmetry breaking and the Higgs mechanism; the complete Standard Model Lagrangian; interactions of particles with matter; accelerators and detectors; deep inelastic scattering and structure func... Detailed Information PHYC90011Type Elective | |

Physical CosmologyElective | 12.5 |

## Physical CosmologyThis subject provides an advanced introduction to physical cosmology. Specific topics may include the isotropic homogeneous Universe, the Robertson Walker metric, the Friedmann equations, baryogenesis, inflation, big-bang nucleosynthesis, the recombination era, density fluctuations as the origin of galaxies, the cosmic microwave background, linear and non-linear growth of structure, the Press-Schechter mass function, reionization of the IGM and gravitational lensing. Examples are drawn from past and current cosmological observations. Detailed Information PHYC90009Type Elective | |

Statistical MechanicsElective | 12.5 |

## Statistical MechanicsThis subject provides an advanced introduction to the mathematical theory of collective phenomena in complex, many-body systems, in equilibrium and far from equilibrium, with an emphasis on critical phenomena and the emergence of long-range order. Specific topics may include phase transitions, transfer matrices, mean-field theory, Landau-Ginzburg theory, renormalization group, diffusive stochastic processes (Fokker-Planck equations), birth-death processes (master equations), kinetic transport, and spatio-temporal pattern formation in unstable nonlinear systems (bifurcations, chaos, reaction-diffusion equations). Examples are drawn from physics, chemistry, biology, and the social sciences. Detailed Information PHYC90010Type Elective | |

General RelativityElective | 12.5 |

## General RelativityThis subject provides an advanced introduction to Einstein's theory of general relativity. Specific topics may inlcude special relativity, manifolds and curvature, experimental tests, Einstein's equations, the Schwarzschild solution and black holes, weak fields and gravitational radiation. Examples will be drawn from particle physics, astrophysics and cosmology. Detailed Information PHYC90012Type Elective | |

Quantum Field TheoryElective | 12.5 |

## Quantum Field TheoryThis subject introduces quantum field theory, the combination of quantum mechanics and relativity that explains the fundamental structure of matter and the physics of the early universe. The course has an emphasis on quantum electrodynamics. Specific topics will include an introduction to classical field theory, the Euler-Lagrange equations and Noether’s theorem; the Dirac and Klein-Gordon equations; the quantisation of free scalar, Dirac and vector fields; covariant perturbation theory, the Smatrix and Feynman diagrams; the computation of elementary processes in quantum electrodynamics. Detailed Information PHYC90008Type Elective | |

Quantum MechanicsElective | 12.5 |

## Quantum MechanicsQuantum Mechanics introduces a dramatically new and rich understanding of the universe. In addition to providing a much deeper insight into the world of atoms and subatomic particles than afforded by classical Newtonian physics, Quantum Mechanics underpins advances in science across all disciplines, from molecular biology to astrophysics. This subject provides a rigorous mathematical formalism for advanced quantum mechanics, laying the foundation for further fundamental theoretical physics and research-level experimental physics in frontier areas such as quantum communication and quantum computation. The subject describes the Hilbert-space formulation of quantum wave mechanics, including ... Detailed Information PHYC90007Type Elective | |

Statistics for BioinformaticsElective | 12.5 |

## Statistics for BioinformaticsBioinformatics involves the analysis of biological data and randomness is inherent in both the biological processes themselves and the sampling mechanisms by which they are observed. This subject first introduces stochastic processes and their applications in Bioinformatics, including evolutionary models. It then considers the application of classical statistical methods including estimation, hypothesis testing, model selection, multiple comparisons, and multivariate statistical techniques in Bioinformatics. Detailed Information BINF90001Type Elective | |

Elements of BioinformaticsElective | 12.5 |

## Elements of BioinformaticsBioinformatics is a key research tool in modern agriculture, medicine, and the life sciences in general. It forms a bridge between complex experimental and clinical data and the elucidation of biological knowledge. This subject presents bioinformatics in the context of its role in science, using examples from a variety of fields to illustrate the history, current status, and future directions of bioinformatics research and practice. Detailed Information BINF90002Type Elective |