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Master of Science - Mathematics and Statistics

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  • Objectives
    After completing this course students should have:

    * discovered the challenge of research in Mathematics and Statistics;
    * a deeper knowledge of Mathematics and Statistics;
    * completed a substantial piece of research; and
    * a sound preparation for future research in Mathematics or Statistics.
  • Academic Title
    Master of Science - Mathematics and Statistics
  • Course description
    Students must complete a total of 200 points over the two year full-time (or four year part-time) program, comprising:

    Discipline subjects
    (137.5 points)

    Students must take 11 of the following subjects:

    Statistics and Stochastic Processes

    o 600-655 Business Forecasting
    o Mathematics of Risk (available semester 2, 2010)
    o 620-618 Probability for Inference
    o 620-620 Statistical Inference
    o 620-624 Stochastic Processes
    o 620-639 Data Mining
    o 620-638 Consulting and Applied Statistics

    Operations Research and Discrete Mathematics

    o 620-616 Optimisation for Industry
    o 620-615 Network Optimisation (not available in 2010)
    o Scheduling and Optimisation (available semester 2, 2010)
    o 620-646 Advanced Discrete Mathematics
    o 620-647 Enumerative Combinatorics (not available in 2010)
    o Experimental Mathematics (available semester 1, 2010)

    Applied Mathematics

    o 620-637 Computational Differential Equations
    o 620-617 Phase Transitions and Critical Phenomena
    o 620-635 Advanced Materials Modelling
    o 620-629 Integrable Models (not available in 2010)
    o 620-644 Mathematical Biology (not available in 2010)
    o Partial Differential Equations (available semester 1, 2010)
    o Random Walks and Random Structures (available semester 2, 2010)

    Pure Mathematics

    o 620-645 Measure theory
    o 620-636 Commutative Algebra
    o 620-619 Representation Theory
    o 620-634 Algebraic Topology
    o 620-630 Algebraic Geometry (not available in 2010)
    o 620-640 Differential Geometry (not available in 2010)
    o 620-628 Functional Analysis (not available in 2010)
    o Differential Topology (available semester 2, 2010)
    o Complex Analysis (available semester 2, 2010)
    o Geometric Group Theory (available semester 2, 2010)

    With the approval of the supervisor and departmental Master program Coordinator, a student will be allowed to substitute up to three of the Discipline Mathematics & Statistics subjects with lower level subjects or subjects from contiguous areas. Of these substitute subjects, up to two can be 200 or 300 level subjects needed to obtain requisite knowledge for Master level Discipline Mathematics & Statistics subjects and up to two can be Master level subjects taught by other Departments of the University.

    Professional tools
    (12.5 points)

    Students undertaking the Master of Science (Mathematics and Statistics program) must take the Professional Tools subject 600-617 Systems Modelling and Simulation, unless they have completed 620-131 Scientific Programming and Simulation (2007) or equivalent. If students have previously completed 620-131 Scientific Programming and Simulation (2007) or equivalent, they must take one of the following Professional Tools subjects:

    Science Tools
    o eScience (available semester 2, 2010)
    o 600-618 Ethics and Responsibility in Science

    Communication Tools
    o 600-616 Science in Context
    o 600-619 Science and Communication

    Research Project (50 points)

    The Research Project is an integral part of the Master of Science (Mathematics and Statistics program) and a thesis is the main requirement for this component. Students must pass the Research Project to be awarded the Degree.

    Students enrolled in the Master of Science (Mathematics and Statistics program) are required to complete a 50 point Research Project. Students may enrol in one or more Research Project subjects as indicated below to ensure they have completed a total of 50 points by the end of their course.

        * 620-649 Research Project - 50 points
        * 620-650 Research Project - 37.5 points
        * 620-651 Research Project - 25.0 points
        * 620-652 Research Project - 12.5 points

    Subject     Semester     Credit Points
    620-630  Algebraic Geometry
    Algebraic geometry is the study of the zero sets of polynomials. As the name suggests, it combines algebra and geometry. It is a fundamental tool in many areas of mathematics, including differential geometry, number theory, integrable systems and in ...     Semester 2     12.50

    620-634  Algebraic Topology
    In this subject we study some of the fundamental questions in topology: classification of topological spaces and continuous maps between them. The aim is to reduce problems in topology to problems in algebra by introducing algebraic invariants associ...     Semester 1     12.50

    600-655  Business Forecasting
    Forecasting is an indispensable part of decision making in business management and government planning. This subject discusses the concept of forecasting and deals with standard forecasting tools. Topics covered include autoregressive, autoregressive...     Semester 2     12.50

    620-636  Commutative Algebra
    Commutative algebra is the basis of modern algebraic geometry. It provides the rigorous foundation for the study of curves and surfaces and their generalisations. Students will study: basic properties of rings, basic properties of modules including N...     Semester 1     12.50

    620-637  Computational Differential Equations
    This subject discusses techniques to determine numerical solutions to a variety of problems commonly encountered in science and engineering. Understanding the behaviour of the mathematical problem gives insight into the pitfalls for the unwary in usi...     Semester 1     12.50

    620-640  Differential Geometry
    In this course students will become familiar with the basic notions of Riemannian metrics and curvature, geodesics and concrete examples such as hypersurfaces in Euclidean space, Lie groups and homogeneous spaces. Some fundamental tools of global dif...     Semester 2     12.50

    620-638  Consulting and Applied Statistics
    This subject is about the application of statistics in real situations. It deals with thinking about data in a broad context; the client consultant relationship; consulting sessions; verbal and written communication skills; organizing the structure o...     Semester 1     12.50

    620-646  Advanced Discrete Mathematics
    The subject consists of four main topics. These are combinatorial logic by way of Sperner’s lemma and Ramsey theory; combinatorics on words and Sturmian sequences; bijective enumeration with applications to maps lattice paths and trees; i...     Semester 2     12.50

    620-647  Enumerative Combinatorics
    The 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 subj...     Semester 1     12.50

    620-628  Functional Analysis
    Functional Analysis is the study of spaces of functions and various structures on these spaces, in particular norms. This subject has important applications to differential and integral equations in mathematics, engineering and physics. The syllabus ...     Semester 2     12.50

    620-629  Integrable Models
    This subject studies integrable dynamical systems using basic ideas from analysis, algebraic combinatorics, representation theory, quantum field theory and algebraic geometry. The KP hierarchy of nonlinear partial differential equations is primarily ...     Semester 2     12.50

    620-644  Mathematical Biology
    Modern techniques have revolutionised biology and medicine, but interpretative and predictive tools are needed. Mathematical modelling is such a tool. It provides explanations for counter intuitive resultsand predictions leading to new experimental d...     Semester 1     12.50

    620-615  Network Optimisation
    Network optimization problems arise from a diversity of areas such as Industry, Management, VLSILayout, Transportation, Telecommunication, Computer Networking, Information Processing, etc. This subject is an introduction to Network Optimization with ...     Semester 2     12.50

    620-616  Optimisation for Industry
    The use of mathematical optimisation is widespread in business, where it is a key management tool for planning and operations. It is also required in many industrial processes and is useful to government and community organizations. This subject will...     Semester 1     12.50

    620-617  Phase Transitions and Critical Phenomena
    The subject introduces the Gibbs ensembles of classical statistical mechanics, the relations to thermodynamics and the modern theory of phase transitions and critical phenomena including the concepts of critical exponents, universality and scaling. A...     Semester 1     12.50

    620-619  Representation Theory
    Symmetries arise in mathematics as groups. Representation Theory is the study of groups via their action on vector spaces. It has important applications in many fields: physics, chemistry, economics, biology and others. This subject provides students...     Semester 1     12.50

    620-624  Stochastic Processes
    The subject discusses 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 in industry. Main concepts include finite dimensional distributions, p...     Semester 2     12.50

    620-645  Measure Theory
    Measure 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 a...     Semester 1     12.50

    620-618  Probability for Inference
    This is an advanced level presenting probability theory from the measure theoretic viewpoint. Topics covered include probability spaces and random variables, the properties of probability measures, Lebesgue decomposition, probability measures on fin...     Semester 1     12.50

    620-620  Statistical Inference
    Classical statistics is concerned with parametric models, which are idealized versions of reality that allow the development of an elegant mathematical theory of inference. Modern Statistics develops methods that weaken the assumptions of these class...     Semester 1     12.50

    620-639  Data Mining
    Data Mining refers to the management and analysis of large data sets. Data Mining became possible with the advent of large-scale data collection and the computing power necessary to process it. It involves all of the following steps 1. Data Warehous...     Semester 2     12.50

    620-635  Advanced Materials Modelling
    This subject focuses on physical principles and techniques for modelling the behaviour of advanced materials, which find applications in modern technological advances ranging from nanoelectromechanical systems and Atomic Force Microscopy to processe...     Semester 2     12.50

    620-649  Research Project
    No description available     Semester 1, Semester 2     50

    620-650  Research Project
    No description available     Semester 1, Semester 2     37.50

    620-651  Research Project
    No description available     Semester 1, Semester 2     25

    620-652  Research Project
    No description available     Semester 1, Semester 2     12.50

    600-618  Ethics and Responsibility in Science
    What is scientific fraud? What should a scientist do when he or she finds fraud is occurring on a scientific or medical research team? How does a scientist write and defend an ethics submission and get it approved? How can a scientist ensure complian...     Semester 2     12.50

    600-619  Science and Communication
    This subject reviews the range of competencies needed to operate effectively in the workplace.Students develop a clear understanding of the nature of managerial work and the kinds of skills required to manage oneself and others in organisations. Comm...     Semester 1     12.50

    600-616  Science in Context
    As a Scientist, one of the main challenges is to communicate scientific knowledge to the wider community. Whether the issues are big or small, communicating complex scientific knowledge needs to be ‘context relevant’. Increas...     Semester 2     12.50

    600-617  Systems Modelling and Simulation
    Modern 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...     Semester 1     12.50

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