## Level 3 Subjects

The following are our third year level subjects. The headings link to the full descriptions in the University Handbook.

MAST30001 Stochastic Modelling

Stochastic processes occur widely in diverse areas such as finance, telecommunications, genetics, chemistry, speech pathology and more. This subject introduces and develops the theory of stochastic processes with an emphasis on Markov chains, and illustrates this theory using a range of examples from the real world.

MAST30005 Algebra

Algebra has a long history of important applications throughout mathematics, science and engineering, and is also studied for its intrinsic beauty. In this subject we study the algebraic laws satisfied by familiar objects such as integers, polynomials and matrices. Abstraction simplifies and unifies our understanding of these structures and enables us to apply our results more broadly. Students will gain experience with abstract algebraic concepts and methods. General structural results are proved and algorithms developed to determine the invariants described

MAST30011 Graph Theory

This subject is an introduction to the modern field of graph theory. It emphasises the relationship between proving theorems in mathematics and the construction of algorithms to find the solutions of mathematical problems, within the context of graph theory. The subject provides material that supplements other areas of study such as operations research and computer science.

MAST30012 Discrete Mathematics

This is a core subject on discrete mathematics and is independent of the second year subject Discrete Maths and Operations Research. The subject consists of five main topics, three of which are bijective aspects of permutations and combinations, recursive structures relating to the Fibonacci sequence, and combinatorics of the Rubik cube. This material is of broad relevance to higher level mathematics, and offers a view of applied mathematics distinct from continuum modelling.

MAST30013 Techniques in Operations Research

This subject introduces a number of basic techniques of operations research. It develops the formulation of operations research models and algorithms with application in production planning, scheduling, inventory management and capital budgeting. Case studies and projects are undertaken and computer packages utilized.

MAST30020 Probability for Inference

This subject provides a bridge between introductory probability and the more rigorous measure theoretic approach. Probability is developed in the framework of measure theory but the emphasis is on the concepts and techniques required for advanced probability, stochastic processes and statistics.

MAST30021 Complex Analysis

Complex analysis is a core subject in pure and applied mathematics, as well as the physical and engineering sciences. While it is true that physical phenomena are given in terms of real numbers and real variables, it is often too difficult and sometimes not possible, to solve the algebraic and differential equations used to model these phenomena without introducing complex numbers and complex variables and applying the powerful techniques of complex analysis.

MAST30022 Decision Making

This subject introduces the essential features of decision-making situations encountered in operations research investigations through the development of basic mathematical approaches. It shows how to construct formal mathematical models for practical decision-making situations such as two-person games, multi-objective optimisation problems and stochastic decision problems. It shows students further uses of linear programming and introduces dynamic programming techniques.

MAST30024 Geometry

This subject introduces three areas of geometry that play a key role in many branches of mathematics and physics. In differential geometry, calculus and the concept of curvature will be used to study the shape of curves and surfaces. In topology, geometric properties that are unchanged by continuous deformations will be studied to find a topological classification of surfaces. In algebraic geometry, curves and surfaces defined by polynomial equations will be explored. Remarkable connections between these areas will be discussed.

MAST30025 Linear Statistical Models

Linear models are central to the theory and practice of modern statistics. They are used to model a response as a linear factor of explanatory variables and are the most widely used statistical models in practice. Starting with examples from a range of application areas this subject develops an elegant unified theory that is illustrated on a variety of common models and experimental designs.

MAST30026 Metric and Hilbert Spaces

This core subject provides a basis for further studies in modern analysis, geometry, topology, differential equations and quantum mechanics. It introduces the idea of a metric space with a general distance function, and the resulting concepts of convergence, continuity, completeness and compactness. The subject also introduces Hilbert spaces: infinite dimensional vector spaces (typically function spaces) equipped with an inner product that allows geometric ideas to be used to study these spaces and the linear maps between them.

MAST30027 Modern Applied Statistics

Modern applied statistics combines the power of modern statistical computing packages and theoretical statistics. It extends linear models to allow responses that are not normally distributed or whose mean is a non-linear function of predictors. It also makes extensive use of computer intensive techniques to explore the sampling distribution of estimators.

MAST30028 Numerical Methods & Scientific Computing

Most mathematical problems arising from the physical sciences, engineering, life sciences and finance are sufficiently complicated to require computational methods for their solution. This subject introduces students to the process of numerical approximation and computer simulation, applied to simple and commonly encountered stochastic or deterministic models. An emphasis is on the development and implementation of algorithms for the solution of continuous problems including aspects of their efficiency, accuracy and stability. Topics covered will include simple stochastic simulation, direct methods for linear systems, data fitting of linear and nonlinear models, and time-stepping methods for initial value problems.

MAST30030 Applied Mathematical Modelling

This subject demonstrates how the mathematical modelling process naturally gives rise to certain classes of ordinary and partial differential equations in many contexts. This includes the modelling of infectious diseases, the flow of traffic and the dynamics of fluids. It advances the student’s knowledge of the modelling process, as well as addressing important mathematical ideas in deterministic modelling and the challenges of system non-linearity.

MAST30031 Methods of Mathematical Physics

This subject builds on, and extends earlier, related undergraduate subjects with topics that are useful to applied mathematics, mathematical physics and physics students, as well as pure mathematics students interested in applied mathematics and mathematical physics.
These include special functions, such as Legendre and Bessel functions, integral equations, more general formulations of vector calculus using differential forms, and advanced techniques from complex analysis.

MAST30032 Biological Modelling & Simulation

This subject introduces the concepts of mathematical and computational modelling of biological systems, and how they are applied to data in order to study the underlying drivers of observed behaviour. The subject emphasises the role of abstraction and simplification of biological systems and requires an understanding of the underlying biological mechanisms. Combined with an introduction to sampling-based methods for statistical inference, students will learn how to identify common patterns in the rich and diverse nature of biological phenomena and appreciate how the modelling process leads to new insight into biological phenomena.

MAST30033 Statistical Genomics

This subject introduces the biology and technology underlying modern genomics data, features of the resulting data types including the frequency and patterns of error and missingness, and the statistical methods used to analyse them. It will include hands-on data analysis using R software. The material covered will span the following four areas: introduction to genomics technology and the resulting data, population genetics including stochastic models and statistical inference, association analysis including tests of association and major sources of confounding, and heritability and prediction both in human genetics and for animal and plant breeding.