# Mathematics

### Mathematics

**MATH1001 Differential Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH1002 Linear Algebra**

*This unit of study does not have Data Audit Committee approval*

This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

**MATH1003 Integral Calculus and Modelling**

**MATH1004 Discrete Mathematics**

This unit provides an introduction to fundamental aspects of discrete mathematics, which deals with 'things that come in chunks that can be counted'. It focuses on the enumeration of a set of numbers, viz. Catalan numbers. Topics include sets and functions, counting principles, Boolean expressions, mathematical induction, generating functions and linear recurrence relations, graphs and trees.

**MATH1005 Statistics**

This unit offers a comprehensive introduction to data analysis, probability, sampling, and inference including t-tests, confidence intervals and chi-squared goodness of fit tests.

**MATH1011 Applications of Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH1013 Mathematical Modelling**

In this unit of study students learn how to construct, interpret and solve simple differential equations and recurrence relations. Specific techniques include separation of variables, partial fractions and first and second order linear equations with constant coefficients. Students are also shown how to iteratively improve approximate numerical solutions to equations.

**MATH1014 Introduction to Linear Algebra**

**MATH1015 Biostatistics**

*This unit of study does not have Data Audit Committee approval*

**MATH1111 Introduction to Calculus - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH1901 Differential Calculus (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH1902 Linear Algebra (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH1903 Integral Calculus and Modelling Advanced**

This unit of study parallels the normal unit MATH1003 but goes more deeply into the subject matter and requires more mathematical sophisticaton.

**MATH1905 Statistics (Advanced)**

**MATH1906 Mathematics (Special Studies Program) A - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH1907 Mathematics (Special Studies Program) B**

**MATH2061 Linear Mathematics and Vector Calculus**

*This unit of study does not have Data Audit Committee approval*

**MATH2065 Partial Differential Equations (Intro)**

**MATH2068 Number Theory and Cryptography**

**MATH2069 Discrete Mathematics and Graph Theory**

*This unit of study does not have Data Audit Committee approval*

**MATH2070 Optimisation and Financial Mathematics**

The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model, log-optimal portfolios and the Kelly criterion; dynamical programming. Some understanding of probability theory including distributions and expectations is required in this part.

Theory developed in lectures will be complemented by computer laboratory sessions using MATLAB. Minimal computing experience will be required.

**MATH2916 Working Seminar A (SSP) - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH2917 Working Seminar B (SSP) - Departmental permission is required for this unit**

*This unit of study does not have Data Audit Committee approval*

**MATH2961 Linear Mathematics and Vector Calculus Adv**

*This unit of study does not have Data Audit Committee approval*

The connection between matrices and linear transformations is studied in detail. Determinants, introduced in first year, are revised and investigated further, as are eigenvalues and eigenvectors. The calculus component of the unit includes local maxima and minima, the inverse function theorem and Jacobians.

There is an informal treatment of multiple integrals: double integrals, change of variables, triple integrals, line and surface integrals, Green's theorem and Stokes' theorem.

**MATH2962 Real and Complex Analysis (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH2965 Partial Differential Equations Intro Adv**

**MATH2968 Algebra (Advanced)**

**MATH2969 Discrete Mathematics and Graph Theory Adv**

*This unit of study does not have Data Audit Committee approval*

**MATH2970 Optimisation and Financial Mathematics Adv**

**MATH2988 Number Theory and Cryptography Advanced**

**MATH3061 Geometry and Topology**

**MATH3063 Differential Equations and Biomaths**

*This unit of study does not have Data Audit Committee approval*

**MATH3066 Algebra and Logic**

*This unit of study does not have Data Audit Committee approval*

The Propositional and Predicate Calculi are studied as model axiomatic systems in their own right, including sketches of proofs of consistency and completeness. The final part of the course introduces precise notions of computability and decidability, through abstract Turing machines, culminating in the unsolvability of the Halting Problem and the undecidability of First Order Logic.

**MATH3068 Analysis**

Power series are not adequate to solve the problem of representing periodic phenomena such as wave motion. This requires Fourier theory, the expansion of functions as sums of sines and cosines. This unit deals with this theory, Parseval's identity, pointwise convergence theorems and applications.

The unit goes on to introduce Bernoulli numbers, Bernoulli polynomials, the Euler MacLaurin formula and applications, the gamma function and the Riemann zeta function. Lastly we return to the foundations of analysis, and study limits from the point of view of topology.

**MATH3075 Financial Mathematics**

**MATH3076 Mathematical Computing**

*This unit of study does not have Data Audit Committee approval*

**MATH3078 PDEs and Waves**

To pass MATH3078, students must achieve satisfactory performance in the in-semester assessment component in order to pass the unit of study.

**MATH3961 Metric Spaces (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3962 Rings, Fields and Galois Theory (Adv)**

*This unit of study does not have Data Audit Committee approval*

The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

**MATH3963 Differential Equations and Biomaths (Adv)**

*This unit of study does not have Data Audit Committee approval*

**MATH3968 Differential Geometry (Advanced)**

**MATH3969 Measure Theory and Fourier Analysis (Adv)**

**MATH3974 Fluid Dynamics (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3975 Financial Mathematics (Advanced)**

**MATH3976 Mathematical Computing (Advanced)**

*This unit of study does not have Data Audit Committee approval*

**MATH3977 Lagrangian and Hamiltonian Dynamics (Adv)**

Students will be expected to solve fully dynamical systems of some complexity including planetary motion and to investigate stability using perturbation analysis. Hamilton-Jacobi theory will be used to elegantly solve problems ranging from geodesics (shortest path between two points) on curved surfaces to relativistic motion in the vicinity of black holes.

This unit is a useful preparation for units in dynamical systems and chaos, and complements units in differential equations, quantum theory and general relativity.

**MATH3978 PDEs and Waves (Advanced)**