MATH305 Partial Differential Equations

Description: MATH305 is in a central area of mathematics, as many physical problems in the world are modelled with partial differential equations. Various types of equations and their solutions are discussed. As many equations cannot be solved in analytical form, numerical methods of solution also are considered. The aim is to develop high level mathematical ability and problem solving skills. student who successfully completes this subject should be able to:
(i) recognise and solve first order partial differential equations;
(ii) classify second order partial differential equations as hyperbolic, elliptic or parabolic;
(iii) use appropriate methods of solution for each of the above types;
(iv) distinguish between methods of solving partial differential equations according to their type;
(v) assess the stability of the numerical methods used to solve partial differential equations;
(vi) demonstrate proficiency by using a laboratory package unassisted to successfully solve partial differential equations

Pre-requisites: MATH201 Multivariate and Vector Calculus and MATH202 Differential Equations, and MATH203 Linear Algebra

Descriptions: MATH201 is one of four core 200 level Mathematics subjects and is a prerequisite. for many 300 level subjects in Mathematics and Statistics. This subject extends the calculus of one variable to the calculus of more than one variable. Applications are given to maxima and minima, multiple integrals, vector calculus, line, surface and volume integrals, and to geometrical problems. A student who successfully completes this subject should be able to:
(i) distinguish space curves and surfaces;
(ii) contrast scalar and vector functions in three-dimensions;
(iii) differentiate functions of more than one independent variable;
(iv) differentiate vectors;
(v) determine rates of change of multivariable and scalar and vector functions;
(vi) manipulate derivative and integral formulations in two or more dimensions where the variables undergo transformation;
(vii) analyse surfaces for maxima and minima;
(viii) differentiate and integrate over three-dimensional space curves and
(ix) differentiate and integrate over three-dimensional surfaces and throughout three-dimensional volumes.

MATH202 is one of four core 200 level Mathematics subjects. This subject introduces the student to various special functions and differential equations and to techniques (both analytic and numerical) for their solution. Topics covered include exact first order equations, Gamma, Beta and Error functions, Laplace transforms, Fourier series, separation of variables for PDE's, basic numerical techniques, computer packages, and comparative accuracy of numerical techniques. A student who successfully completes this subject should be able to:
(i) evaluate and manipulate relevant integrals in terms of Gamma, Beta and Error functions;
(ii) recognise and evaluate integro-differential equations able to be solved by Laplace transform methods, and then solve them;
(iii) express relevant functions using their Fourier series or other representations;
(iv) solve partial differential equations by separation of variables techniques;
(v) compare methods of solving differential equations numerically and assess their accuracy;
(vi) use a laboratory package for solving differential equations.

MATH203 is one of four core 200 level Mathematics subjects. The study of systems of linear equations is important not only to mathematicians but also to scientists and engineers. Study of these systems is done both theoretically and numerically with geometrical interpretations given. It aims to build on students' knowledge of matrix algebra and vector analysis.
A student who successfully completes this subject should be able to:
(i) identify vector spaces and subspaces of vector spaces and find bases for them;
(ii) relate row and column spaces and null spaces to the solution of Ax- = b- and be able to discern relationships between the solution x- of a linear system and its coefficient matrix;
(iii) determine whether transformations are linear and perform simple geometry of linear transformations in R2;
(iv) diagonalise square matrices;
(v) solve linear systems numerically by a variety of direct and indirect methods;
(vi) use a matrix laboratory package for a variety of algebraic tasks.

MATH321 Numerical Analysis

Description: MATH321 is designed to extend the ideas developed in MATH202 and MATH203 as to how numerical and computational mathematics can be used to solve problems that have no analytic solution. The foci are problems in linear algebra and applications to real world problems. Specific techniques include algorithms for calculating eigenvalues and eigenvectors of a matrix. On successful completion of this subject, a student should be able to
(i) perform matrix decomposition by various methods;
(ii) determine the effectiveness of various numerical methods;
(iii) maximise the efficiency of various algorithms;
(iv) identify special matrices and implement appropriate methods;
(v) apply singular value decomposition where necessary;
(vi) be proficient in the use of a laboratory package for solving numerical linear algebra problems.

Pre-requisites: MATH202 and MATH203

Description: see above

MATH323 Topology and Chaos

Description: MATH323 aims to develop critical understanding and problem-solving skills in the context of topology and chaos theory. It is intended to convey some of the impact of chaos theory in other areas and encourage interest of the student in phenomena such as the Koch curve. Some concepts discussed are notions of distance, dynamical systems, fractals and the Mandelbrot set. Students who successfully complete this subject should be able to:
(i) define some of the basic concepts of topology;
(ii) see connections between topological ideas and chaotic phenomena;
(iii) deduce some elementary results for chaotic phenomena ;
(iv) apply some results of fixed point theory to derive some results in mathematical analysis;
(v) use and appreciate the need for rigorous argument when proving results in topology and chaos;
(vi) illustrate the way in which topological concepts can clarify and enhance the understanding of some topics in other areas.

Pre-requisites: MATH222 Continuous and Finite Mathematics

Description: MATH222 is for students who wish to continue in the mathematical analysis strand. Continuous Mathematics is concerned with the continuation of concepts introduced in first year calculus, including those of convergent sequence, continuous function and the integral of a function. Finite Mathematics is strictly independent of earlier work, but is related to first year algebra. A student who successfully completes this subject should be able to :
(i) construct proofs relating to convergent sequences, continuous functions, sequences and series of functions, and number theory;
(ii) identify situations where the interchange of integrals with limiting processes is valid;
(iii) calculate the Fourier series of various functions and/or calculate the iterations of some functions, and demonstrate an understanding of some of the problems associated with these procedures;
(iv) solve difference equations and present knowledge of some of their applications;
(v) describe some topics in number theory and/or combinatorics and of some of their applications; and
(vi) demonstrate an appreciation and understanding of the role of proof, problem-solving and clarity of argument in a mathematical context.

MATH345 Mathematics Project B

Description: The subject is a project individually chosen for the student, at a level appropriate to the 300 classification. The content may consist of (1) a placement in business or industry where substantial use is made of mathematical techniques; or (2) a project directed towards independent investigation by the student, written and/or oral presentations, and substantial interaction of the student with the supervisors of the project and other members of staff; or (3) a project directed to mastery of a mathematical package or language, with specific use of the package or language in some application or area of mathematics; or (4) a project of research collaboration with a member or members of staff, of which written and spoken presentation would be a part. Other projects which are appropriate but not primarily in one of these single categories may occur, such as a project combining features of (1) and (2).

Pre-requisites: Only available to mathematics (honours) students

MATH371 Special Topics in Inductrial and Applied Mathematics 3

Description: Entry to this subject is at the discretion of the Head of the School of Mathematics and Applied Statistics. This subject may not be offered in any particular year. MATH371 is one of a number of elective subjects available to students enrolled in the degree courses offered by the School. The aim of this subject is to provide students with specialist applied mathematical skills. Topics will be selected from the areas of interest of staff members of the School or visiting staff members.
In 2006, topics covered will include: Optimisation, Neural networks, Logistics, Operations Research.

STAT332 Multiple Regression and Time Series

Pre-requisites: STAT332 is an advanced course covering relationships between variables and the analysis of observational studies and designed experiments. Topics covered include multiple linear regression, non-linear regression, generalised linear regression, ARIMA models, forecasting of time series and Box-Jenkin's approach. A student who successfully completes this subject should be able to: (i) explain the theory and techniques of model building; (ii) apply the theory and techniques to practical problems and to use these methods for prediction purposes; (iii) undertake model building and forecasting for problems representative of those arising in industry and commerce.

Pre-requisites: STAT232 Estimation Hypothesis Testing

Description: STAT232 develops techniques of statistical inference and statistical analysis. The inference techniques are sampling distributions (such as chi-squared, t and F distributions), methods and criteria of estimation, and hypothesis testing. The analysis techniques are nonparametric testing (such as the sign, median and Wilcoxon tests), simple linear regression and one and two-way analysis of variance.

A student who successfully completes this subject should be able to: (i) apply appropriate parametric and non-parametric tests and present the conclusions of that analysis; (ii) interpret and model practical problems; (iii) explain the basic concepts of sampling theory, point and interval estimation and hypothesis testing; (iv) derive the details (such as the distribution of the test statistics, their expected mean squares, and the power functions) of the tests studied and similar tests; (v) apply and interpret appropriate procedures from a statistical package such as JMP.

STAT333 Statistical Inference and Multivariate Analysis

Description: STAT333 covers inference (estimation and hypothesis testing) in both one and many dimensions. Topics covered include transformations, maximum likelihood and minimum variance unbiased estimation, the likelihood ratio, score and Wald tests, vector random variables, the multivariate Normal distribution, principal components analysis, factor analysis and discriminant analysis.
A student who successfully completes this subject should be able to (i) explain the principles of statistical inference and the use of some standard procedures; (ii) derive good parameter estimators and tests of hypotheses in a wide range of circumstances; (iii) perform various forms of inference when the type of distribution being considered is unknown; (iv) explain the general techniques of considering more than one dependent variable at a time; (v) apply appropriate statistical procedures to the analysis of multivariate data; (vi) apply and interpret appropriate procedures from a statistical package such as SAS.

Pre-requisites: see above

Description : see above

INFO411 Data Mining and Knowledge Discovery

Description: Introduction to Data Mining and Knowledge Discovery, Data Bases and Warehouses, Data Structures, Exploratory Data Analysis Techniques, Association Rules, Artificial Neural Networks, Tree Based Methods, Clustering and Classification Methods, Regression Methods, Overfitting and Inferential Issues, Use of Data Mining packages.

After successful completion of this subject, students should be able to plan and carry out analyses of large and complex data sets and to identify useful relationships and important subgroups in those datasets.

Pre-requisites: 36 cp (Knowledge of mathematical and statistical notation at an introductory level.)

STAT904 Statistical Consulting

Description: Project management; Client liaison; Problem identification; Consulting ethics and principles; Sources of data; Choosing design and analysis procedures; Common problems in statistical consulting; Setting sample size - power calculations; Consulting case studies; Report writing.

A student who successfully completes this subject should be able to: (i) conduct efficiently a consulting session with a client; (ii) find information on statistical methodology using the resources of the Library and the World Wide Web ; (iii) explain the important principles behind designing and conducting an experiment or sample survey; (iv) determine appropriate statistical procedures to use on a wide variety of data sets; (v) apply and interpret procedures from a statistical package