MATH313 Industrial Mathematical Modelling

6 credit points

Pre-Requisites: MATH202 or (MATH283 & MECH343)

Description: MATH313 is designed to develop mathematical modelling skills by the examination of case studies relevant to industry. The basic equations are derived from first principles and used to study the transfer of mass and heat, diffusion, solidification and combustion. In addition, the subject aims to improve oral presentation skills by making tutorial participation an assessable component of the subject.

Objectives:
A student who successfully completes this subject should be able to:
(i) construct a mathematical model for an industrial process involving mass diffusion, heat conduction, change of phase, and combustion;
(ii) express such a mathematical model in dimensionless form, identifying the important dimensionless parameters of a process;
(iii) solve standard fixed and free boundary value problems of heat conduction;
(iv) present and explain mathematical models and their solutions to colleagues/employers.



MATH321 Numerical Analysis

Pre-requisites: MATH202 & MATH203

Equivalence: MATH311

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.

Objectives: 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.

Coordinator: Grant Cox


MATH324 Calculus of Variations and Geometry

Pre-Requisites: MATH201and MATH203

Description: This subject is about classical calculus of variations and geometric analysis of curves and surfaces. These areas and the links between them are central to much modern mathematical analysis and also find diverse applications in engineering, physics and biology. This subject builds on students' knowledge of calculus and linear algebra to represent curves and surfaces and their properties, particularly their curvature, analytically, and to develop several important and widely applicable tools for optimisation of energies in various contexts.

Objectives: On successful completion of this subject, students will be able to: - Formulate and solve problems in classical calculus of variations and in geometry; - Define, understand and utilize some key geometric concepts about curves and surfaces; - Apply ideas from calculus and linear algebra and problem solving skills in contexts of this subject; - Understand and appreciate some fundamental mathematical theorems and their proofs; - Clearly present mathematical concepts in written form, demonstrating skill in constructing clear mathematical arguments.

Lecturer: Graham Williams

Coordinator: James McCoy


STAT332 Multiple Regression and Time Series

Pre-Requisites: STAT232

Description: 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.

Objectives: 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.

Coordinator: Yan-Xia Lin

STAT333 Statistical Inference and Multivariate Analysis

Pre-Requisites: STAT232

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.

Objectives: 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.

Coordinator: Chandra Gulati