Postgraduate Courses in the
School of Computing Sciences
MSc Computational Mathematics
Introduction
Aims and Objectives
This course aims to equip students with a thorough bedrock of the mathematical techniques and computing skills relevant to the design and analysis of engineering systems for which there is currently a major shortage of specialists.
Graduates of this course will typically find employment as mathematical modellers, systems analysts or programmers in a range of scientific and engineering research and development establishments specialising in computational methods for the mathematical modelling and computer simulation.
Alternatively, their new skills may facilitate development in previously professional careers.
What is CM?
Developments in computer technology have provided engineers and scientists with tools of increasing power and sophistication. This has led to a greater use of mathematical modelling and simulation as the basis for the analysis and design of engineering systems, thus providing a more flexible and economic approach to the traditional methods which relied heavily on costly experimentation and the building of scale models.
Computational mathematics is about exploiting computers to execute discrete models, which are based on numerical techniques, to solve the complex mathematical formulations required to describe a range of engineering problems.
The visualization of the solutions, using advanced computer graphics, is another important aspect of computational mathematics which is increasingly necessary in order to communicate the characteristics of the resultant numeric field to the engineer and scientist. Thus, computational mathematics can be thought of as the "field of study required to generate a virtual world for analysing the behaviour and characteristics of engineered systems".
Who is The Masters Degree For?
The course is a conversion course for graduates from a non-computing subject area who have a numerate academic background. The teaching focuses on the expertise within the Centre for Engineering Mathematics in the Department of Mathematical Sciences. The course can either be taken full-time (one academic year) or part-time over a period of two years.
Candidates should have a degree, or equivalent, in a mathematical, scientific or engineering discipline. No specific computing background is required.
Course Structure
The course is organised into two parts; the first part is taught and is based on eight modules delivered over two Semesters. The third Semester is devoted to a research thesis on an industrial project. All taught modules are assessed by a combination of examination, course and/or project work.
In addition to formal lectures, students are invited to attend a series of
seminars run by the Department of Mathematical Sciences, in which personnel
from both academic and industrial organizations present research papers and
information on software products and their applications.
Semester
Module Title
Semester 1
Programming And Software Engineering
Computational Methods
Advanced Mathematical Methods
Computer Graphics And Visualisation
Semester 2
Finite Difference Analysis
Finite Element Analysis
Signal Processing And Control
Computational Fluid Dynamics
Summer Period
Project
Course Syllabus
Semester One
A programming approach to software engineering, covering modular programming in FORTRAN-77 and C, the definition planning and development phases of programming, software testing techniques, reliability and maintenance, object oriented programming (in C++). The use of Fortran 90 as an emerging standard for computational and engineering mathematics is also addressed.
This module covers numerical methods of solution to the varying types of linear equations which occur in discrete mathematics, in particular those that arise through the use of finite difference and finite element analysis.
This module introduces advanced methods of mathematical analysis which focus on areas which are fundamental to mathematical modelling and numerical analysis. The purpose of this module is to instruct students on those methods which are either used directly for describing problems in engineering mathematics or are used indirectly for the analysis of computational algorithms. The course covers ordinary and partial differential equations, integral transform techniques and matrix analysis.
The numeric field produced by a computer simulation is of little use to the engineering unless it can be visualized interactively, ideally in real time. This module explores the computer graphics algorithms available for the representation of multi-dimensional numeric fields.
Semester Two
Presents the mathematical and computational background to the finite difference method, and discusses the types of engineering problems to which the method can be applied. A number of case studies are considered in which the programming aspects necessary for developing efficient code are explored in detail. The case studies include solutions to first and second order boundary value problems, steady state and time dependent thermal transfer problems, vibrating systems in 1D and 2D and some elementary aspects of Computational Fluid Dynamics.
Discusses the Finite Element Method as a general approximation method for the numerical solution to structural analysis and physical problems described by field equations in continuous media (thermal transfer properties and vibration analysis of product models for example). The Boundary Value Method is also introduced and the computational aspects of employing this technique discussed.
This course covers a selection of subjects which focus attention on methods of processing digital signals from a variety of systems but with an emphasis on control systems. Instruction is given on how to formulate algorithms, design and test code for a variety of DSP problems which include aspects of telecommunications, acoustics and control engineering.
The objective of this module is to provide a basic presentation of CFD emphasising the fundamentals and surveying a number of solution techniques. After introducing and deriving from first principles the fundamental fluid equations of motion, it is shown how, under certain conditions and geometrical configurations, the behaviour of a fluid can be cast in terms of a single or set of Partial Differential Equations of a given class (Elliptic, Parabolic, Hyperbolic).
Solution techniques covered in the modules on Finite Difference and Finite Element Analysis are then used to solve the problems discussed on the course. The application of the Finite Volume Technique in CFD is also presented.
Summer Period
The project is undertaken in association with an external organization in industry, commerce or the public sector. It is expected that employed part-time students will undertake projects within their places of work. The project provides the opportunity to develop, to demonstrate and to appraise skills acquired from the course in the solution of a practical problem subject to typical commercial constraints.
A report is to be written, describing the work undertaken on the project and students are also required to give a presentation. Assessment is continuous throughout the project timescale.
Further Information
Assessment
All taught modules are assessed by a combination of examination, course or practical work. The modules all contain a practical programming element in which students develop a library of software routine which can be used both for the research thesis and future employment. This library is assessed at the end of the course.
For contact details, see foot of page.
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