Teaching

I am involved in one level one module,Calculus Investigations and one level 3 module, Numerical Analysis . I also supervise final year projects

Calculus Investigations

This is a level 1 mathematics module which is delivered in semester one and then followed by Linear Algebra in semester 2. The module consolidates A-level material, particularly work covering functions, differentiation and integration and then extends the calculus with an important application of power series expansions. The material in Calculus Investigations and in Linear Algebra  introduces many important concepts that are key to the application of mathematics and statistics in a wide variety of different areas and which are developed further at level 2. I am both happy to help students out of class should the need arise. The on-line teaching material for the module can be accessed by clicking here. This link will be open until all students on the module have Blackboard access.

Numerical Analysis 2

Rhys Gwynllyw [rhys.gwynllyw@uwe.ac.uk ] is the module leader. I teach the first semester material covering the numerical analysis of methods for solving ordinary differential equations. The second semester material covering the numerical analysis methods solving partial differential equations is delivered by Rhys. Numerical Analysis is the area of mathematics devoted to the analysis of numerical methods. Numerical methods are methods of solving mathematical problems by approximate means that return numerical solutions to the problem. A course in numerical analysis must necessarily involve the ability to write and code numerical algorithms and check the numerical solutions for accuracy. The coursework is set up so that students can practice writing numerical code and receive assistance and feedback throughout the first term. It is very satisfying to write your own code and get results that would take an age if doing the calculations by hand. The course will empower you to tackle problems that you initially thought you might not be able to solve. and many students find that they are using some of the techniques and skills learnt within the final year project.

Mathematical Project

This year I am supervising two final year projects. One project is looking at the traffic flow problems using the Optimal Velocity model and the second project is an investigation into different forms of bifurcations that can be found in the impact oscillator. The final year project gives students the opportunity to study in considerable detail some aspects of mathematics that interest them. Other projects that I have supervised include the pricing of financial options using the Balck-Scoles equation and the motion of the inverted double pendulum. As part of his project on the motion of the inverted pendulum, Danny Hoskins built a rig to demonstrate the theoretical prediction that a stable inverted double pendulum could actually be realised in practice even though this seems quite counter-intuitive.

Research

Fluid Dynamics

I have always been interested in interfacial stability and have studied interfacial instability using asymptotic and numerical techniques. More recently I have extended work that looks at disturbance energy growth and considered what happens for the two-fluid scenario. Two students have completed Ph.Ds in this area under my supervision, Matthew South and Satish Malik. Malik extended the results of South to include three dimensional disturbances. It is shown that transient three dimensional disturbances grow significantly more than transient two dimensional disturbances.

Problems previously identified by South and Hooper with non-convergence associated with the presence of the interface were overcome by replacing the interface by a miscible layer. Malik and Hooper identified the onset of an interfacial type instability with a decrease of miscible layer thickness.

In collaboration with Prof. R.Grimshaw, Loughborough University, I have studied nonlinear instability at the interface. Our most recent work was the study of a simple model of two coupled nonlinear ordinary differential equations in order to understand the interplay between transient linear growth and nonlinear effects.

For more details, see the Applied Mathematics Research Group

Selected Papers

S.Malik and A Hooper (2007) Three dimensional disturbances in channel flow.

Physics of Fluids19 052102 (18 pages) http://dx.doi.org/10.1063/1.2721600

S.Malik and A Hooper (2005) Linear Stability and Energy Growth of Viscosity Stratified Flows

Physics of Fluids 17 1-8. http://dx.doi.org/10.1063/1.1834931

A.P.Hooper and R.Grimshaw (2001) Transient Linear Growth and Nonlinear Effects.

Studies in Applied Mathematics, 106 47-68

S.N.Timoshin and A.P.Hooper(2000) Mode coalescence in a two-fluid boundary-layer stability problem.

Physics of Fluids, 12 1969-1978.

M.South and A.P.Hooper (1999) Linear growth in two-fluid Poiseuille flow.

J.Fluid Mech. 231 121-139

A.P.Hooper and M.South (1996) Eigenvalues and Disturbance Growth in Channel Flow of Two Superposed Viscous Fluids. Published in Advances in Multi- Fluid Flows SIAM Proceedings Series.

A.P. Hooper and R.Grimshaw (1996) Two dimensional disturbance growth of linearly stable viscous shear flows. Phys.Fluids 8 1424-1432

See a Full List of Research Papers

Research into Mathematics Education

I have collaborated in a number of mathematics education projects including PUTMaths First, a project to provide pre-university support in mathematics for Access students in Computing, Engineering and Science and Data Skills for Business, a project which to identified the extent of the graduate skills shortage in data handling in the SW region and to produced a distance-learning course in data analysis for business practitioners.

For more details see the Applied Mathematics Research Group, Research into Mathematics Education

Selected Publications

Golden, K and Hooper, (2006), A Transition Course prior to University Entry, Int. Conf. on the Teaching of Maths., Istanbul.

A Hooper and K Golden (2005) Updates from teaching and learning projects: A Transitional Course for Students Prior to University Entry MSOR Connections 4 no.4

Golden, K and Hooper, A.P., (2005) Transition Course for students prior to university entry

http://www.engsc.ac.uk/nef/events/helmconf_programme.asp#mathsup

Outreach work

I am involved in the following initiatives working with schools:

The Mathematics Challenge - delivered to year 10 pupils. This is an open-ended investigation based on some aspect of the GCSE curriculum, designed to raise aspirations with respect to mathematics.

The Maths Event Day - a day of workshops and talks for year 12 students. Its aim is to encourage AS-level maths students to continue their study of mathematics at A2 level and beyond.

The UWE/Schools Liaison group - a liaison group of maths teachers, UWE maths lecturers and LEA representatives. The group is a forum to discuss ideas and exchange views.

CPD days for teachers - The department runs a CPD programme for teachers. I have assisted at the CPD day for Mechanics and for Complex Numbers. For details of the 2008 programme, click here .