- PhD
- MSc
- Numerical analysis
- Numerical linear algebra
- Numerical solution of elliptic PDEs
- Numerical optimisation and large-scale problems
- Numerical solution of evolutionary equations
- Scientific Computing
- Programming and Discrete Mathematics
- Related courses

### Postgraduate

### Undergraduate

#### MSc in Modern Applications of Mathematics

Members of the numerical analysis group regularly teach modules and supervise the writing of dissertations on this MSc. The MSc gives a broad training in applied and computational mathematical mathematics and is an excellent prepartion for joining our PhD programme. Here is a list of recent MSc dissertations.

- Jenkins, S.
*Regularisation Parameter Estimation in Variational Data Assimilation*. (2010) - Burton, G.
*Numerical Evaluation of Option Prices*. (2008) - Dickinson, C.
*Numerical Solution of Richards Equation*. (2008) - Norton, T.
*Symplectic Runge Kutta Methods*. (2010) - Hodge, C.
*Spectral Clustering and Half-lives of Eigenflows*. (2010) - Suryanarayana, G.
*Multilevel Wiener-Hopf Monte-Carlo simulation for Levy processes*. (2011) - Cook, S.
*Error analysis in electrical impedance tomography imaging*. (2011) - Blake, J
*Preconditioning of iterative methods for the transport equation*. (2011) - Norton, T.
*Symplectic numerical methods and applications*. (2011)

#### PhD in Mathematical Sciences

We are always looking for motivated and able students to join our group and study for a PhD. As well as undertaking research, PhD students are encouraged to take modules through the Mathematics Taught Course Centre run jointly with the Universities of Bristol, Imperial, Oxford, and Warwick. Recent PhD dissertations include the following

- Stoyanov, Z.
*The symmetric eigenvalue problem: stochastic perturbation theory and some network applications*. (2008) - Shanks, D.
*Robust solvers for large indefinite systems in seismic inversion*. (2015) - Jenkins, S.
*Numerical Model Error in Data Assimilation*. (2015) - Blake, J.
*Domain Decomposition Methods for Nuclear Reactor Modelling with Diffusion Acceleration*. (2016) - Cook, S.
*Adaptive Mesh Methods for Numerical Weather Prediction*. (2016) - Teckentrup, A.
*Multilevel Monte Carlo methods and uncertainty quantification*. (2013) - Giani, S.
*Convergence of Adaptive Finite Element Methods for Elliptic Eigenvalue Problmes with Applications to Photonic Crystals*. (2008) - Norton, R.
*Numerical Computation of Band Gaps in Photonic Crystal Fibres*. (2008) - Hewitt, L. L.
*General Linear Methods for the Solution of ODEs*. (2009) - Buckeridge, S. D.
*Numerical Solution of Weather and Climate Systems*. (2010) - Akinola, R. O.
*Numerical Solution of Linear and Nonlinear Eigenvalue Problems*. (2010) - Scheben, F.
*Iterative Methods for Criticality Computations in Neutron Transport Theory*. (2011) - Walsh, E. J.
*Moving Mesh Methods for Problems in Meteorology*. (2010) - Millward, R. R.
*A New Adaptive Multiscale Finite Element Method with Applications to High Contrast Interface Problems*. (2011) - Kim, T.
*Asymptotic and Numerical Methods for High-Frequency Scattering Problems*. (2012) - Akinola, R.
*Numerical solution of linear and nonlinear eigenvalue problems*. (2008) - Pring, S.
*Discontinuous maps with applications to impacting systems*. (2009) - Green, S.
*Statics and dynamics of mechanical lattices*. (2009) - Browne, P.
*Topology optimization of linear elastic structures*. (2013) - Mora, K.
*Non-smooth dynamical systems and applications*. (2014)

#### Related courses

Numerical Analysis has strong links with several other areas of mathematics, in particular PDEs and probability, and thus attending courses in these areas would stand any budding numerical analysts in good stead!

#### MA40050 Numerical optimisation and large-scale problems

#### Rob Scheichl

The minimisation of an objective function subject to constraints is a key problem in scientific computing. This course develops numerical techniques and looks at very large optimisation problem, such as those arising from constrained differential equations.

#### MA20222 Numerical analysis

#### Tony Shardlow

This course introduces the fundamental ideas of computer arithmetic and the convergence and accuracy of numerical algorithms. Specific problems are chosen from polynomial interpolation, quadrature, and the solution of linear system of equations.

#### MA40177 Scientific Computing

#### DOLGOV

The aim is to teach an understanding and appreciation of issues arising in the computational solution of challenging scientific and engineering problems, including familiarity with scientific libraries and parallel programming.

#### XX10190 Programming and Discrete Mathematics

#### Melina Freitag and James Davenport (Computer Science)

This first-year undergraduate course teaches generic programming skills and a range of topics in discrete mathematics which are connected to computation.

#### MA30051 Numerical linear algebra

#### Melina Freitag

The two fundamental problems in linear algebra are (1) solving linear systems of equations and (2) solving algebraic eigenvalue problems. We introduce numerical methods for both these problems and analyse their behaviours.

#### MA30170 Numerical solution of elliptic PDEs

#### Silvia Gazzola

PDEs are fundamental to many models in science and engineering and in this course we introduce the widely used finite element method for elliptic PDEs. The method is a very flexibe approach to approximating the solution of a PDE with a computer.

#### MA40171 Numerical solution of evolutionary equations

#### Ivan Graham

This course focuses on time dependent (hyperbolic and parabolic) PDEs, introducing time stepping methods and approximations in space to find effective computational methods.