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Computational Mathematics with Modelling MSc

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  • Objectives
    This taught MSc course aims to provide a thorough grounding in modern numerical analysis, keeping in mind a balance between the theoretical and the practical. The practical aspects of the subject are emphasised by providing intensive instruction in those areas of Numerical Analysis which are useful in industry and of which the academic staff, through their applied research and consultative activities, have specialist knowledge. The course also contains lectures on mathematical modelling in which case studies, often related to the research interests of the staff, are presented. The course differs from those at other universities in that it covers a wider spectrum of numerical methods. The computational aspects of these methods are emphasised by the recent introduction of more laboratory work into the course. The University Computer Centre is housed in the same building as Mathematics and Statistics, making its facilities readily accessible to students on the course. In addition, the School has its own powerful Silicon Graphics computer, a 48-transputer machine, and a laboratory equipped with powerful microcomputers and workstations which provide further support for students on the course.
  • Entry requirements
    Entry Requirements At least a 2:2 degree in mathematics or a subject with a high mathematics content
  • Academic Title
    Computational Mathematics with Modelling MSc
  • Course description
    This course provides a thorough grounding in modern numerical analysis, keeping in mind a balance between the theoretical and the practical. The practical aspects of the subject are emphasised by providing intensive instruction in those areas of Numerical Analysis useful in industry and of which the academic staff, through their applied research and consultative activities, have specialist knowledge.

    The course differs from those at other universities in that it covers a wider spectrum of numerical methods. The computational aspects of these methods are emphasised by the recent introduction of more laboratory work into the course.

    Course Details

    Modules (all core)

        * Computational Methods
          Main topics of study include:LaTeX2e: the notion of a mark-up language, document style and structure, mathematical typesetting, crossreferencing; MATLAB programming: data types and structures, arithmetic operations, functions, input and output, interface programming, graphics; implementation of numerical methods.

        * Numerical and Variational Methods for PDEs
          Main topics of study include:calculus of variations; finite element methods for elliptic problems; an abstract overview of the finite element procedure including Galerkin orthogonality and best approximation in the energy norm; error analysis for the finite element method; numerical methods for time-dependent problems; advanced techniques of the finite element method.

        * Stochastic Models and Mathematical Finance
          Main topics of study include: stochastic processes; random walk; Markov chains; Poisson process and its relatives; economic and probability background; mathematical finance in discrete time; Brownian motion; mathematical finance in continuous time.

        * Methods of Mathematical Modelling
          Main topics of study include: principles of modelling; methods of analysing models;
          examples of models; boundary integral methods; integral equations.

        * Dissertation
          The dissertation has a long-established tradition in Numerical Analysis research and the specialist interests of staff are often reflected in the dissertation topics undertaken. However our students are also permitted to suggest their own dissertation topics. Examples from recent years include:
              o Fluid sloshing in an axisymmetric container
              o Heat loss from buildings
              o Contrived chaos in the numerical solution of dynamical systems

    Students who reach a satisfactory standard in the examinations may proceed to the MSc dissertation; those who do not may be considered for the award of a Postgraduate Diploma or Postgraduate Certificate.

    A Master's degree is awarded to students who achieve a satisfactory standard in their dissertation. Students who fail to reach such a standard may be permitted to submit a project report leading to the award of a Postgraduate Diploma.

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