Lecturer	Chris Farmer
Degrees	2009: Trinity Term — MSc in Mathematical Modelling and Scientific Computing
Term	Trinity Term 2009  (12 lectures)

Synopsis

The course will be informal, discussing and linking selected topics needed when mathematical modelling is used for making practical decisions. The course covers topics that are not usually discussed but are often essential for modelling and simulation in a practical context.

Topics include:

1. Why do modelling and simulation? Examples from climate modelling, oil recovery, ground water contamination and medical imaging will be used to illustrate the answer.
2. Ways of building models. This will outline methods from physics, applied mathematics and statistics.
3. Building simulators. Numerical methods suitable for computer simulators will be discussed. In particular the finite volume method will be described and some hints will be given on how to write code for solving elliptic and other partial differential equations.
4. How to model the geometry of physical objects and how to build grids for the finite volume method.
5. How to solve inverse problems. An introduction to interpolation viewed as an inverse problem will start the topic. Then the theory of Bayesian sequential filtering for time dependent problems will be derived. The difficulties of implementing Bayesian ideas in practice are outlined, and some recent progress that partially overcomes the difficulties will be presented.
6. Finally the mathematics underpinning simulation used for computing optimal decisions and control policies will be introduced.

Reading list

• C.L. Farmer. Geological modelling and reservoir simulation. Article in 'Mathematical Methods and Modelling in Hydrocarbon Exploration and Production', Editors: Armin Iske and Trygve Randen, Springer-Verlag, Heidelberg. ISBN: 3-540-22536-6, 2005, pp 119-212. (Please email the author if you would like a pdf of this article.)
• J. P. Kaipio and E. Somersalo. Statistical and Computational Inverse Problems. Springer, Berlin, 2004.
• S. M. LaValle. Planning Algorithms. Cambridge University Press, 2006. See Planning Algorithms

Taking our courses

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Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.