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Most mathematical problems arising from the physical sciences, engineering, life sciences and finance are sufficiently complicated to require computational methods for their solution. This subject introduces students to the process of numerical approximation and computer simulation, applied to simple and commonly encountered stochastic or deterministic models. An emphasis is on the development and implementation of algorithms for the solution of continuous problems including aspects of their efficiency, accuracy and stability. Topics covered will include simple stochastic simulation, direct methods for linear systems, data fitting of linear and nonlinear models, and time-stepping methods for initial value problems.
Intended learning outcomes
On completion of this subject, students should:
- Understand the significance and role of both roundoff error and truncation error in some standard problems in scientific computing;
- Be able to write simple numerical programs that utilize a numerical Problem-Solving Environment such as Matlab or NumPy;
- Appreciate the role of computer simulation, as a third method in science, distinct from theory and experiment
- Understand the distinction between the simulation of stochastic and deterministic models
- Be able to use appropriate numerical techniques when undertaking a mathematical or modelling investigation
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments;
- computer skills: the ability to use mathematical computing packages.
Last updated: 22 November 2023