Approximation: Theory and Methods

• Credit value: 30 credits at Level 6
• Convenor and tutor: Andrew Bowler
• Assessment: short, problem-based assignments (20%) and a three-hour examination (80%)

In this module we will study the theory and methods of mathematical approximation. These methods have numerous real-world applications in areas such as science, engineering, economics and finance.

Indicative module syllabus

• Errors
• Systems of linear equations
• Eigenvalues and eigenvectors
• Quadrature
• Asymptotic behaviour of functions
• Algorithms and complexity
• Nonlinear equations

By the end of this module, you will have:

• knowledge and understanding of, and the ability to use, mathematical techniques
• knowledge and understanding of a range of results in mathematics
• an awareness of the use of mathematics and/or statistics to model problems in the natural and social sciences, and the ability to formulate such problems using appropriate notation
• an understanding of the importance of assumptions and an awareness of where they are used and the possible consequences of their violation
• knowledge and understanding of the processes and limitations of mathematical approximation and computational mathematics
• knowledge and understanding of a range of modelling techniques, their conditions and limitations, and the need to validate and revise models
• a deeper knowledge of some particular areas of mathematics, in particular, Fourier series, error bounds, systems of linear equations, eigenvalues and eigenvectors, quadrature, integration and differential equations.