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MA265 Methods of Mathematical Modelling 3 

Lecturer: Marie-Therese Wolfram

Term(s): Term 1

Status for Mathematics students: Core for Maths

Commitment: 30 one hour lectures plus assignments

Assessment: 85% by 2 hour examination, 15% coursework

Formal registration prerequisites: None

Assumed knowledge:

Useful background:


Leads to: The following modules have this module listed as assumed knowledge or useful background:

Aims: The module gives an introduction to the theory of optimisation as well as the fundamentals of approximation theory.


  1. Recap: necessary and sufficient conditions for local min/max, convex functions and sets, Jensen’s inequality, level sets.
  2. Iterative algorithms: gradient descent and line search methods
  3. Newton's method
  4. Linear programming with applications in economics and data science
  5. Constrained optimisation
  6. Introduction to Neural Networks
  7. Approximation theory: polynomial approximation, rational approximation, trigonometric approximation
  8. Discrete Fourier and Cosine Transform with applications in imaging and signal processing
  9. Introduction to Wavelets


  • understand critical points of multivariable functions

  • apply various techniques to solve nonlinear optimisation problems and understand their applications, in economics and data science

  • use Lagrange multipliers and the Karush–Kuhn–Tucker conditions to solve constrained nonlinear optimisation problems

  • understand the basic concepts of approximation theory

  • obtain an understanding of different approximation techniques used in the digital sciences


  • Endre Sueli and David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003
  • S. Boyd. ‘Convex optimization’, Cambridge University Press 2004
  • J. D. Powell, ‘Approximation Theory and Methods’, Cambridge University Press, 1981
  • N. Trefethen, ‘Approximation Theory and Practice’


Additional Resources