MA265 Methods of Mathematical Modelling 3
Lecturer: MarieTherese 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:
 MA141 Analysis 1
 MA139 Analysis 2
 MA144 Methods for Mathematical Modelling 2
 MA150 Algebra 2
 MA124 Maths by Computer
Useful background:
Synergies:
Leads to: The following modules have this module listed as assumed knowledge or useful background:
 MA398 Matrix Analysis and Algorithms
 MA3K1 Mathematics of Machine Learning
 MA3K9 Mathematics of Digital Signal Processing
 MA3H7 Control Theory
Aims: The module gives an introduction to the theory of optimisation as well as the fundamentals of approximation theory.
Content:
 Recap: necessary and sufficient conditions for local min/max, convex functions and sets, Jensen’s inequality, level sets.
 Iterative algorithms: gradient descent and line search methods
 Newton's method
 Linear programming with applications in economics and data science
 Constrained optimisation
 Introduction to Neural Networks
 Approximation theory: polynomial approximation, rational approximation, trigonometric approximation
 Discrete Fourier and Cosine Transform with applications in imaging and signal processing
 Introduction to Wavelets
Objectives:

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
Books:
 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’