Core modules
Numerical Algorithms and Optimisation
Numerical Algorithms and Optimisation teaches you the theory and implementation of a set of computational algorithms that provide the fundamental toolkit for advanced data analysis, simulation and optimisation. The syllabus will be drawn from the following list of topics:
- Algorithmic structures (iteration, recursion, memoization) and computational complexity
- Data structures (linked lists, stacks and queues, binary indexed trees)
- Sorting and search algorithms
- Fast Fourier Transform
- Topics in numerical linear algebra: solving linear systems, conjugate gradient algorithm, singular value decomposition
- Unconstrained continuous optimisation: multivariate minimisation, Nelder-Mead algorithm, automatic differentiation, gradient descent
- Constrained continuous optimisation: method of Lagrange multipliers, linear programming
Data Analysis and Machine Learning
This is a core module for the MSc in Mathematics of Systems. The main aims are to provide a broad knowledge of modern techniques of exploratory data analysis, time series modelling and forecasting, and a short introduction to machine learning.
Stochastic Modelling and Random Processes
The main aims are to provide a broad background in theory and applications of complex networks and random processes, and related practical and computational skills to use these techniques in applied mathematical research and modelling. You will become familiar with basic network theoretic definitions, commonly used network statistics, probabilistic foundations of random processes, some commonly studied Markov processes/chains, and the links between these topics through random graph theory.
Topics in Mathematical Modelling
This is a core module for the Mathematics for Real-World Systems II CDT. The aim is to introduce you to cutting-edge topics in mathematical modelling that cover the application areas of the CDT: biomedical science, epidemiology, socio-technical systems, and industrial processes and optimisation. The topics covered will be used as examples to illustrate fundamental modelling approaches, in particular multiscale modelling and hybrid modelling, which bridges the divide between a-priori and data-driven methods.
Research Study Group MSc Project
This is a core module for the MathSys CDT, in which you will work in groups on research projects provided by external partners of the Centre. This module relies on knowledge gained in core MathSys MSc taught modules preparing you for research collaborations and teamwork skills. You will learn how to apply the skills and methods you have acquired in the MSc taught programme on a research project related to real-world problems. You will undertake research in groups under the guidance of a CDT core staff member and an external partner.
Individual Research MSc Project
This is a core module for summer MSc research for the MathSys CDT, involving projects from academic supervisors and external partners of the Centre. The module enables you to apply the techniques and skills acquired in the taught component of the MSc to real-world research projects, guiding you for the choice of your PhD research.
Optional modules
As an MSc student you will also choose two optional modules from the Warwick postgraduate provision. Previously these have included:
- Mathematics and biophysics of cell dynamics
- Medical statistics with advanced topics
- Population dynamics: ecology and epidemiology
- Computational methods for complex systems
- Probabilistic and statistical inference
- Statistical mechanics and its applications to complex systems
- Machine learning
- Natural language processing
- Mathematical economics
- Complexity in social science
- Bayesian forecasting and intervention
- Applied and numerical analysis of PDEs
- Scientific computing
- Multiscale modelling methods and applications
- Continuum mechanics
