Explore our Mathematics of Systems taught Master's degree.

P-G1PF

MSc leading to PhD

4 years full-time

3 October 2022

Mathematics Institute

University of Warwick

The Mathematics of Systems programme takes the form of a 1+3 year MSc and PhD.

The full-time MSc year is dedicated to developing a broad portfolio of mathematical techniques and partaking in small research problems with a strong emphasis on applied questions and practical approaches. The PhD years train you into an independent researcher developing and using new mathematics to solve real-world systems challenges under the guidance of two supervisors and in the context of real-world systems problems coming from our external partners or others, in health, industry and finance.

The MathSys 1+3 year programme trains students in the advanced quantitative skills and applied mathematical modelling critical to address today’s challenges in biomedicine and health sectors, modern industry and the digital economy.

MathSys is a Centre for Doctoral Training funded by the EPSRC, with support from external partners and the University of Warwick. It is dedicated to tackling real-world problems that require developing novel mathematical methods for multi-scale, machine-learning and hybrid modelling.

MathSys is an inclusive CDT with a strong creative and collaborative ethos, and benefits from its own dedicated facilities. We will train you to think broadly and combine cutting-edge mathematical skills with the ability to understand and model real-world systems, analyse complex data sets, work well in multidisciplinary teams and be excellent communicators.

Our core funding provides stipends and fees for 10 students per year (under UKRI funding restrictions) on a competitive basis, including three fully-funded international studentships.

More information on the application process for MathSys, along with details of forthcoming Open Days, can be found on the MathSys website.

Skills from this degree

• Core and specialist mathematics for tackling real-world problems
• Complex data analysis
• Machine learning
• Computational techniques
• A range of mathematical modelling methodologies
• Presentation skills
• Multidisciplinary teamwork
• Research methods

A 1+3 year MSc and PhD.

The full-time MSc year is dedicated to developing a broad portfolio of mathematical techniques and investigating two research problems, with a strong emphasis on applied questions and practical approaches.

The MathSys cohort is typically 15-20 for the MSc year.

Contact hours will vary between 20+ per week for the taught component and 2+ per week for the Research Project components.

Terms One and Two comprise taught modules assessed through exams and vivas, and optional modules are usually taken in Term Two. The student cohort then addresses research problems motivated by external partners in small groups. After the Research Study Group project, each student pursues their own Individual Research Project supervised by a Warwick academic. Both research projects are evaluated by written and presented work.

Upon successfully completing the MSc year (or equivalent training), students may progress to a three-year PhD supervised by a Warwick academic and a representative of an external partner organisation. The CDT has a portfolio of available projects; however, the PhD project can also be determined by the student, with the proviso that it involves the application of mathematics to a real-world problem and that a suitable supervisor can be found.

Reading lists

Most departments have reading lists available through Warwick Library. If you would like to view reading lists for the current cohort of students you can visit our Warwick Library web page.

Your timetable

Your personalised timetable will be complete when you are registered for all modules, compulsory and optional, and you have been allocated to your lectures, seminars and other small group classes. Your compulsory modules will be registered for you and you will be able to choose your optional modules when you join us.

First Class Honours degree or very strong 2:i (or equivalent) in Mathematics, Physics, Statistics, Computer Science or other degree with high mathematical content.

• Band A
• IELTS overall score of 6.5, minimum component scores not below 6.0.

There are no additional entry requirements for this course.

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

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 

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