Mathematics (with optional Placement/Project year) MSc

Program Overview

This applied and computational Mathematics program focuses on developing subject-specific and transferable skills valued by employers. Students will engage in projects linked to the research team's work, utilizing specialist computing facilities and a well-stocked library. The program offers a Research Dissertation module, and an optional Project/Placement year, providing opportunities for practical experience and career advancement.

Program Outline

Degree Overview:

Our course focuses on applied and computational Mathematics, which is our team’s research specialism and a skill set highly valued by employers. You will have the opportunity to develop subject-specific skills (applicable in, for example, the biosciences, finance sector and engineering) and key transferable skills (including IT, problem solving, and written and oral communication). Formal teaching will be delivered at Exton Park, Chester. We have put together a course to cater for the needs of both Single Honours Mathematics graduates and graduates who have studied Mathematics as part of a degree – for example, you may have studied Mathematics as part of a joint honours course or as part of a physics-related degree. You will have the opportunity to work on projects directly linked to the degree team’s own research, which includes work of both a theoretical and practical nature. You will also have access to specialist mathematics computing facilities and a well-stocked library, including electronic resources. We have several resources in place to facilitate part-time study, and we welcome enquiries from people who wish to pursue their academic studies while remaining in employment. There is an option to choose a Project/Placement year for this course, at an additional cost.

Outline:

Modules

You will be taught about the development of mathematical systems and how they are used to simulate and better understand real-world systems. You will be introduced to a variety of theoretical tools for analysing and solving such systems. Additionally, you’ll be introduced to industrially used software, and complete your dissertation. If you choose a placement or project year, the Research Dissertation module will be replaced by a placement or project module.

• Research Methods and ICT for Mathematics (Compulsory)
This module is designed with dual objectives. Firstly to provide an in-depth introduction to algorithms and the process of translating these into computer programs, using state-of-the-art software tools. This will provide you with a solid foundational understanding to tackle any future computational and programming challenges. Secondly, you will develop important research and writing skills. You will learn to use LaTeX, an industry-standard typesetting system for produce professional scientific documents.
• Numerical Methods: Convergence & Stability Theory (Compulsory)
Ordinary differential equations (ODEs) play a crucial role in modelling many problems in science and engineering. Despite their significance, finding analytic solutions for these differential equations is often challenging. In this module, we will study the methods for numerically solving ODEs, analysing their behaviour, and gaining practical experience in their application. Our focus will be on first-order ODEs, examining a variety of algorithms such as forward and backward Euler, the family of Runge-Kutta methods, and multistep methods. We will discuss the zero stability, absolute stability, and convergence of the proposed numerical methods. To implement these methods in practice, we will utilise ODE solvers in MATLAB and Python to address different types of differential equations. Additionally, we will consider the finite difference method for solving the boundary value problems and the heat equation.
• Functional Analysis (Compulsory)
Functional analysis is a field with widespread applications throughout applied mathematics and science. It provides the fundamental underpinnings which allows us to analyse and find approximate solutions for many challenging problems in ordinary and partial differential equations, such as the heat equation, wave equation and various quantum phenomena. In this module students will discover that the formal notions and techniques developed in analysis can be applied more generally to infinite-dimensional spaces endowed with notions of distance that generalise the properties of Euclidean distance. Throughout the module, students will gain familiarity with the definitions of these more general spaces, including Metric Spaces, Normed Spaces and Inner Product Spaces. We will explore examples where the points in these spaces are functions, sequences or even operators between spaces, rather than vectors of real or complex numbers.
• Stochastic Calculus, Stochastic Differential Equations and Applications (Compulsory)
Stochastic differential equations (SDEs) model evolution of systems affected by randomness. They offer a beautiful and powerful mathematical language in an analogous way to what ordinary differential equations (ODEs) do for deterministic systems. SDEs have found many applications in diverse disciplines such as biology, physics, chemistry and the management of risk. Replacing the classical Newton-Leibnitz calculus with (Ito) stochastic calculus, we are able to build a new and complete theory of existence and uniqueness of solutions to SDEs. Ito's formula proves to be a powerful tool to solve SDEs. This leads to many new and often surprising insights about quantities that evolve under randomness.This module provides the student with the necessary language and methods for investigating applications of and solutions to stochastic differential equations.
• Mathematical Ecology (Compulsory)
Mathematical ecology harnesses advanced models and analytical tools to understand and describe the dynamics of individual species, ranging from the propagation of COVID-19 to the spread of wildfires, as well as the relationships between different species and their environment in ecosystems, for example in predator-prey dynamics and the invasive behaviour of cancer cells. Mathematical ecology can also help us to understand natural patterns, such as the arrangement of leaves on plants and the markings on animal coats, by employing models such as reaction-diffusion systems. So we can finally answer: "How the Leopard got its spots?"
• Partial Differential Equations (Compulsory)
Partial differential equations(PDEs) serve as mathematical models for a wide range of physical, biological, and economic phenomena and are foundational tools across various branches of pure and applied mathematics. In 1822, Fourier provided uniform solutions for significant PDEs, such as the wave and heat equations, along with Laplace's equation. This course will concentrate on these three equations, considering auxiliary initial or boundary conditions. Throughout the course, we will explore diverse techniques, including separation of variables, Fourier methods, Laplace transform methods, among others, to effectively solve various types of partial differential equations.
• Research Dissertation (Compulsory)
The research project gives the student an opportunity to apply theory learned on the programme and to develop skills of self-discipline, project management and written communication. Students will negotiate with tutors the precise title and objectives of the project. Students will study the art of mathematical writing and communication. Tutors will provide appropriate levels of support and advice.

Assessment:

Assessment is through a combination of examination and coursework, including worksheets, investigations and small projects. Your dissertation will give you the opportunity to work on a larger research project.

Teaching:

We employ a variety of study methods, such as lectures, tutorials (including one-to-one), problem-solving classes and workshops.

Careers:

Examples of destinations of previous students on the programme include: MPhil/PhD study (including industrial-based projects), data science and modelling roles in industry (including the pharmaceutical industry), commerce and the public sector, roles in financial institutions, teaching and education, and IT.

Other:

More than half of the research our departments produce is world-leading or internationally excellent, according to the Research Excellence Framework (2021). Our portfolio contains work that is at the forefront of its subject discipline, which brings changes to policy, practice and services that benefit the economic, social and cultural wellbeing of our region and the wider community. You will be allocated a Personal Academic Tutor (PAT). Your PAT is there to provide you with academic advice and guidance, and whilst your PAT is primarily concerned with your academic progression, you should feel free to consult them at any time about any personal issues you may have. If your PAT cannot help you directly, they will always suggest other sources of support, advice and guidance.

Tuition Fees and Payment Information:

Home Students

• £8,505 for the full course (2024/25)

International/EU Students

• £14,750 for the full course (2024/25)
• The professional placement/project year will cost an additional £2,650 (due at the start of the second year of the course), totaling £17,400 for the full course fee 2024/25.
• The University of Chester offers generous international and merit-based scholarships for postgraduate study, providing a significant reduction to the published headline tuition fee.
You will automatically be considered for these scholarships when your application is reviewed, and any award given will be stated on your offer letter.

Additional Costs

• If you are living away from home during your time at university, you will need to cover costs such as accommodation, food, travel and bills.
• There may also be additional costs for photocopying and printing.