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- Mathematics
MSc — 2024 entry Mathematics
Our Mathematics MSc degree offers an advanced exploration of mathematical theory, techniques, and applications across various disciplines. Mathematics serves as the foundation for understanding and solving complex problems in fields such as science, engineering, finance, and technology, making it a versatile and highly sought-after area of study.
UK students: you can apply by 1 September 2024
Why choose
this course?
From the ancient cultures of Greece, Egypt, Mesopotamia, India, China and beyond, to the modern era and across the globe, mathematics has played a central role in all aspects of the advancement of society. The subject remains at the heart of science and those who study mathematics find it immensely rewarding.
In our experience, candidates will usually pursue a mathematics degree at masters level for one or more of the following reasons:
- Many students undertake our MSc to enhance their career prospects
- Others see it as a crucial staging post on the path to a PhD
- Some approach the subject on account of the intellectual excitement and pleasure that it can bring as mathematics purely for the sake of mathematics.
Our MSc Mathematics has been designed to satisfy the needs of candidates with any of these goals in mind.
Statistics
94%
of our mathematics postgraduate taught students go on to employment or further study (Graduate Outcomes 2024, HESA).
What you will study
Our MSc benefits from the wide range of research being carried out in the School of Mathematics and Physics.
The taught courses and dissertation topics available to you are closely aligned with some of the activities of the research groups within the School. These include:
- Data science and dynamics
- Dynamical systems and partial differential equations
- Fields, strings and geometry
- Mathematics of life and social sciences
- Nonlinear waves and geometric fluid dynamics
- Quantum foundations.
During the first two semesters, you can choose a range of taught courses. These will be followed by an extended research project conducted over the summer under the supervision of a member of staff, which culminates with you writing your MSc dissertation.
The structure of our programmes follows clear educational aims that are tailored to each programme. These are all outlined in the programme specifications which include further details such as the learning outcomes:
Modules
Modules listed are indicative, reflecting the information available at the time of publication. Modules are subject to teaching availability, student demand and/or class size caps.
The University operates a credit framework for all taught programmes based on a 15-credit tariff, meaning all modules are comprised of multiples of 15 credits, up to a maximum of 120 credits.
Course options
Year 1
Semester 1
Optional
This module is an introduction to classical and modern methods in the Calculus of Variations. Variational methods have many applications in Mathematics, Physics and Engineering. Examples will be included in the module to illustrate the theory of the Calculus of Variations in practice. This module complements module material in MAT3004 Introduction to Function Spaces, and MAT3008 Lagrangian & Hamiltonian Dynamics, but these modules are not pre-requisite.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsAsset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models. The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”. The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived. The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives).
View full module detailsMathematics underpinning real-world uncertain events has become indispensable in many applications, including in particular financial markets. This module will begin with the introduction to probability theory and stochastic processes, with an emphasis on the Ito calculus for treating functions of Brownian motion. Such functions are commonly used in financial markets to model asset price dynamics, required for the valuation of financial contracts. The module then discusses structures of financial markets, with an emphasis on the equity market. Several of the standard and exotic contingent claims will be introduced, and the need for mathematical models for the valuation and risk management of these products will be explained. The pricing of a standard call option will then be worked out in a single-period binomial model, for which option price will be worked out in two ways: first using the portfolio replication and no arbitrage argument, and second using the risk-neutral expectation argument. The model is then extended into multi-period binomial tree model, leading to the Cox-Ross-Rubinstein option pricing formula. Finally, a continuous-time geometric Brownian motion model, originally introduced by Samuelson, will be considered, and used to deduce the famous Black-Scholes option pricing formula. This can be applied for the purpose of both pricing, as well as risk-management purposes, which will be demonstrated by working out the hedging strategy. The meaning of the pricing formula, and how it can be used in practical investment banking context, will be explained.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsThis module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsSemester 2
Compulsory
The dissertation consists of a written report of around 50 pages completed by the student towards the end of their programme of study. The report is based on a major piece of work that involves applying material encountered in the taught component of the programme and extending that knowledge with the student's contribution, under the guidance of a supervisor. The work for the dissertation and the writing up begins approximately May/June, continues through the Summer and the dissertation report is submitted in late Summer. The work may, but need not, involve original research. It may instead consist of a substantial literature survey on a specific topic.
View full module detailsOptional
Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThe module is an introduction to nonlinear partial differential equations (PDEs) with a focus on hyperbolic and dispersive PDEs. The module takes key classes of equations as the organising centre. Each class of PDEs is considered and the properties, analytical techniques, and analysis of each is taken in turn.
View full module detailsGroup theory is a branch of mathematics developed to understand symmetries, which are powerful tools for understanding the properties of complex mathematical problems and physical systems. Group representations map abstract group elements to linear transformations on vector spaces. Representation theory allows us to better understand the properties of symmetry groups, and leads to powerful and compact solutions of otherwise difficult and intractable problems. This module builds on groups theory in MAT1031 Algebra and MAT2048 Groups & Rings.
View full module detailsRiemannian geometry is the study of geometric properties of spaces, called manifolds, typically in higher dimensions, which are described smoothly by sets of well-defined co-ordinates. The emphasis is on how mathematically to understand the notion of distance via a metric on such spaces, and how this is used to investigate key associated geometric concepts. Students are introduced to the key concepts of manifolds and metrics, with illustrative examples such as spheres, hyperbolic spaces and Lie groups. The module continues with geodesics, isometries, covariant derivatives, the Levi Civita connection, and concludes with curvature and its properties. Modules in Curves and Surfaces and in Manifolds and Topology contain related material.
View full module detailsThis module introduces programming in Python for data science, with a focus on data pre-processing, data mining and analysis, machine learning and deep learning. Besides the practical hands-on experience with writing code, this course also covers the theoretical background on different data analysis techniques and machine learning approaches. The goal is to develop an understanding of how information can be extracted from data and how this information can be further used to make predictions, but importantly how this is done practically in terms of writing clear and transparent source code. Using real-world data sets and illustrative examples, this course will help to develop a theoretical understanding of data science as well as practical experience by developing useful software tools. Many of the techniques acquired through this module are likely to be of potential use in the dissertation project.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThis 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsThe presentations of the module will focus on data-driven methods for the analysis of dynamical systems and time-series data and on related machine learning problems such as dimensionality reduction, manifold learning, regression, and classification. Python will be used to implement data-driven methods. The methods will then be applied to typical benchmark problems such as chaotic dynamical systems, metastable stochastic systems, and fluid dynamics problems, but also, for instance, to image classification problems to highlight similarities with classical supervised learning applications.
View full module detailsOptional modules for Year 1 (full-time) - FHEQ Levels 6 and 7
Except for the dissertation, all modules are optional, subject only to the requirements noted above (e.g., for the MSc, a minimum of 150 credits must be at Level 7). Also, students should take no more than 4 modules in any semester.
In any given year, a subset of the optional modules will be delivered.
General course information
Contact hours
Contact hours can vary across our modules. Full details of the contact hours for each module are available from the University of Surrey's module catalogue. See the modules section for more information.
Timetable
Course timetables are normally available one month before the start of the semester.
New students will receive their personalised timetable in Welcome Week, and in subsequent semesters, two weeks prior to the start of semester.
Please note that while we make every effort to ensure that timetables are as student-friendly as possible, scheduled teaching can take place on any day of the week (Monday – Friday). Wednesday afternoons are normally reserved for sports and cultural activities. Part-time classes are normally scheduled on one or two days per week, details of which can be obtained from Academic Administration.
Location
Stag Hill is the University's main campus and where the majority of our courses are taught.
We offer careers information, advice and guidance to all students whilst studying with us, which is extended to our alumni for three years after leaving the University.
Mathematics is of paramount importance to all aspects of science, technology and modern finance. The logical insights, analytical skills and intellectual discipline gained from mathematical studies are highly sought after in all of these areas, as well as in a broad range of other disciplines such as law, business, management, and even the creative arts. There’s also a strong demand for new mathematics teachers in schools at all levels, both in the UK and abroad.
As well as being designed to ensure that candidates meet the needs of future employers, our MSc provides a solid foundation from which to pursue further research in mathematics, or one of the many other disciplines to which mathematical ideas and techniques are applied.
94 per cent of our mathematics postgraduate taught students go on to employment or further study (Graduate Outcomes 2024, HESA).
UK qualifications
A minimum of a 2:1 in a relevant UK honours degree, or a recognised equivalent international qualification.
We may be able to take relevant work experience into consideration if you don't meet these requirements. If you have at least one year of relevant experience in a full-time graduate-level role (or a minimum of two years’ experience in a relevant graduate-level part-time role) please provide full details of your role and responsibilities in your personal statement and CV when you submit your application.
English language requirements
IELTS Academic: 6.5 overall with 6.0 in writing and 5.5 in each other element.
These are the English language qualifications and levels that we can accept.
If you do not currently meet the level required for your programme, we offer intensive pre-sessional English language courses, designed to take you to the level of English ability and skill required for your studies here.
Recognition of prior learning
We recognise that many students enter their course with valuable knowledge and skills developed through a range of ways.
If this applies to you, the recognition of prior learning process may mean you can join a course without the formal entry requirements, or at a point appropriate to your previous learning and experience.
There are restrictions for some courses and fees may be payable for certain claims. Please contact the Admissions team with any queries.
Fees per year
Explore UKCISA’s website for more information if you are unsure whether you are a UK or overseas student. View the list of fees for all postgraduate courses.
September 2024 - Full-time - 1 year
- UK
- £11,900 per year
- Overseas
- £22,900 per year
- These fees apply to students commencing study in the academic year 2024-25 only. Fees for new starters are reviewed annually.
Payment schedule
- Students with Tuition Fee Loan: the Student Loans Company pay fees in line with their schedule (students on an unstructured self-paced part-time course are not eligible for a Tuition Fee Loan).
- Students without a Tuition Fee Loan: pay their fees either in full at the beginning of the programme or in two instalments as follows:
- 50% payable 10 days after the invoice date (expected to be October/November of each academic year)
- 50% in January of the same academic year.
- Students on part-time programmes where fees are paid on a modular basis: cannot pay fees by instalment.
- Sponsored students: must provide us with valid sponsorship information that covers the period of study.
The exact date(s) will be on invoices.
Additional costs
Books/stationery/admin: £10.
Funding
You may be able to borrow money to help pay your tuition fees and support you with your living costs. Find out more about postgraduate student finance.
Scholarships and bursaries
Discover what scholarships and bursaries are available to support your studies.
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We will continue to accept applications from UK students until 1 September 2024.
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Our code of practice for postgraduate admissions policy explains how the Admissions team considers applications and admits students. Read our postgraduate applicant guidance for more information on applying.
About the University of Surrey
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Terms and conditions
When you accept an offer to study at the University of Surrey, you are agreeing to follow our policies and procedures, student regulations, and terms and conditions.
We provide these terms and conditions in two stages:
- First when we make an offer.
- Second when students accept their offer and register to study with us (registration terms and conditions will vary depending on your course and academic year).
View our generic registration terms and conditions (PDF) for the 2023/24 academic year, as a guide on what to expect.
Disclaimer
This online prospectus has been published in advance of the academic year to which it applies.
Whilst we have done everything possible to ensure this information is accurate, some changes may happen between publishing and the start of the course.
It is important to check this website for any updates before you apply for a course with us. Read our full disclaimer.