Program Overview

Mathematics (MMath)

Award: Master of Mathematics

Typical Offer: AAA

View full entry requirements

Duration: 4 years

Course Type: Full-time

Campus: Highfield

UCAS Course code: G103

About this course

On this MMath Mathematics degree, you’ll work with leading researchers who’ll introduce you to pure and applied maths. Learn advanced mathematical and statistical concepts, covering topics from cryptography to black holes. You’ll graduate with the technical skills sought after by employers in finance, commerce, industry and research.

The first 3 years of this integrated master's degree are similar to both the Mathematics and the Mathematics with Statistics courses, covering:

• algebra
• calculus
• number theory
• statistics
• mathematical modelling

In the fourth year, you’ll study advanced concepts such as representation theory, harmonic analysis, advanced general relativity or Lie groups.

There is also an MMath Mathematics with Statistics pathway available as part of this programme. Following the Statistics pathway you could study topics such as machine learning, survival analysis and other modern applications of statistics.

As part of this course you’ll:

• study advanced research methods in algebra, analysis, geometry and topology
• have the option to specialise in statistics
• undertake an individual research project in a field of your choice
• use our student centre, a dedicated learning and social space for maths students
• use mathematical and computational packages such as Python and the statistics package 'R'

You’ll be taught through a combination of lectures and workshops, by leading researchers in fields, such as group theory, the mathematics of nature and experimental design.

We regularly review our courses to ensure and improve quality. This course may be revised as a result of this. Any revision will be balanced against the requirement that the student should receive the educational service expected.

Entry requirements

A-levels

AAA or AABB including Mathematics (grade A)

A-levels additional information

If a STEP paper is taken alongside three A-levels then the offer will be AAB including Mathematics (grade A). We accept either of the two STEP papers. For more details about STEP see the Admissions Testing Service Website.

A-levels with Extended Project Qualification

If you are taking an EPQ in addition to 3 A levels, you will receive the following offer in addition to the standard A level offer: AAB including Mathematics (grade A) and grade A in the EPQ

A-levels contextual offer

We are committed to ensuring that all applicants with the potential to succeed, regardless of their background, are encouraged to apply to study with us. The additional information gained through contextual data allows us to recognise an applicant's potential to succeed in the context of their background and experience. Applicants who are highlighted in this way will be made an offer which is lower than the typical offer for that programme.

International Baccalaureate Diploma

Pass, with 36 points overall with 18 at Higher Level, including 6 points from Higher Level Mathematics (Preferred Mathematics module is Analysis and Approaches, but Applications and Interpretation also considered)

International Baccalaureate contextual offer

We are committed to ensuring that all learners with the potential to succeed, regardless of their background, are encouraged to apply to study with us. The additional information gained through contextual data allows us to recognise a learner’s potential to succeed in the context of their background and experience. Applicants who are highlighted in this way will be made an offer which is lower than the typical offer for that programme.

Course structure

This 4-year course allows you to study topics in pure or applied mathematics in depth. There is an optional stream that lets you specialise in statistics.

The first 3 years of the course are similar to the BSc Mathematics programme. The fourth year has more emphasis on independent study including a year-long supervised dissertation. You'll study challenging Masters level mathematics giving you a taste of mathematical research. These modules provide the foundation for a career as a professional mathematician.

You don't need to select your modules when you apply. Your academic tutor will help you to customise your course.

Year 1 overview

You'll cover the fundamentals, such as linear algebra and calculus. While calculus may already be familiar, you’ll gain a deeper understanding of the underlying ideas. Linear algebra begins with the algebra of vectors and matrices, before delving into more rigorous and abstract concepts, such as groups and fields.

You'll also get a taste of different areas of mathematics, such as:

• number theory
• probability and statistics
• dynamics
• operational research

This allows you to gain experience, before deciding what to do next.

Year 2 overview

Key modules continue to build your foundational knowledge. These include analysis and the techniques of partial differential equations and Fourier theory.

You'll also get a choice of modules to allow you to pursue a specific interest. Options include:

• Group Theory: this is one of the great simplifying and unifying ideas in modern mathematics. Group theory encodes symmetries algebraically.
• Fluid Dynamics: you’ll apply the techniques you’ve learned from complex numbers and multivariable calculus to model airflow over a wing or water flow through a propeller.

You can also choose options from financial mathematics. These cover how securities are evaluated, and how investment projects are appraised. You could learn about modelling of random processes though Markov chains and stochastic differential equations.

If you have chosen the statistics stream, you'll start specialising in statistics in your second year, learning about statistical distributions and modelling.

Year 3 overview

From pure mathematics you could study:

• Galois theory
• number theory
• infinite dimensional spaces
• algebraic invariants of a shape

Or, you could apply your statistical knowledge to the design of experiments or to simulating statistical events.

In applied mathematics you could:

• model black holes and cosmology
• model epidemics and biochemical reactions
• learn about Laplace and Fourier transforms
• study solutions of the Navier-Stokes equation

You could also choose from topics in optimisation, actuarial mathematics or modern applications of mathematics such as machine learning and social networks.

You’ll also carry out a project, choosing from:

• Maths and your Future: working in small teams to analyse data and apply your mathematical learning to a problem raised by a local or national employer
• Mathematical Investigation and Communication: learning independently about new areas of mathematics or applying your skills of modelling and computation
• Communicating and Teaching Mathematics: acting as an ambassador for mathematics in schools and gaining classroom experience

Year 4 overview

In the final year, you'll carry out an individually supervised year-long dissertation on a topic of your choice.

You'll also select from a wide range of advanced modules. You could learn key ideas from pure mathematics, such as homology or geometric group theory. You could choose to specialise in applications of mathematics, such as advanced general relativity or gravitational waves.

Alternatively, following the statistics pathway you could study topics such as machine learning, survival analysis and other modern applications of statistics.

Modules

The modules outlined provide examples of what you can expect to learn on this degree course based on recent academic teaching. As a research-led University, we undertake a continuous review of our course to ensure quality enhancement and to manage our resources. The precise modules available to you in future years may vary depending on staff availability and research interests, new topics of study, timetabling and student demand.

Year 1 modules

You must study the following modules in year 1:

• Dynamics and Relativity
• First Year Mathematics Workshop
• Linear Algebra I
• Linear Algebra II
• Number Theory

Year 2 modules

You must study the following modules in year 2:

• Analysis
• Partial Differential Equations

You must also choose from the following modules in year 2:

• Algorithms
• Fields and Fluids
• Financial Mathematics
• Geometry and Topology
• Group Theory
• Operational Research II
• Statistical Distribution Theory
• Statistical Modelling I
• Stochastic Processes
• Vector Calculus and Complex Variable

Year 3 modules

You must choose your modules from the following modules in year 3:

• Actuarial Mathematics I
• Actuarial Mathematics II
• Advanced Fluid Dynamics
• Advanced Partial Differential Equations
• Algebraic Topology
• Algorithms
• Complex Analysis
• Fields and Fluids
• Financial Mathematics
• Further Number Theory
• Galois Theory
• Geometry and Topology
• Graph Theory
• Hilbert Spaces
• Integral Transform Methods
• Learning and Teaching Mathematics
• Mathematical Biology
• Mathematical Finance
• Mathematical Programming
• Numerical Methods
• Operational Research II
• Optimization
• Relativity, Black Holes and Cosmology
• Statistical Distribution Theory
• Statistical Inference
• Statistical Methods in Insurance
• Statistical Modelling I
• Statistical Modelling II
• Stochastic Processes
• Structure and Dynamics of Networks
• Survival Models

Year 4 modules

You must study the following module in year 4:

• MMath Project

You must also choose from the following modules in year 4:

• Advanced General Relativity
• Advanced Partial Differential Equations
• Complex Function Theory
• Design of Experiments
• Differential Geometry and Lie Groups
• Flexible Regression
• Geometric Group Theory
• Gravitational Waves
• Harmonic Analysis
• Homotopy and Homology
• Hyperbolic Geometry
• Integral Transform Methods
• Introduction to Semigroup Theory
• Machine Learning
• Modelling with Differential Equations
• Modules and Representations
• Numerical Methods
• Statistical Computing
• Structure and Dynamics of Networks
• Survival Models

Learning and assessment

The learning activities for this course include the following:

• classes and tutorials
• coursework
• independent learning (studying on your own)

Course time

How you'll spend your course time:

• Year 1: 33% scheduled learning & teaching, 67% independent learning
• Year 2: 33% scheduled learning & teaching, 67% independent learning
• Year 3: 25% scheduled learning & teaching, 75% independent learning
• Year 4: 16% scheduled learning & teaching, 84% independent learning

How we'll assess you

• coursework, laboratory reports and essays
• written exams

Your assessment breakdown

• Year 1: 69% written exam, 31% coursework
• Year 2: 80% written exam, 20% coursework
• Year 3: 65% written exam, 35% coursework
• Year 4: 30% written exam, 70% coursework

Careers and employability

Employability skills

This degree will allow you to develop and evidence subject-specific and targeted employability skills. This includes the required skill set for a range of future careers, further study, or starting your own business.

The skills you can expect to focus on and gain from this course include:

• Research
• Critical thinking
• Self-management
• Communication
• Problem solving

The employability and enterprise skills you'll gain from this course are reflected in the Southampton skills model. When you join us you'll be able to use our skills model to track, plan, and benefit your career development and progress.

Career pathways

Graduates commonly work in a range of organisations or sectors including:

• Education
• Engineering
• Finance
• Banking
• Accountancy
• Government
• Insurance
• IT
• Business consultancy
• Marketing
• Market research
• Health
• Oil
• Nuclear
• Research
• Space science
• Astronomy

Careers directly related to this course:

• Actuary
• Actuarial analyst
• Chartered accountant
• Data analyst
• Data scientist
• Investment analyst
• Research scientist (maths)
• Secondary school teacher
• Software engineer
• Statistician

Wider career opportunities:

• Academic researcher
• Financial manager
• Game designer
• Machine learning engineer
• Management consultant
• Meteorologist
• Operational researcher
• Quantity surveyor
• Finance manager
• University lecturer

Fees, costs and funding

Tuition fees

Fees for a year's study:

• UK students pay £9,535.
• EU and international students pay £23,400.

What your fees pay for

Your tuition fees pay for the full cost of tuition and standard exams.

Find out how to:

• pay your tuition fees
• calculate your student finances

Accommodation and living costs, such as travel and food, are not included in your tuition fees. There may also be extra costs for retake and professional exams.

Explore:

• accommodation costs
• living costs
• budgeting advice
• fees, charges, and expenses regulations

Bursaries, scholarships and other funding

If you're a UK or EU student and your household income is under £36,200 a year, you may be able to get a University of Southampton bursary to help with your living costs. Find out about bursaries and other funding we offer at Southampton.

If you're a care leaver or estranged from your parents, you may be able to get a specific bursary.

Get in touch for advice about student money matters.

Scholarships and grants

You may be able to get a scholarship or grant to help fund your studies.

We award scholarships and grants for travel, academic excellence, or to students from under-represented backgrounds.

Support during your course

The Student Hub offers support and advice on money to students. You may be able to access our Student Support fund and other sources of financial support during your course.

Funding for EU and international students

Find out about funding you could get as an international student.

How to apply

When you apply use:

• UCAS course code: G103
• UCAS institution code: S27

Apply for this course

What happens after you apply?

We will assess your application on the strength of your:

• predicted grades
• academic achievements
• personal statement
• academic reference

We'll aim to process your application within 2 to 6 weeks, but this will depend on when it is submitted. Applications submitted in January, particularly near to the UCAS equal consideration deadline, might take substantially longer to be processed due to the high volume received at that time.

Equality and diversity

We treat and select everyone in line with our Equality and Diversity Statement.

Got a question?

Please contact our enquiries team if you're not sure that you have the right experience or qualifications to get onto this course.

Email: [insert email] Tel: +44(0) [insert phone number]