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. Find out why, when, and how we might make changes.
Our courses are regulated in England by the Office for Students (OfS).
Learn more about this subject area
Course location
This course is based at Highfield.
Awarding body
This qualification is awarded by the University of Southampton.
Download the Course Description Document
The Course Description Document details your course overview, your course structure and how your course is taught and assessed.
Entry requirements
For Academic year 202425
A-levels
AAA or AABB including Mathematics (grade A)
A-levels additional information
Offers typically exclude General Studies and Critical Thinking.
If an additional Mathematics qualification (STEP grade 2/MAT/TMUA) is taken alongside three A-levels then the offer will be AAB including Mathematics (grade A). We accept any of the three STEP papers. For more details about the STEP and TMUA papers 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. The contextual offer for this programme is AAB including A in Maths.
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.
International Baccalaureate Career Programme (IBCP) statement
Offers will be made on the individual Diploma Course subject(s) and the career-related study qualification. The CP core will not form part of the offer. Where there is a subject pre-requisite(s), applicants will be required to study the subject(s) at Higher Level in the Diploma course subject and/or take a specified unit in the career-related study qualification. Applicants may also be asked to achieve a specific grade in those elements. Please see the University of Southampton International Baccalaureate Career-Related Programme (IBCP) Statement for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
BTEC
D in the BTEC National Extended Certificate plus AA from two A levels including Mathematics
DD in the BTEC National Diploma plus A in A level Mathematics
We do not accept BTEC National Extended Diploma unless A level Mathematics is taken alongside this qualification. If it has, the offer would be DDD plus A in A level Mathematics.
RQF BTEC
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.
Additional information
Applicants who have not studied mathematics at A-level can apply for the Engineering/Physics/Mathematics Foundation Year
QCF BTEC
D in the BTEC Subsidiary Diploma plus AA from two A levels including Mathematics
DD in the BTEC Diploma plus A in A-level Mathematics
We do not accept the BTEC Extended Diploma unless A level Mathematics is taken alongside this qualification. If it has, the offer would be DDD plus A in A level Mathematics.
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.
Access to HE Diploma
60 credits with a minimum of 45 credits at Level 3, all of which must be at Distinction
Access to HE additional information
Mathematics must be studied to level 3, A-level standard to be considered
Irish Leaving Certificate
Irish Leaving Certificate (first awarded 2017)
H1 H1 H2 H2 H2 H2 including Mathematics at H2
Irish Leaving Certificate (first awarded 2016)
A1, A1, A1, A1, A1, A1 including Mathematics
Scottish Qualification
Offers will be based on exams being taken at the end of S6. Subjects taken and qualifications achieved in S5 will be reviewed. Careful consideration will be given to an individual’s academic achievement, taking in to account the context and circumstances of their pre-university education.
Please see the University of Southampton’s Curriculum for Excellence Scotland Statement (PDF) for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
Cambridge Pre-U
D3 D3 D3 in three Principal subjects including Mathematics
Cambridge Pre-U additional information
Cambridge Pre-U's can be used in combination with other qualifications such as A Levels to achieve the equivalent of the typical offer
Welsh Baccalaureate
AAA from 3 A levels including Mathematics or AA from two A levels including Mathematics and A from the Advanced Welsh Baccalaureate Skills Challenge Certificate
Welsh 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.
T-Level
There are no T levels accepted for this programme.
Other requirements
GCSE requirements
Applicants must hold GCSE English language (or GCSE English) (minimum grade 4/C)
Find the equivalent international qualifications for our entry requirements.
English language requirements
If English isn't your first language, you'll need to complete an International English Language Testing System (IELTS) to demonstrate your competence in English. You'll need all of the following scores as a minimum:
IELTS score requirements
- overall score
- 6.5
- reading
- 6.0
- writing
- 6.0
- speaking
- 6.0
- listening
- 6.0
We accept other English language tests. Find out which English language tests we accept.
You might meet our criteria in other ways if you do not have the qualifications we need. Find out more about:
- our Access to Southampton scheme for students living permanently in the UK (including residential summer school, application support and scholarship)
- skills you might have gained through work or other life experiences (otherwise known as recognition of prior learning)
Find out more about our Admissions Policy.
Foundation year for engineering, physics, maths and geophysics
A foundation year will give you the skills and knowledge to progress to this course if you don't have the right qualifications for direct entry.
It could be the right option if you:
- have A levels, or equivalent international qualifications, in subjects other than the ones needed for direct entry
- have international qualifications in relevant subjects but not at A level equivalent
- have a BTEC Extended Diploma in a relevant subject
- are studying an Access course in a relevant subject
- are a mature student with relevant experience or study
You'll also need to show that you have strong maths skills.
Find full details on our Engineering, Maths, Physics, Geophysics Foundation Year page.
For Academic year 202526
A-levels
AAA or AABB including Mathematics (grade A)
A-levels additional information
Offers typically exclude General Studies and Critical Thinking.
If an additional Mathematics qualification (STEP grade 2/MAT/TMUA) is taken alongside three A-levels then the offer will be AAB including Mathematics (grade A). We accept any of the three STEP papers. For more details about the STEP and TMUA papers 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.
International Baccalaureate Career Programme (IBCP) statement
Offers will be made on the individual Diploma Course subject(s) and the career-related study qualification. The CP core will not form part of the offer. Where there is a subject pre-requisite(s), applicants will be required to study the subject(s) at Higher Level in the Diploma course subject and/or take a specified unit in the career-related study qualification. Applicants may also be asked to achieve a specific grade in those elements. Please see the University of Southampton International Baccalaureate Career-Related Programme (IBCP) Statement for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
BTEC
D in the BTEC National Extended Certificate plus AA from two A levels including Mathematics
DD in the BTEC National Diploma plus A in A level Mathematics
We do not accept BTEC National Extended Diploma unless A level Mathematics is taken alongside this qualification. If it has, the offer would be DDD plus A in A level Mathematics.
RQF BTEC
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.
Additional information
Applicants who have not studied mathematics at A-level can apply for the Engineering/Physics/Mathematics Foundation Year
QCF BTEC
D in the BTEC Subsidiary Diploma plus AA from two A levels including Mathematics
DD in the BTEC Diploma plus A in A-level Mathematics
We do not accept the BTEC Extended Diploma unless A level Mathematics is taken alongside this qualification. If it has, the offer would be DDD plus A in A level Mathematics.
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.
Access to HE Diploma
60 credits with a minimum of 45 credits at Level 3, all of which must be at Distinction
Access to HE additional information
Mathematics must be studied to level 3, A-level standard to be considered
Irish Leaving Certificate
Irish Leaving Certificate (first awarded 2017)
H1 H1 H2 H2 H2 H2 including Mathematics at H2
Irish Leaving Certificate (first awarded 2016)
A1, A1, A1, A1, A1, A1 including Mathematics
Scottish Qualification
Offers will be based on exams being taken at the end of S6. Subjects taken and qualifications achieved in S5 will be reviewed. Careful consideration will be given to an individual’s academic achievement, taking in to account the context and circumstances of their pre-university education.
Please see the University of Southampton’s Curriculum for Excellence Scotland Statement (PDF) for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
Cambridge Pre-U
D3 D3 D3 in three Principal subjects including Mathematics
Cambridge Pre-U additional information
Cambridge Pre-U's can be used in combination with other qualifications such as A Levels to achieve the equivalent of the typical offer
Welsh Baccalaureate
AAA from 3 A levels including Mathematics or AA from two A levels including Mathematics and A from the Advanced Welsh Baccalaureate Skills Challenge Certificate
Welsh 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.
T-Level
There are no T levels accepted for this programme.
Other requirements
GCSE requirements
Applicants must hold GCSE English language (or GCSE English) (minimum grade 4/C)
Find the equivalent international qualifications for our entry requirements.
English language requirements
If English isn't your first language, you'll need to complete an International English Language Testing System (IELTS) to demonstrate your competence in English. You'll need all of the following scores as a minimum:
IELTS score requirements
- overall score
- 6.5
- reading
- 6.0
- writing
- 6.0
- speaking
- 6.0
- listening
- 6.0
We accept other English language tests. Find out which English language tests we accept.
You might meet our criteria in other ways if you do not have the qualifications we need. Find out more about:
- our Access to Southampton scheme for students living permanently in the UK (including residential summer school, application support and scholarship)
- skills you might have gained through work or other life experiences (otherwise known as recognition of prior learning)
Find out more about our Admissions Policy.
Foundation year for engineering, physics, maths and geophysics
A foundation year will give you the skills and knowledge to progress to this course if you don't have the right qualifications for direct entry.
It could be the right option if you:
- have A levels, or equivalent international qualifications, in subjects other than the ones needed for direct entry
- have international qualifications in relevant subjects but not at A level equivalent
- have a BTEC Extended Diploma in a relevant subject
- are studying an Access course in a relevant subject
- are a mature student with relevant experience or study
You'll also need to show that you have strong maths skills.
Find full details on our Engineering, Maths, Physics, Geophysics Foundation Year page.
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: enquiries@southampton.ac.uk
Tel: +44(0)23 8059 5000
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.
Want more detail? See all the modules in the course.
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. Find out why, when and how we might make changes.
Year 1 modules
You must study the following modules in year 1:
Calculus
This module provides a bridge between A-level mathematics and university mathematics. Some of the material will be similar to that in A-level Maths and Further Maths but will be treated in more depth, and some of the material will be new. Topics of study ...
Dynamics and Relativity
This module is designed to introduce students to central elements of applied mathematics. It assumes no prior knowledge of particular applications, but assumes a working understanding of basic vector algebra and simple differential equations. The module p...
First Year Mathematics Workshop
Introduction to Probability and Statistics
The theory and methods of Statistics play an important role in all walks of life, society, medicine and industry. They enable important understanding to be gained and informed decisions to be made, about a population by examining only a small random sampl...
Linear Algebra I
Linear maps on vector spaces are the basis for a large area of mathematics, in particular linear equations and linear differential equations, which form the basic language of the physical sciences. This module restricts itself to the vector space R^n to ...
Linear Algebra II
Building on the intuitive understanding and calculation techniques from Linear Algebra I, this module introduces the concepts of vector spaces and linear maps in an abstract, axiomatic way. In particular, matrices are revisited as the representation of a ...
Multivariable Calculus
This module introduces the main ideas and techniques of differential and integral calculus of functions of two or more variables. One of the pre-requisites for MATH2003, MATH2011, MATH2014, MATH3033, MATH2038, MATH2039, MATH2045 and MATH2040
Number Theory
The aim of this module is to introduce students to some of the basic ideas of number theory, and to use this as a context in which to discuss the development of mathematics through examples, conjectures, theorems, proofs and applications. The module will ...
Operational Research I and Mathematical Computing
The module has two parts. The first part provides an introduction to the topic of operational research (OR). The key role of using models in OR to obtain solutions of practical problems arising in a variety of contexts is emphasised. Some classical pro...
Year 2 modules
You must study the following modules in year 2:
Analysis
The notion of limit and convergence are two key ideas on which rest most of modern Analysis. This module aims to present these notions building on the experience gained by students in first year Calculus module. The context of our study is: limits and co...
Partial Differential Equations
Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. The module will aim to stress the importance of both theory and applications of differential equations. The module begin...
You must also choose from the following modules in year 2:
Algorithms
Algorithms are systematic methods for solving mathematical problems, such as sorting numbers in ascending order, finding the cheapest way to ship goods on the road network or finding the shortest path in a graph. They can be regarded as practical applicat...
Fields and Fluids
Over the last four hundred years progress in understanding the physical world (theoretical physics) has gone hand in hand with progress in the mathematical sciences, so much so that the terms applied mathematics and theoretical physics have come to be alm...
Financial Mathematics
This module provides a solid mathematical introduction to the subject of Compound Interest Theory and its application to the analysis of a wide variety of complex financial problems, including those associated with mortgage and commercial loans, the valua...
Geometry and Topology
Geometry has grown out of efforts to understand the world around us, and has been a central part of mathematics from the ancient times to the present. Topology has been designed to describe, quantify, and compare shapes of complex objects. Together, geome...
Group Theory
Group theory is one of the great simplifying and unifying ideas in modern mathematics. It was introduced in order to understand the solutions to polynomial equations, but only in the last one hundred years has its full significance, as a mathematical for...
Maths and your Future
Maths in your Future will help you prepare for what comes after you graduate. You will apply your mathematical skills to an employer-raised problem and, in parallel, develop your professional skills.
Operational Research II
A variety of OR techniques are covered in lectures and assessed by examination. Workshops develop skills with computer modelling software (discrete-event simulation and linear programming). Other skills that are developed within the module are group w...
Statistical Distribution Theory
Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distrib...
Statistical Modelling I
Simple linear regression is developed for one explanatory variable using the principle of least squares. The extension to two explanatory variables raises the issue of whether both variables are needed for a well-fitting model, or whether one is sufficien...
Stochastic Processes
The module will introduce the basic ideas in modelling, solving and simulating stochastic processes.
Vector Calculus and Complex Variable
In the first part of this module we build on multivariate calculus studied in the first year and extend it to the calculus of scalar and vector functions of several variables. Line, surface and volume integrals are considered and a number of theorems inv...
Year 3 modules
You must choose your modules from the following modules in year 3:
Actuarial Mathematics I
This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flow...
Actuarial Mathematics II
Synopsis: The module extends the mathematical framework developed in MATH3063 in order to enable modelling of long term financial transactions where the various cash flows are contingent on the death or survival of several lives, or where there are sever...
Advanced Fluid Dynamics
Modelling fluid flow requires us first to extend vector calculus to include volumes that change with time. This will allow us to rephrase Newton’s second law of motion, that the force is equal to the time derivative of the linear momentum, in a way that ...
Advanced Partial Differential Equations
Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.
Algebraic Topology
Topology is concerned with the way in which geometric objects can be continuously deformed to one another. It can be thought of as a variation of geometry where there is a notion of points being "close together" but without there being a precise measure o...
Algorithms
Algorithms are systematic methods for solving mathematical problems, such as sorting numbers in ascending order, finding the cheapest way to ship goods on the road network or finding the shortest path in a graph. They can be regarded as practical applicat...
Communicating and Teaching Mathematics
This module runs under the national Undergraduate Ambassadors Scheme (www.uas.ac.uk) and provides an opportunity for students to act as ambassadors for their disciplines. For Mathematics students this will usually be in mathematics and mathematical skills...
Complex Analysis
Complex Analysis is the theory of functions in a complex variable. While the initial theory is very similar to Analysis (i.e, the theory of functions in one real variable as seen in the second year), the main theorems provide a surprisingly elegant, found...
Fields and Fluids
Over the last four hundred years progress in understanding the physical world (theoretical physics) has gone hand in hand with progress in the mathematical sciences, so much so that the terms applied mathematics and theoretical physics have come to be alm...
Financial Mathematics
This module provides a solid mathematical introduction to the subject of Compound Interest Theory and its application to the analysis of a wide variety of complex financial problems, including those associated with mortgage and commercial loans, the valua...
Further Number Theory
Number Theory is the study of integers and their generalisations such as the rationals, algebraic integers or finite fields. The problem more or less defining Number Theory is to find integer solutions to equations, such as the famous Fermat equation x^n ...
Galois Theory
This module is designed for students in their third year and aims to introduce the basic concepts and techniques of Galois theory, building on earlier work at level 2. As such, it will provide an introduction to core concepts in rings, fields, polynomials...
Geometry and Topology
Geometry has grown out of efforts to understand the world around us, and has been a central part of mathematics from the ancient times to the present. Topology has been designed to describe, quantify, and compare shapes of complex objects. Together, geome...
Graph Theory
Graph theory was born in 1736 with Euler’s solution of the Königsberg bridge problem, which asked whether it was possible to plan a walk over the seven bridges of the town without re-tracing one’s steps. Euler realised that the problem could be rephrased ...
Hilbert Spaces
This module is an introduction to the functional analysis of Hilbert spaces. The subject of functional analysis builds on the linear algebra studied in the first year and the analysis studied in the second year. Initially pivotal in Fourier theory and di...
Integral Transform Methods
Many classes of problems are difficult to solve in their original domain. An integral transform maps the problem from its original domain into a new domain in which solution is easier. The solution is then mapped back to the original domain with the inver...
Learning and Teaching Mathematics
This module offers an opportunity to learn about mathematics education. We explore different perspectives on the teaching and learning of mathematics drawing on research and theoretical considerations. You will also experience a range of research-informed...
Mathematical Biology
Biology is undergoing a quantitative revolution, generating vast quantities of data that are analysed using bioinformatics techniques and modelled using mathematics to give insight into the underlying biological processes. This module aims to give a flavo...
Mathematical Finance
Following an initial discussion of the assessment and measurement of investment risk, mean-variance portfolio theory is introduced and used to determine the risk and return for a portfolio of risky assets, the composition of the optimal such portfolio, an...
Mathematical Investigation and Communication
The module consists of three parts : 1. Introductory/revision lectures on the use of mathematical resources for original research, report writing, oral presentation skills and associated report and presentation software (1 week). 2. Group research pro...
Mathematical Programming
- Linear programs: their basic properties; the simplex algorithm. - Duality: the relationship between a linear program and its dual, duality theorems, complementarity, and the alternative; sensitivity analysis. - The interior point method for convex op...
Mathematics Project
For students on some degree programmes this Semester 2 project is compulsory; for most students it is optional. The project typically entails a weekly visit to a supervisor who advises and assists the student in the study of a particular topic. A disserta...
Maths and your Future
Maths in your Future will help you prepare for what comes after you graduate. You will apply your mathematical skills to an employer-raised problem and, in parallel, develop your professional skills.
Numerical Methods
Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding. Often in mathematics, it is possible to prove the existence of a solution to a given problem, ...
Operational Research II
A variety of OR techniques are covered in lectures and assessed by examination. Workshops develop skills with computer modelling software (discrete-event simulation and linear programming). Other skills that are developed within the module are group w...
Optimization
Module Contents: This module discusses continuous optimization problems where either the objective function or constraint functions or both are nonlinear. It explains optimality conditions, that is, which conditions an optimal solution must satisfy. It in...
Relativity, Black Holes and Cosmology
This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is cu...
Statistical Distribution Theory
Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distrib...
Statistical Inference
Statistical inference involves using data from a sample to draw conclusions about a wider population. Given a partly specified statistical model, in which at least one parameter is unknown, and some observations for which the model is valid, it is possibl...
Statistical Methods in Insurance
Statistical Modelling I
Simple linear regression is developed for one explanatory variable using the principle of least squares. The extension to two explanatory variables raises the issue of whether both variables are needed for a well-fitting model, or whether one is sufficien...
Statistical Modelling II
The module Statistical Modelling II covers in detail the theory of linear regression models, where explanatory variables are used to explain the variation in a response variable, which is assumed to be normally distributed. However, in many practical situ...
Stochastic Processes
The module will introduce the basic ideas in modelling, solving and simulating stochastic processes.
Structure and Dynamics of Networks
Networks are ubiquitous in the modern world: from the biological networks that regulate cell behaviour, to technological networks such as the Internet and social networks such as Facebook. Typically real-world networks are large, complex, and exhibit both...
Survival Models
This module introduces some of the fundamental ideas and issues of lifetime and time-to-event data analysis, as used in actuarial practice, biomedical research and demography.
Year 4 modules
You must study the following module in year 4:
You must also choose from the following modules in year 4:
Advanced General Relativity
General relativity is the theory of spacetime and gravity developed by Einstein. This module aims to develop a geometric understanding of general relativity and explore advanced applications of GR. In particular, we will study the physics of black holes (...
Advanced Partial Differential Equations
Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.
Complex Function Theory
This is a structured reading module designed for MMath students in their fourth year. The module introduces the basic concepts and techniques of Complex Function Theory based on rational and elliptic functions, viewed as meromorphic functions on the spher...
Design of Experiments
When planning experiments, it is essential that the data collected are as relevant and informative as possible. The statistical principles for the design of experiments include the choice of optimal or good treatments sets and appropriate replication of t...
Differential Geometry and Lie Groups
This is a compulsory lecture module for MMath students in their fourth year. The module will begin by looking at differential manifolds and the differential calculus of maps between manifolds. Manifolds are an abstraction of the idea of a smooth surfa...
Flexible Regression
This module will introduce and develop flexible statistical modelling methods that allow for general and complex forms of data to be modelled, extending ideas already encountered in earlier modules on linear and/or generalised linear modelling. The two ma...
Geometric Group Theory
Students will be able to apply logic and reason to prove basic results in geometric group theory. They will be able to use the geometry of the hyperbolic plane and other related simple geometric artefacts to demonstrate many of the standard features of ge...
Gravitational Waves
This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology. Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These ...
Harmonic Analysis
Harmonic analysis extends key ideas of Fourier analysis from Euclidean spaces to general topological groups. A fundamental goal is understanding algebras of functions on a group in terms of elementary functions. These correspond t the idea representing ...
Homotopy and Homology
Homotopy theory is the study of continuous deformations. A geometric object may be continuously deformed by pulling, stretching, pressing or compressing, but not by tearing or puncturing (which are discontinuous). Two objects can then be regarded as equiv...
Hyperbolic Geometry
This is a structured self-study module designed for MMath students in their fourth year. In this module, we take a guided tour of the hyperbolic plane, H, exploring its geometry and the group preserving its geometric structure. The hyperbolic plane arises...
Integral Transform Methods
Many classes of problems are difficult to solve in their original domain. An integral transform maps the problem from its original domain into a new domain in which solution is easier. The solution is then mapped back to the original domain with the inver...
Introduction to Semigroup Theory
This is a structured module, partly delivered by self-study and partly by lectures, designed for MMath students in their fourth year. A semigroup is a non-empty set on which is defined an associative binary operation. Unlike a group, a semigroup needn'...
Machine Learning
The purpose of the module will be to introduce students to the fundamentals of machine learning, i.e. computational methods for statistical learning, prediction and decision-making using data. The basic principles of predictive modelling will be outlined,...
Modelling with Differential Equations
The emphasis of this module is on the methods required to develop mathematical models using differential equations to understand physical problems. The module involves both conventional lectures as well as discussion lectures. The discussion lectures comp...
Modules and Representations
This module provides an introduction to the theory of modules over a principal ideal domain and the representation theory of finite groups, two basic tools in advanced mathematics.
Numerical Methods
Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary di...
Statistical Computing
This module consists of lecturers and associated practical sessions. The first part will focus on basic statistical programming in R. The second part will provide an introduction to some modern computational statistical methods and their implementation in...
Structure and Dynamics of Networks
Networks are ubiquitous in the modern world: from the biological networks that regulate cell behaviour, to technological networks such as the Internet and social networks such as Facebook. Typically real-world networks are large, complex, and exhibit both...
Survival Models
This module introduces some of the fundamental ideas and issues of lifetime and time-to-event data analysis, as used in actuarial practice, biomedical research and demography Co-Requisite: MATH6122
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
Study time
Your scheduled learning, teaching and independent study for year 1:
How we'll assess you
- coursework, laboratory reports and essays
- written exams
Your assessment breakdown
Year 1:
Year 2
Study time
Your scheduled learning, teaching and independent study for year 2:
How we'll assess you
- coursework, laboratory reports and essays
- written exams
Your assessment breakdown
Year 2:
Academic support
You’ll be supported by a personal academic tutor and have access to a senior tutor.
Course leader
Peter Kropholler is the course leader.
Careers
Employability is an essential part of our maths courses, ensuring you are equipped for a successful postgraduate career or further study. You can take optional ‘maths and your future’ module designed to boost your professional skills.
You’ll graduate with transferable skills that will qualify you to work in a range of fields and industries.
Our maths graduates have gone on to work as:
- actuaries
- economists
- statisticians
- programmers
- software developers
- accountants
- business analysts
- financial analysts
- financial managers
The University’s UoS Internships Programme can help you find a paid work placement during the Easter or summer vacation.
Careers services at Southampton
We are a top 20 UK university for employability (QS Graduate Employability Rankings 2022). Our Careers, Employability and Student Enterprise team will support you. This support includes:
- work experience schemes
- CV and interview skills and workshops
- networking events
- careers fairs attended by top employers
- a wealth of volunteering opportunities
- study abroad and summer school opportunities
We have a vibrant entrepreneurship culture and our dedicated start-up supporter, Futureworlds, is open to every student.
Work in industry
You’ll have the opportunity to take a paid year in employment between your second and third year.
Fees, costs and funding
Tuition fees
Fees for a year's study:
- UK students pay £9,250.
- EU and international students pay £22,300.
Your fees will remain the same each year from when you start studying this course. This includes if you suspend and return.
What your fees pay for
Your tuition fees pay for the full cost of tuition and standard exams.
Find out how to:
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:
Bursaries, scholarships and other funding
If you're a UK or EU student and your household income is under £25,000 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 Services Centre 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
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: enquiries@southampton.ac.uk
Tel: +44(0)23 8059 5000
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