Mathematics and Statistics MMath
Explore topics across mathematics and statistics with our accredited MMath Mathematics and Statistics course. Gain the fundamental knowledge that every statistician needs for a successful career and complete a major research project.
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A Levels
AAA -
UCAS code
G110 -
Duration
4 years -
Start date
September
- Accredited
- Course fee
- Funding available
- Optional placement year
- Study abroad
Explore this course:
Course description
Why study this course?
Accredited by the RSS for the purpose of eligibility for Graduate Statistician status.
The Times and Sunday Times Good University Guide 2025.
Opt to spend a full year on a work placement. Our students have secured placements with a range of organisations, including Intel, the Met Office, HSBC, Deloitte, Morgan Stanley, and the Civil Service.
Gain research experience through the Sheffield Undergraduate Research Experience or Undergraduate Research Internship schemes.

This four-year accredited MMath Mathematics and Statistics course will give you the advanced problem-solving skills, statistical knowledge and research experience you’ll need for a successful career.
Learn how to find patterns in huge data sets, draw conclusions and think of creative solutions on our Royal Statistical Society accredited course.
In your first year you’ll focus on fundamental concepts. You’ll cover essential topics such as calculus, algebra, modelling and data science. You’ll hone your problem solving abilities, develop programming skills using Python and R, and learn to present your work as a professional mathematician using LaTeX.
In your second year you’ll learn how to apply your statistics knowledge to increasingly complex problems, through statistical modelling and computer simulations.
In addition to core modules, you’ll get the chance to enhance your knowledge of pure and applied mathematics through optional modules, covering topics such as algebraic structures, special relativity and differential equations.
In your third year, you’ll continue to develop your statistical knowledge. You’ll learn how to design experiments and collect data, how statistics are used in clinical trials of new drugs and how data can predict the likely outcome of an event. You can also choose from a range of more in-depth optional modules, such as mathematical biology, operations research and game theory, and financial mathematics and time series.
In your fourth year, you’ll gain valuable independent research experience by working on a research project. You’ll spend a large part of your final year investigating a real-world problem of your choice, alongside an active researcher who is an expert in your chosen area.
You’ll develop valuable project planning, problem solving and software skills. You’ll also learn how to present mathematics, statistics and other technical information, and gain experience communicating your findings verbally and in writing.
Whether you want a career in finance, technology or big data, you’ll also be able to tailor your degree to your goals through optional modules, equipping yourself with the skills and knowledge you need to succeed in your career.
Accredited by the Royal Statistical Society (RSS) for the purpose of eligibility for Graduate Statistician status
Modules
UCAS code: G110
Years: 2026
Core modules:
- Introduction to University Mathematics
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This core module is designed to consolidate A-level material and explore topics in mathematics that you'll use throughout your degree. You'll also be introduced to core skills, such as mathematical literacy, communication and problem-solving.
20 credits
Throughout this module you'll develop a strong foundation in core mathematics. You'll consider techniques for solving equations, special functions, calculus, vectors, complex numbers, and finite and infinite series. - Geometry, Matrices and Multivariate Calculus
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This core module is designed to further develop your knowledge of the core mathematics you'll use across your degree.
20 credits
You'll learn about two-dimensional coordinate geometry, discussing the theory of matrices geometrically and algebraically. You'll also define and evaluate derivatives and integrals for functions that depend on more than one variable, with an emphasis on functions of two variables.
Throughout this module you'll continue to develop your employability skills, exploring the career options open to mathematics graduates. You'll also work with your coursemates to undertake a group project on sustainability. - Foundations of Pure Mathematics
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The module aims to give an overview of basic constructions in pure mathematics; starting from the integers, we develop some theory of the integers, introducing theorems, proofs, and abstraction. This leads to the idea of axioms and general algebraic structures, with groups treated as a principal example. The process of constructing the real numbers from the rationals is also considered, as a preparation for “analysis”, the branch of mathematics where the properties of sequences of real numbers and functions of real numbers are considered.
20 credits - Probability and Data Science
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Probability theory is branch of mathematics concerned with the study of chance phenomena. Data science involves the handling and analysis of data using a variety of tools: statistical inference, machine learning, and graphical methods. The first part of the module introduces probability theory, providing a foundation for further probability and statistics modules, and for the statistical inference methods taught here. Examples are presented from diverse areas, and case studies involving a variety of real data sets are discussed. Data science tools are implemented using the statistical computing language R.
20 credits - Mathematical Investigation Skills
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This module introduces topics which will be useful throughout students’ time as undergraduates and in employment. These skills fall into two categories: computer literacy and presentation skills. One aim of this module is to develop programming skills within Python to perform mathematical investigations. Students will also meet the typesetting package LaTeX, the web design language HTML, and Excel for spreadsheets. These will be used for making investigations, and preparing reports and presentations into mathematical topics.
20 credits - Mathematical modelling
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Mathematics is the language of science. By framing a scientific question in mathematical language, it is possible to gain deep insight into the empirical world. This module aims to give students an appreciation of this astonishing phenomenon. It will introduce them to the concept of mathematical modelling via examples from throughout science, which may include biology, physics, environmental sciences, and more. Along the way, a range of mathematical techniques will be learned that tend to appear in empirical applications. These may include (but not necessarily be limited to) difference and differential equations, calculus, and linear algebra.
20 credits
In your second year, you’ll continue to build your fundamental knowledge of mathematics and statistics, which you’ll apply to increasingly complex problems.
Example core modules:
- Linear Algebra and Advanced Calculus
- Analysis
- Statistical Inference and Modelling
- Stochastic Modelling
You’ll also have the opportunity to enhance your knowledge of pure and applied mathematics, through optional modules covering topics such as algebraic structures, special relativity and differential equations.
In your third year, you’ll develop your expertise in the areas of mathematics that appeal to you most by choosing a specialist pathway. You can also choose to take our mathematics and statistics project and skills module to either complement or replace one of these pathways.
Pure mathematics pathway example modules:
- Metric Spaces and Measure Theory
- Topics in Algebra
Applied mathematics pathway example modules:
- Mathematical Biology
- Mathematical Physics and Analytical Dynamics
Probability and statistics pathway example modules:
- Bayesian Statistics and Generalised Linear Models
- Medical Statistics and Sampling Theory
You’ll have the opportunity to tailor your degree to your interests by choosing from a range of optional modules, including topics such as financial mathematics, machine learning, knot theory, and operations research and game theory.
Core modules:
- Machine Learning
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Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits - Generalised Linear Models
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This module introduces the theory and application of generalised linear models. These models can be used to investigate the relationship between some quantity of interest, the 'dependent variable', and one or more 'explanatory' variables; how the dependent variable changes as the explanatory variables change. The term 'generalised' refers to the fact that these models can be used for a wide range of different types of dependent variable ,continuous, discrete, categorical, ordinal etc. The application of these models is demonstrated using the programming language R.
15 credits - Bayesian Statistics and Computational Methods
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This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - Mathematics and Statistics Project
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This module forms the final part of the SoMaS project provision at Level 4 and involves the completion, under the guidance of a research active supervisor, of a substantial project on an advanced topic in Mathematics or Statistics. Training is provided in the use of appropriate computer packages for the presentation of mathematics and statistics and guidance on the coherent and accurate presentation of technical information.
45 credits
Optional modules:
A student will take 15 credits (one module) from this group.
- Financial Mathematics
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The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance, and includes a project.
15 credits - Further Topics in Mathematical Biology
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This module focuses on the mathematical modelling of biological phenomena. The emphasis will be on deterministic models based on systems of differential equations. Examples will be drawn from a range of biological topics, which may include the spread of epidemics, predator-prey dynamics, cell biology, medicine, or any other biological phenomenon that requires a mathematical approach to understand. Central to the module will be the dynamic consequences of feedback interactions within biological systems. In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used. If you did not take Scientific Computing at Level 2, you may still be able to enrol on this module, but you will need to obtain permission from the module leader first.
15 credits - Advanced Quantum Mechanics
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Quantum mechanics at an intermediate to advanced level, including the mathematical vector space formalism, approximate methods, angular momentum, and some contemporary topics such as entanglement, density matrices and open quantum systems. We will study topics in quantum mechanics at an intermediate to advanced level, bridging the gap between the physics core and graduate level material. The syllabus includes a formal mathematical description in the language of vector spaces; the description of the quantum state in Schrodinger and Heisenberg pictures, and using density operators to represent mixed states; approximate methods: perturbation theory, variational method and time-dependent perturbation theory; the theory of angular momentum and spin; the treatment of identical particles; entanglement; open quantum systems and decoherence. The problem solving will provide a lot of practice at using vector and matrix methods and operator algebra techniques. The teaching will take the form of traditional lectures plus weekly problem classes where you will be provided with support and feedback on your attempts.
15 credits - Advanced Particle Physics
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The module provides students with a comprehensive understanding of modern particle physics. Focusing on the standard model, it provides a theoretical underpinning of this model and discusses its predictions. Recent developments including the discovery of the Higgs Boson and neutrino oscillation studies are covered. A description of the experiments used to probe the standard model is provided. Finally the module looks at possible physics beyond the standard model.
15 credits - Probability with Measure Theory
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Probability is a relatively new part of mathematics, first studied rigorously in the early part of 20th century. This module introduces the modern basis for probability theory, coming from the idea of 'measuring' an object by attaching a non-negative number to it. This might refer to its length or volume, but also to the probability of an event happening. We therefore find a close connection between integration and probability theory, drawing upon real analysis. This rigorous theory allows us to study random objects with complex or surprising properties, which can expand our innate intuition for how probability behaves. The precise material covered in this module may vary according to the lecturer's interests.
15 credits - Topics in Mathematical Physics
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This unit will introduce students to advanced concepts and techniques in modern mathematical physics, in preparation for research-level activities.
15 credits
It is assumed that the student comes equipped with a working knowledge of analytical dynamics, and of non-relativistic quantum theory.
We will examine how key physical ideas are precisely formulated in the language of mathematics. For example, the idea that fundamental particles arise as excitations of relativistic quantum fields finds its mathematical realisation in Quantum Field Theory. In QFT, particles can be created from the vacuum, and destroyed, but certain other quantities such as charge, energy, and momentum are conserved (after averaging over quantum fluctuations).
We will examine links between conservation laws and invariants, and the underlying (discrete or continuous) symmetry groups of theories. We will also develop powerful calculation tools. For example, to find the rate of creation of new particles in a potential, one must evaluate the terms in a perturbative (Feynman-diagram) expansion.
For details of the current syllabus, please consult the module leader. - Mathematical Modelling of Natural Systems
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Mathematical modelling enables insight into a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.
15 credits - Further Topics in Number Theory
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Elementary number theory has been seen in a number of earlier modules. To go further, however, additional input is needed from other areas of pure mathematics - analysis and algebra. For example, the distribution of prime numbers is intricately related to the complex analytic properties of the Riemann zeta function And one can ask similar questions to those we ask about prime numbers for the rational numbers over, for example, quadratic fields. This module will treat examples of further topics in number theory, accessible with the aid of advanced mathematical background.
15 credits
The content of our courses is reviewed annually to make sure it's up-to-date and relevant. Individual modules are occasionally updated or withdrawn. This is in response to discoveries through our world-leading research; funding changes; professional accreditation requirements; student or employer feedback; outcomes of reviews; and variations in staff or student numbers. In the event of any change we will inform students and take reasonable steps to minimise disruption.
Learning and assessment
Learning
To make sure you get the skills and knowledge that every mathematician needs, you’ll learn through lectures, small group tutorials and problems classes, programming classes, and research projects.
Assessment
You’ll be assessed in a variety of ways, depending on the modules you take. This can include quizzes, examinations, presentations, participation in tutorials, projects, coursework and other written work.
Entry requirements
With Access Sheffield, you could qualify for additional consideration or an alternative offer - find out if you're eligible.
The A Level entry requirements for this course are:
AAA
including Maths
- A Levels + a fourth Level 3 qualification
- AAB, including A in Maths + A in a relevant EPQ; AAB, including A in Maths + B in A Level Further Maths
- International Baccalaureate
- 36, with 6 in Higher Level Maths (Analysis and Approaches); 34, with 6 in Higher Level Maths (Analysis and Approaches), and A in a maths-based extended essay
- BTEC Extended Diploma
- D*DD in Engineering with Distinctions in all Maths units
- BTEC Diploma
- DD + A in A Level Maths
- T Level
- Not accepted
- Scottish Highers + Advanced Higher/s
- AAAAB + A in Maths
- Welsh Baccalaureate + 2 A Levels
- A + AA, including Maths
- Access to HE Diploma
- Award of the Access to HE Diploma in a relevant subject, with 45 credits at Level 3, including 39 at Distinction (to include Maths units) and 6 at Merit
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We will give your application additional consideration if you have passed the Sixth Term Examination Paper (STEP), STEP 2 or STEP 3, at grade 3 or above. We do not consider STEP results in place of a third A Level
The A Level entry requirements for this course are:
AAB
including A in Maths
- A Levels + a fourth Level 3 qualification
- AAB, including A in Maths + A in a relevant EPQ; AAB, including A in Maths + B in A Level Further Maths
- International Baccalaureate
- 34, with 6 in Higher Level Maths (Analysis and Approaches)
- BTEC Extended Diploma
- DDD in Engineering with Distinctions in all Maths units
- BTEC Diploma
- DD + A in A Level Maths
- T Level
- Not accepted
- Scottish Highers + Advanced Higher/s
- AAABB + A in Maths
- Welsh Baccalaureate + 2 A Levels
- B + AA, including Maths
- Access to HE Diploma
- Award of the Access to HE Diploma in a relevant subject, with 45 credits at Level 3, including 36 at Distinction (to include Maths units) and 9 at Merit
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We will give your application additional consideration if you have passed the Sixth Term Examination Paper (STEP), STEP 2 or STEP 3, at grade 3 or above. We do not consider STEP results in place of a third A Level
You must demonstrate that your English is good enough for you to successfully complete your course. For this course we require: GCSE English Language at grade 4/C; IELTS grade of 6.5 with a minimum of 6.0 in each component; or an alternative acceptable English language qualification
Equivalent English language qualifications
Visa and immigration requirements
Other qualifications | UK and EU/international
If you have any questions about entry requirements, please contact the school/department.
Graduate careers
School of Mathematical and Physical Sciences
You won’t be short of career options with a degree in mathematics from Sheffield. Our courses are designed to give you the skills that will help you succeed in your chosen career. Employers hire our graduates because of their ability to analyse problems and reach a solution in a clear, precise and logical way.
A mathematics degree from Sheffield can take you far, whatever you want to do. Whether you want a job that involves doing lots of complex calculations, or one where you help businesses, charities and policymakers to find the best solutions to real-world problems.
Many of our graduates also choose to pursue a research career and go on to do PhDs at top universities.
Strong mathematical skills open all kinds of doors, from banking, insurance and pensions; software development at tech companies and encryption services at security agencies; to mapping the spread of disease and predicting demand for services for healthcare providers.
Our graduates go on to work for companies such as BAE Systems, Barclays, Dell, Deloitte, Goldman Sachs, HSBC, IBM, Lloyds, PwC, Unilever, the Civil Service and the NHS.
School of Mathematical and Physical Sciences
Research Excellence Framework 2021

The School of Mathematical and Physical Sciences is leading the way with groundbreaking research and innovative teaching.
Our mathematicians and statisticians have expertise across pure mathematics, applied mathematics, probability and statistics.
We focus on a variety of topics, from the most abstract questions in number theory to the calculations helping to understand climate change.
Mathematics and statistics students are based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces. To help our students feel part of a community, the Sheffield University Mathematics Society, SUMS, organise activities ranging from charity fundraisers to nights out.
Our students can also take part in problem-solving sessions, the Sheffield Space Initiative, and an LGBT+ support group for maths students.
University rankings
A world top-100 university
QS World University Rankings 2026 (92nd) and Times Higher Education World University Rankings 2025 (98th)
Number one in the Russell Group
National Student Survey 2024 (based on aggregate responses)
92 per cent of our research is rated as world-leading or internationally excellent
Research Excellence Framework 2021
University of the Year and best for Student Life
Whatuni Student Choice Awards 2024
Number one Students' Union in the UK
Whatuni Student Choice Awards 2024, 2023, 2022, 2020, 2019, 2018, 2017
Number one for Students' Union
StudentCrowd 2024 University Awards
A top 20 university targeted by employers
The Graduate Market in 2024, High Fliers report
Student profiles
What it's really like to study in the School of Mathematical and Physical Sciences
We asked some of our students and graduates to share their experiences of studying at the University of Sheffield, and to tell us what they've ended up doing with their degree.
Fees and funding
Fees
Additional costs
The annual fee for your course includes a number of items in addition to your tuition. If an item or activity is classed as a compulsory element for your course, it will normally be included in your tuition fee. There are also other costs which you may need to consider.
Funding your study
Depending on your circumstances, you may qualify for a bursary, scholarship or loan to help fund your study and enhance your learning experience.
Use our Student Funding Calculator to work out what you’re eligible for.
Placements and study abroad
Placement
Our students have secured placements with a range organisations, including Intel, the Met Office, HSBC, Deloitte, Morgan Stanley and the Civil Service.
Another great way to gain extra experience and inform future career aspirations is by applying to join the Sheffield Undergraduate Research Experience (SURE) or Undergraduate Research Internship schemes. You’ll spend around six weeks working in one of our research groups over the summer, pursuing research in an area of mathematics that you’re excited about.
Study abroad
Visit
University open days
We host five open days each year, usually in June, July, September, October and November. You can talk to staff and students, tour the campus and see inside the accommodation.
Subject tasters
If you’re considering your post-16 options, our interactive subject tasters are for you. There are a wide range of subjects to choose from and you can attend sessions online or on campus.
Offer holder days
If you've received an offer to study with us, we'll invite you to one of our offer holder days, which take place between February and April. These open days have a strong department focus and give you the chance to really explore student life here, even if you've visited us before.
Campus tours
Our weekly guided tours show you what Sheffield has to offer - both on campus and beyond. You can extend your visit with tours of our city, accommodation or sport facilities.
Apply
The awarding body for this course is the University of Sheffield.
Recognition of professional qualifications: from 1 January 2021, in order to have any UK professional qualifications recognised for work in an EU country across a number of regulated and other professions you need to apply to the host country for recognition. Read information from the UK government and the EU Regulated Professions Database.
Any supervisors and research areas listed are indicative and may change before the start of the course.