Mathematics MMath

2025-26 entry
School of Mathematical and Physical Sciences

Preparation for a career in research, whether you want to work on solutions to abstract mathematics problems or apply your problem solving skills to challenges in industry. In your final year, you’ll complete a major research project.

Key details

Explore this course:

    Course description

    Why study this course?

    Leading maths research

    96% of our research is rated as world-leading or internationally excellent, according to the Research Excellence Framework 2021.

    Real-world problem solving

    Research unanswered questions, from the most abstract research in areas like algebraic geometry and number theory, to the calculations behind animal movements and black holes.

    Everyone is welcome

    There’s a place at Sheffield for everyone who enjoys mathematics. Find a warm welcome at our active student society (SUMS), regular maths challenges, and a dedicated LGBT+ student group for maths students.

    Set up for a successful career

    Careers and employability skills are built into our maths degree programmes. We organise regular events and networking opportunities with employers like Goldman Sachs, Unilever, and the NHS who hire our graduates to solve problems.

    Extended research projects

    Investigate a real-world problem of your choice in your final year research project, alongside an active researcher. This will also help you hone those presentation and project management skills, so you’ll know how to present maths and statistics and other technical information.

    Students in a maths lecture

    Tackle some of the most intriguing maths problems, and develop the advanced tools you’ll need to tackle real-world problems in a logical, analytical way.

    Whether your passion is solving abstract research problems, or you like the idea of applying those same skills to data science or maybe finance, a Mathematics MMath at the University of Sheffield is the right place to begin.

    Year one is the essentials – calculus, algebra, modelling, data science – and you work with your personal tutor to hone your problem solving abilities and develop the broader career skills that all employers value.

    We’ll take you into the world of techniques that are used to understand the spread of infectious disease and climate change. And in your second year, you’ll add to your growing toolbox, developing programming skills using Python and R, and learning to present your work as a professional mathematician using LaTeX.

    The second half of your degree is yours to shape from optional modules, following your interests, and laying down the knowledge and experience you need to follow your chosen career path.

    In year four, you’ll investigate a real-world or pure maths problem of your choice, alongside an active researcher – collaborating with mathematicians who are advancing the field. Together, we’ll mould you into a candidate that would be prized in academia, or any graduate position you choose.

    Second-year Maths student Amelia takes us through a busy day of lectures before heading to Netball practice to unwind

    Modules

    A selection of modules are available each year - some examples are below. There may be changes before you start your course. From May of the year of entry, formal programme regulations will be available in our Programme Regulations Finder.

    Choose a year to see modules for a level of study:

    Title: Mathematics MMath course structure
    UCAS code: G103
    Years: 2023, 2024
    First year

    Core modules:

    Mathematics Core

    Mathematics Core covers topics which continue school mathematics and which are used throughout the degree programmes: calculus and linear algebra, developing the framework for higher-dimensional generalisation.  This material is central to many topics in subsequent courses.  At the same time, small-group tutorials with the Personal Tutor aim to develop core skills, such as mathematical literacy and communication, some employability skills and problem-solving skills.

    40 credits
    Foundations of Pure Mathematics

    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
    Mathematical modelling

    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
    Probability and Data Science

    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

    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

    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'll consult and inform students in good time and take reasonable steps to minimise disruption.

    Learning and assessment

    Learning

    You'll learn through lectures, problems classes in small groups and research projects. Some modules also include programming classes.

    We invest to create the right environment for you. That means outstanding facilities, study spaces and support, including 24/7 access to our online library service.

    Study spaces and computers are available to offer you choice and flexibility for your study. Our five library sites give you access to over 1.3 million books and periodicals. You can access your library account and our rich digital collections from anywhere on or off campus. Other library services include study skills training to improve your grades, and tailored advice from experts in your subject.

    Learning support facilities and library opening hours

    Assessment

    You will 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.

    Programme specification

    This tells you the aims and learning outcomes of this course and how these will be achieved and assessed.

    Find programme specification for this course

    Entry requirements

    With Access Sheffield, you could qualify for additional consideration or an alternative offer - find out if you're eligible.

    Standard offer

    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)
    BTEC Extended Diploma
    D*DD in Engineering with Distinctions in all Maths units
    BTEC Diploma
    DD + A in A Level Maths
    Scottish Highers + 1 Advanced Higher
    AAAAB + A in Maths
    Welsh Baccalaureate + 2 A Levels
    A + AA including Maths
    Access to HE Diploma
    Award of 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
    Other requirements
    • 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

    Access Sheffield offer

    The A Level entry requirements for this course are:
    AAB
    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
    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
    Scottish Highers + 1 Advanced Higher
    AAABB + A in Maths
    Welsh Baccalaureate + 2 A Levels
    B + AA including Maths
    Access to HE Diploma
    Award of 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
    Other requirements
    • 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

    English language requirements

    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

    Pathway programme for international students

    If you're an international student who does not meet the entry requirements for this course, you have the opportunity to apply for a pre-masters programme in Science and Engineering or Business, Social Sciences and Humanities at the University of Sheffield International College. This course is designed to develop your English language and academic skills. Upon successful completion, you can progress to degree level study at the University of Sheffield.

    If you have any questions about entry requirements, please contact the school/department.

    Graduate careers

    School of Mathematical and Physical Sciences

    Strong mathematics skills open all kinds of doors for our graduates: from banking, insurance and pensions, to software development at tech companies and encryption services at security agencies. They also work for businesses with vast amounts of data to process and inform new products and services.

    Organisations that have hired Sheffield maths graduates include AstraZeneca, BAE Systems, Barclays, Bet365, Dell, Deloitte, Goldman Sachs, GSK, HSBC, IBM, Lloyds, PwC, Unilever, the Civil Service and the NHS. Lots of our students also go on to do PhDs at world top 100 universities.

    Your career in mathematics and statistics

    Student Hailey Pottinger stood in front of a brick wall smiling

    I've found that employers always value the skills that maths students can bring to a role

    Hailey Pottinger Mathematics MMath

    After graduating, Hailey joined the NHS Graduate Management Training Scheme. The mathematical and problem solving skills Hailey learned during her MMath degree helped her secure her place on the scheme, and management roles in the NHS.

    Will Oxley

    My maths education in Sheffield has prepared me very well for conducting research

    Will Oxley Mathematics MMath

    As an undergraduate maths student, will took part in a series of research projects that led to four publications in academic journals. He's now working on a PhD at the University of Cambridge.

    Elizabeth Sheppeck

    My degree was a big enabler in me getting my job

    Elizabeth Sheppeck Mathematics MMath

    Elizabeth did a project on relativity during her maths degree, and is now training to become a finance leader in the aerospace and defence industry.

    School of Mathematical and Physical Sciences

    96 per cent of our mathematical sciences research is rated as world-leading or internationally excellent.

    Research Excellence Framework 2021

    Why study mathematics and statistics?

    The School of Mathematical and Physical Sciences is leading the way with groundbreaking research and innovative teaching. We provide our students with the skills and knowledge to support them in a wide range of careers.

    Mathematicians at the University of Sheffield work on a wide range of topics, from the most abstract research in areas like algebraic geometry and number theory, to the calculations behind animal movements and black holes. They’ll guide you through the key concepts and techniques that every mathematician needs to understand and give you a huge range of optional modules to choose from.

    We want mathematics and statistics students to feel part of a community. At the heart of this is the Sheffield University Mathematics Society, or SUMS, who organise activities throughout the academic year, from charity fundraisers to nights out. Our students also take part in pizza lectures, rocket engineering projects, international maths challenges, and an LGBT+ support group for maths students.

    Mathematics and statistics students are based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces. It's right next door to the UK’s number one students’ union, down the road from the 24/7 library facilities at the Information Commons and the Diamond, and a short walk from the city centre.

    School of Mathematical and Physical Sciences

    University rankings

      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 2023, High Fliers report

      A top-100 university: 12th in the UK and 98th in the world
    Times Higher Education World University Rankings 2025

    Student profiles

    Freya Davies

    I love the mathematics course and the city experience is great

    Freya Davies Mathematics MMath

    Freya has enjoyed the pure maths and mechanics on her degree so far, as well as the experience of living in the city.

    Frederick Carter

    If you have a passion for mathematics, you should definitely consider this course

    Frederick Carter Mathematics MMath

    Choosing to study maths was an easy choice for Frederick. At Sheffield, he's been able to explore fascinating topics such as group theory.

    Yihui Tong

    I have built a thorough knowledge of both pure and applied mathematics

    Yihui Tong Mathematics MMath

    Yihui enjoyed choosing from a wide range of modules and developed an interest in solar physics, which she plans to study further as a postgraduate researcher.

    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.

    Examples of what’s included and excluded

    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

    You may have the opportunity to add an optional placement year as part of your course, converting the four year course to a five-year Degree with Placement Year.

    A placement year will help you to:

    • gain an insight into possible careers
    • develop a range of transferable skills
    • build a professional network
    • get a feel for what you do and don’t like doing
    • add valuable work experience to your CV
    • gain experience of applying for jobs and interview practice
    • apply elements of academic learning in the workplace

    Study abroad

    Spending time abroad during your degree is a great way to explore different cultures, gain a new perspective and experience a life-changing opportunity that you will never forget. 

    You can apply to extend this course with a year abroad, usually between the second and third year. We have over 250 University partners worldwide. Popular destinations include Europe, the USA, Canada, Australia, Singapore and Hong Kong. 

    Find out more on the Global Opportunities website.

    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.

    Open days: book your place

    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.

    Upcoming taster sessions

    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.

    Campus tour: book your place

    Apply

    Make sure you've done everything you need to do before you apply.

    How to apply When you're ready to apply, see the UCAS website:
    www.ucas.com

    Not ready to apply yet? You can also register your interest in this course.

    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.

    Our student protection plan

    Terms and Conditions upon Acceptance of an Offer

    2025-2026

    Make sure you've done everything you need to do before you apply.

    How to apply When you're ready to apply, see the UCAS website:
    www.ucas.com

    Not ready to apply yet? You can also register your interest in this course.

    Preparation for a career in research, whether you want to work on solutions to abstract mathematics problems or apply your problem solving skills to challenges in industry. In your final year, you’ll complete a major research project.

    No No