Mathematics and Philosophy BSc

2025-26 entry
School of Mathematics and Statistics
Department of Philosophy

Learn to approach abstract problems in a reasoned, logical way. Choose from a huge range of options that introduce you to major thinkers and ask fundamental questions to challenge your understanding of the world.

Key details

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    Course description

    Students in a maths lecture

    Hone your talent for abstract, logical reasoning as you tackle fundamental questions and challenge your understanding of the world around us.

    This dual honours degree introduces you to essential maths skills and major schools of thought. Together these will create a varied, powerful box of tools which you’ll apply to increasingly complex problems – exploring aspects such as logic, ethics and politics, feminism, the arts and death.

    Some module options include more project work, and many give you the chance to put your mathematics skills into practice in different contexts and scenarios. By the time you graduate, you’ll have the knowledge and experience to follow any number of career paths.

    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.
    • Become an expert in solving problems - this dual course equips you with the ability to combine abstract and logical thinking, and approach challenges from new perspectives.
    • Tailor your degree - optional mathematics and philosophy modules, allowing you to focus on the areas you enjoy the most.
    • Welcoming community for everyone - we have an active student society (SUMS), regular maths challenges, and a dedicated LGBT+ student group for maths students. The Department of Philosophy is rated 1st in the Russell Group for student voice, and 3rd in the Russell Group for student satisfaction in the National Student Survey 2021.

    Dual and combined honours degrees

    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.

    Title: Mathematics and Philosophy BSc course structure 2023-24
    UCAS code: VG51
    Years: 2023
    First year

    Core maths 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

    You must take at least 40 credits of Philosophy modules. You must take:
    Writing Philosophy (details below) and at least one other core Philosophy module (20 credits) from the list below:

    Writing Philosophy

    Philosophical writing is a skill that you, the student, must hone early on in order to succeed in your degree. It is also a transferable skill that will serve you in your post-academic career. Philosophical writing combines the general virtues of clarity, organisation, focus and style found in other academic writing with particular philosophical virtues, namely, the ability to expose the implicit assumptions of analysed texts and to make explicit the logical structure of one's own and other people's arguments. A precondition of philosophical writing is a unique form of textual analysis that pays particular attention to its argumentative structure. In this module you will learn and practice philosophical writing. You will learn how to read in preparation for philosophical writing, learn how to plan an essay, learn how to rework your drafts and learn how to use feedback constructively. You will write five drafts and five essays and will have one on on tutorial on each essay you write. The lectures in the course will be split between lectures of the art of writing and lectures on philosophical topics in the domain of fact and value. Essay topics will be based on the topical lectures and their associated readings

    20 credits
    Mind and World

    This module aims to introduce a range of topics from epistemology, metaphysics, and the philosophy of mind. The module aims to outline some philosophical problems and topics from these areas, and in doing so show how these areas connect and thereby show how philosophical thinking can be unified and interconnected across these subjects.

    20 credits
    Ethics and Society

    This module aims to introduce a range of topics from certain overlapping areas of philosophical research relating to normative and practical matters: in particular, dealing with ethical theory, applied ethics, moral theory, moral psychology, and politics. The module aims to outline some major philosophical problems and topics from these areas, while also showing how the underlying concerns of the areas are connected to broad underlying philosophical concerns.

    20 credits
    Ethics and Society

    This module aims to introduce a range of topics from certain overlapping areas of philosophical research relating to normative and practical matters: in particular, dealing with ethical theory, applied ethics, moral theory, moral psychology, and politics. The module aims to outline some major philosophical problems and topics from these areas, while also showing how the underlying concerns of the areas are connected to broad underlying philosophical concerns.

    20 credits

    Maths options:

    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

    Philosophy options:

    Death

    This module is mainly about death itself . What is death? What happens to us when we die? Could there be an afterlife? Would it be a good thing if there were? What is it about death that we dislike so much, or that makes it bad? Is it rational, or even possible to fear death? What is the right attitude towards our own death? Do we have moral duties towards the dead? The course will clarify these questions and attempt to answer them. Readings will be taken from both historical and contemporary sources.

    10 credits
    Philosophy of Sex

    Sex is one of the most basic human motivators, of fundamental importance in many people's lives, and a topic of enormous moral, religious, and political contention. No surprise, then, that it turns out to be of great philosophical interest. We will discuss moral issues related to sex' asking when we might be right to judge a particular sex act to be morally problematic; and what political significance (if any) sex has. We will also discuss metaphysical issues, such as the surprisingly difficult questions of what exactly sex is and what a sexual orientation is. Throughout our study, we will draw both on philosophical sources and on up-to-date contemporary information.

    10 credits
    Philosophy of Religion

    This course will pose and try to answer philosophical questions about religion. These include questions about the nature of religion. For instance does being religious necessarily involve believing in the existence of a God or Gods? And is religious faith compatible with adherence to the scientific method? Other questions that the course will cover include questions about the theistic notion of God. Does the idea of an all-powerful being make sense? Is an all-knowing God compatible with human freedom? And is an all-powerful, all-knowing and perfectly good creator of the universe compatible with the existence of evil? Further questions concern God and morality. Is it true that if there is no God, then there is no right and wrong? The course will examine philosophical arguments for the existence of God, and question whether these arguments are sound.

    10 credits
    Ethics in Antiquity: East and West

    How should we live? What are the right values and principles by which we should guide our lives? What weight should we give to considerations of morality and justice? Are there fixed truths about these matters or are they just determined by choice or convention? Ethics is concerned with questions such as these. This course will engage with such questions by examining some important and influential texts from the ancient world, both Western and Eastern, including key writings by the Greek philosopher Plato and the Chinese philosopher Zhuangzi.   

    10 credits
    History of Philosophical Ideas

    The history of philosophy is made up of a series of debates between competing philosophical traditions and schools: for example, idealists argue with realists, rationalists with empiricists. And at different times, distinctive philosophical movements have dominated the discussion, such as pragmatism, existentialism, phenomenology, analytic philosophy, and critical theory. This module will introduce you to some of these central movements and traditions in the history of philosophy from Plato onwards, and the key philosophical concepts and issues that they have brought in to western thought.

    10 credits
    Philosophy of Science - Why Trust Science?

    Science plays an important role in modern society. We trust science on a day to day basis as we navigate our worlds. What is about science that makes it so trustworthy? Why is science a good guide for understanding the world? The aim of this half-module is to introduce some of the philosophical issues that arise in science and through reflecting on science. Most of the questions considered concern the epistemology of scientific knowledge and methodology: what are scientific theories, what counts as evidence for these theories, what is the relationship between observation and theory, is there a scientific method, what distinguishes science from other ways of understanding the world, and how does the social structure of science help or hinder science in studying the world. This module aims to introduce these questions as philosophical issues in their own right and within in the context of the history of the philosophy of science.

    10 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, seminars, 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 online 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:
    AAB
    including A in Maths

    A Levels + a fourth Level 3 qualification
    ABB including A in Maths + B in a relevant EPQ; ABB 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

    Access Sheffield offer

    The A Level entry requirements for this course are:
    ABB
    including A in Maths

    A Levels + a fourth Level 3 qualification
    ABB including A in Maths + B in a relevant EPQ; ABB including A in Maths + B in A Level Further Maths
    International Baccalaureate
    33 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
    AABBB + A in Maths
    Welsh Baccalaureate + 2 A Levels
    B + AB including A in Maths
    Access to HE Diploma
    Award of Access to HE Diploma in a relevant subject, with 45 credits at Level 3, including 30 at Distinction (to include Maths units), and 15 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 department.

    Graduate careers

    School of Mathematics and Statistics

    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

    Department of Philosophy

    Studying philosophy will develop your ability to analyse and state a case clearly, evaluate arguments and be precise in your thinking. These skills will put you in a strong position when it comes to finding employment or going on to further study.

    Our graduates work in teaching, law, social work, computing, the civil service, journalism, paid charity work, business, insurance and accountancy. Many also go on to study philosophy at postgraduate level.

    Sonia Nayyar in her graduation gown holding her degree certificate

    My degree has given me an excellent grounding in mathematical concepts I use every day

    Sonia Nayyar Mathematics BSc

    After graduating from Sheffield with a BSc in Mathematics, Sonia went on to work for a financial, actuarial and business consultancy, putting the analytic and logical thinking skills she learned during her degree to daily use.

    Matt sat at a desk in an office with lots of plants in the background

    How I'm using my maths skills to program software

    Matthew Jenkins Mathematics BSc

    After graduating, Matthew used the University Careers Service to help him find a job, and he now develops software in the marine navigation industry.

    A profile image of Rachael Batteson smiling in front of a yellow background

    I analyse the cost-effectiveness of new drugs, to see if they are viable to be accepted within the NHS, or other countries' health care systems

    Rachael Batteson BSc Mathematics

    Rachael works in health economics, using the analysis and problem solving skills she got from her maths degree to assess the viability of new drugs.

    School of Mathematics and Statistics

    Why study mathematics and statistics?

    When new students join the School of Mathematics and Statistics, we want them 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.

    Staff in the School of Mathematics and Statistics 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.

    The department is based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces for our students. It’s right next door to the Students' Union, and just down the road from the 24/7 library facilities at the Information Commons and the Diamond.

    School of Mathematics and Statistics

    Department of Philosophy

    We pride ourselves on the diversity of our modules and the high quality of our teaching. Our staff are among the best in the world at what they do. They're active researchers so your lectures and seminars are informed, relevant and exciting. We'll teach you how to think carefully, analytically and creatively.

    Our staff and students use philosophy to engage with real world issues. You will be able to use what you learn to make a difference in the community, through projects like Philosophy in the City, an innovative and award-winning programme that enables students to teach philosophy in schools, homeless shelters and centres for the elderly.

    Our students run a thriving Philosophy Society and the only UK undergraduate philosophy journal. Our Centre for Engaged Philosophy pursues research into questions of fundamental political and social importance, from criminal justice and social inclusion to climate ethics, all topics that are covered in our teaching.

    Philosophy changes our perspective on the world, and equips and motivates us to make a difference.

    The Department of Philosophy is based at 45 Victoria Street at the heart of the University campus. We're close to the Diamond and the Information Commons, as well as Jessop West, which houses our fellow Arts & Humanities departments of History, English and Languages & Cultures.

    Department of Philosophy

    Why choose Sheffield?

    The University of Sheffield

      Number one in the Russell Group
    National Student Survey 2023 (based on aggregate responses)

      92 per cent of our research is rated as world-leading or internationally excellent
    Research Excellence Framework 2021

      Top 50 in the most international universities rankings
    Times Higher Education World University Rankings 2023

      Number one Students' Union in the UK
    Whatuni Student Choice Awards 2023, 2022, 2020, 2019, 2018, 2017

      Number one for teaching quality, Students' Union and clubs/societies
    StudentCrowd 2023 University Awards

      A top 20 university targeted by employers
    The Graduate Market in 2023, High Fliers report


    School of Mathematics and Statistics

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

    Research Excellence Framework 2021

    Department of Philosophy

    1st in the Russell Group for Student Voice

    National Student Survey 2021

    3rd in the Russell Group for student satisfaction

    National Student Survey 2021

    Student profiles

    Guopeng Li sat in front of a plain white wall and a plant

    I think second and third year are genuinely designed to suit different people with different career pathways

    Guopeng Li BSc Mathematics

    After moving from China to Sheffield for his degree, Guopeng has found a way to tailor his degree to suit his future career paths, and has found Sheffield to be an easy city to settle in to.

    Elisabeth Chan

    As a dual degree student, you have access to activities organised by the two departments you're in

    Elisabeth Chan Mathematics and Philosophy BSc

    Elisabeth has developed programming skills from her mathematics modules and picked up some useful essay-writing skills from philosophy.

    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 three year course to a four-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

    With our third year Work Place Learning module, you can spend time with an organisation from the Sheffield voluntary or private sector, gaining skills and experience relevant to philosophy in an applied setting. You can also take part in the award-winning Philosophy in the City group, which introduces school children to philosophical ideas they can apply to everyday life. All of these experiences will help you build a compelling CV.

    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.

    Learn to approach abstract problems in a reasoned, logical way. Choose from a huge range of options that introduce you to major thinkers and ask fundamental questions to challenge your understanding of the world.