Mathematics and Philosophy BSc

2025-26 entry
School of Mathematical and Physical Sciences
School of History, Philosophy and Digital Humanities

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


    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
    UCAS code: VG51
    Years: 2023, 2024
    First year

    Core modules:

    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.  Short writing exercises will help you hone specific writing skills. You will bring these skills together by writing a number of complete essays. The lectures in the course will be split between lectures on 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
    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

    Optional modules:

    A student will take a minimum of 20 credits (one module) and a maximum of 40 credits (two modules) from this group.

    Mind and World

    This module is an introduction to a range of topics in epistemology, metaphysics, and the philosophy of mind. In the first half of the module we consider questions such as: How should we understand knowledge? What implications does cognitive and cultural diversity have for our understanding of knowledge? Should we privilege some points of view? Should we trust others? Can we wrong them if we don't? And what should we say about disagreement? In the second half of the module we ask questions such as: Is the mind a physical thing? Can a machine have a mind? Can you survive the destruction of your body? Do you have free will? And can a machine be responsible for its own actions?

    20 credits
    Reason and Argument

    This module teaches basic philosophical concepts and skills to do with argument.  The first part of the course deals with arguments in ordinary language.  It teaches techniques for recognizing, interpreting, analyzing, and assessing arguments of various kinds.  It also teaches important concepts related to arguments, such as truth, validity, explanation, entailment, consistency, and necessity.  The second part of the course is a basic introduction to formal logic.  It teaches how to translate ordinary-language arguments into formal languages, which enables you to rigorously prove validity, consistency, and so on.

    20 credits
    Ethics and Society

    This module introduces students to some core questions in ethics, political philosophy, and social philosophy. We ask questions such as: What is a good life for you? What is a morally good life? Does being virtuous matter? What kind of moral consideration do we owe to non-human animals and the environment? Turning to political philosophy, we consider how societies should be organised if they are to realise values such as freedom, equality, and community. How should we understand these values? And what role might the state play in promoting (or undermining) them? We also look at some questions in social philosophy. For example: What are social groups? And when and why are social norms oppressive?

    20 credits

    Optional modules:

    A student will either take up to 20 credits (two modules) from this group.

    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

    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 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
    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
    Truth, Reality and Virtual Reality

    This module examines the idea that there is an objective reality to which the things we say and believe are answerable, which makes some claims true and others false. The emphasis is not so much on the question of whether and how we know things, but on metaphysical questions concerning truth and reality. 'What is Truth?' is one of these questions. Different attempts to define truth - including the Correspondence Theory of truth and the Pragmatic Theory of truth will be examined. Another question the course will tackle is the question of whether relativism about reality can be successfully refuted. And the module will address arguments relating to virtual reality, including arguments to the conclusion that what we think of as the real world is in fact a simulation, and arguments that call into question the supposed difference between reality and virtual reality. There are political and moral questions that hinge on answers to our metaphysical questions. The aim of the module is to introduce theories, concepts and frameworks that will be helpful to attempts to grapple with the metaphysical questions and further questions that hinge on them.

    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

    Optional modules:

    Or a student will take up to 20 credits (one module) from this group.

    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

    Optional modules:

    Or a student will take up to 20 credits from this group.

    History and Culture in China

    This module explores what it means to study China at university level, and considers how 'area studies' research on China fits within disciplines such as history and cultural studies. We will consider how histories and cultural understandings of China are built with the following in mind: how researchers use primary evidence such as texts, documents and/or images to understand social change; and how to navigate key debates in a field and evaluate competing arguments. You will finish this module with a deeper understanding of our core topic and the disciplinary approaches that frame it, and a foundation in critical research and writing skills that you can apply and develop in further study.

    We will work on a combination of new and established research to explore one core topic: In 2022-2023 we will explore the history of twentieth-century Shanghai as seen from the grassroots.

    20 credits
    History and Culture in Japan

    This module explores what it means to study Japan at university level, and considers how `area studies' research on Japan fits within disciplines such as history, comparative literature and cultural studies. We will work on a combination of new and established research to explore one core topic. We will consider how studies of Japan are built, how researchers use primary evidence in text and/or images to understand change; how to navigate key debates in a field and evaluate competing arguments. You will finish this module with a deeper understanding of our core topic and the disciplinary approaches that frame it, and a foundation in critical research and writing skills that you can apply and develop in further study.

    We will work on a combination of new and established research to explore one core topic: in 2022-2023 we will explore Japanese literature in the twentieth century as a frame for understanding modern Japanese history.

    20 credits
    Critical Curriculum Study

    The curriculum is often taken for granted by those who experience it, such as parents, students and teachers. This module poses questions about curriculum - what is it and who is it for? Different perspectives on curriculum are explored to establish a framework for critical curriculum study. After examining school curriculum reform both in England and in international contexts, the module will focus in depth on a single case study curriculum in England. This focused study will be carried out from the perspective of curriculum history, policy reform, analysis and implementation through research involving classroom-based curriculum development.

    20 credits
    Social and Historical Constructions of Childhood

    In this module students will explore how childhood has been portrayed across different societies and at different times, and will examine how childhoods are shaped and influenced by the societies in which children live, learn and are cared for. Through a series of lectures, group work and individual study tasks, students will think about the ways in which childhood has changed over time and how different views and perspectives on childhood create different expectations of children. Through the study of historical and social constructions of childhood, students will develop a fuller understanding of how ways of working with children can be shaped by external influences.

    20 credits
    Varieties of English

    This module looks at accent and dialect variation in the English language, in the UK and beyond. It will provide you with the tools to analyse and discuss variation in English words, sounds, and grammar. During the module you will collect your own data and learn how to analyse and visualise it. The module will develop your awareness of sociolinguistic aspects of the English language, and the relationship between language variation and change. You will be encouraged to consider your own experiences of language attitudes, language change, and language variation in order to reflect on the extraordinary diversity of the English language today.

    20 credits
    The Sounds of English

    This module is an introduction to the subdisciplines of Linguistics known as Phonetics and Phonology, focusing specifically on the sounds of the English language. It is designed to provide you with an understanding of the key concepts and terminology necessary to describe and explain sounds of English and of other languages. It will equip you with the practical skills necessary to transcribe and write about sounds. It serves as an essential basis for more advanced linguistic study.

    10 credits
    The Structures of English

    This module is an introduction to the syntax of natural languages, providing an essential grammatical base for more advanced studies in linguistic theory, historical linguistics, and sociolinguistics. This module is intended as a sister module to the 10-credit 'Sounds of English' module, which runs in parallel. It is designed to provide a firm grounding in the descriptions of sentence structure(s) cross-linguistically, and to introduce students to the tools used to describe syntactic structures, and the main methods of syntactic argumentation. The lectures will cover major topics in the formal description of morpho-syntax, while the seminar workshops will provide hands-on experience in analysing and thinking about sentence structure.

    10 credits
    Early Englishes

    This module is of particular interest to anyone who wants to know more about the first 1000 years of English language and literature. Early Englishes works backward over a whole millennium of English, 1600 to 600. Each week's lectures and seminar focus on one century and one text representative of that century (for example, Margery Kempe's Book, Chaucer's Canterbury Tales, and Beowulf). We will use a variety of techniques - literary, linguistic, anthropological, cultural-historical - to analyse each text, thereby opening up discussion of issues that preoccupied the English of the time, from glorious monster-slaying to the first expressions of love and desire, from religious devotion to comedy, from the power of insults to the status of English. We will investigate international influences on English language and literature, explore medieval worldviews and how they might differ from modern ones, and query what it means when we say something is medieval. No prior knowledge of Old or Middle English is necessary; students will be given the opportunity to examine texts in the original language but where necessary translations will be provided.

    20 credits
    Foundations in Literary Study: Biblical and Classical Sources in English Literature

    The Bible, Greek and Roman mythology, represent some of the central sources for European literary imaginations. In this module you will explore the range of literature indebted to biblical and classical literature, themes, and characters. Featuring a range of lecturers from across the School of English, the module will help you learn to think critically about biblical and classical themes such as divine destruction, love, gender, homecoming, colonialism, nostalgia, and empire, and read a variety of authors, from Amelia Lanyer and Shakespeare to Derek Walcott and Margaret Atwood. When we understand the ways in which biblical and classical writers shaped their narratives, and how creative authors revised, resisted or radicalised their themes, we have several important keys to unlock crucial facets of English literary tradition.

    20 credits
    Contemporary Literature

    This module introduces you to a diverse range of texts in English (prose, poetry, and film) with a focus on texts published since 2000. Texts will be chosen to provoke thinking and debate on urgent and controversial topics that might include: globalisation and neoliberalism; ecology and animal lives; artificial intelligence and the posthuman; political activism and social justice; migration and displacement; state violence and armed conflict. We will discuss formally and conceptually challenging works, raise ethical and philosophical questions and begin to discover how current critical and theoretical approaches can help us to engage with contemporary texts.

    20 credits
    The 'Disenchantment' of Early Modern Europe, c. 1570-1770

    This module explores the fundamental shifts in mental attitudes and public behaviour that occurred in Europe between the age of the Reformation and the age of the Enlightenment. The central focus of the course will be the examination of the supernatural - religious beliefs, but also witchcraft and magic. You will explore the changing ways in which beliefs impinged on people's lives at various social levels. You will also have an opportunity to study the impact on people's world views of such changes as rising literacy, urbanisation, state formation and new discoveries about the natural world. All these will be investigated in the institutional contexts of state and church and the ways in which they sought to channel and mould beliefs and behaviour. This module enables you to understand how the early modern period is distinctive from and links medieval and later modern historical studies.

    20 credits
    Music in a Global Context

    Whatever kind of music study you decide to specialise in, you'll do it better if you see it in the context of music as a phenomenon common to all humanity. You'll understand what's different about your own chosen field but also how the music you love derives from diverse cultural sources.In this module we examine how any music uses specific ways of organising sound to serve particular cultural purposes. You'll learn to recognise and describe diverse musical styles, research them through scholarly sources, present an analysis using appropriate audio-visual technology, and take control of the transferable skills you're developing.

    20 credits
    Music Psychology

    In this module you will engage with some of the most provocative questions about musical thought and behaviour: What are the characteristics of the musical mind? Why do we feel emotions when listening to or performing music? How does music and music therapy influence our health and wellbeing? Can music make you smarter? The module is designed such that no prior formal musical or psychological training is necessary.

    You will develop knowledge of the scientific methods used to study music from a psychological perspective, and how findings can inform applications in education, healthcare, and the creative industries.

    10 credits
    Technologies for Music

    Nowadays, most forms of music-related study involve music technologies. This module introduces you to a range of pertinent technologies, focussing around using computer in four key areas; sound recording, editing, transformation and representation, and a more general approach to computing required to complete tasks in many music modules. In each case, you will experience some of the many ways in which specific technologies serve many different music disciplines. You will go onto learn the essential principals of those technologies, before learning how they work in practice. By the end of the module, you will be versed in basics of digital audio, microphone choices and placement, sound recording techniques, wave-editing, MIDI, sound effect and plugins, file types and format, digital transcription and scoring and visual representation of sound. You will engage with University systems and through period of reflection complete a portfolio that contextualises your transferable skills.

    10 credits
    Religion in Britain

    This module provides an introduction to the critical study of religion, engaging with definitions, key concepts and different methods used in studying Religion in our society. We will examine theories, social trends, and sociological research, as well as debates in the society and the media, in order to better understand religious diversity in Britain today. We will study religious rituals and traditions, as well as atheism, humanism, spirituality, and mindfulness. We will examine key themes in the contemporary sociology of religion, such as secularism, fundamentalism, and pluralism, and consider empirical research on global religious trends, and British religiosity.
    The students will also have an opportunity to do some fieldwork, as one of the assignments is a mini-ethnography project, as students choose a religious community and visit them to observe lived religion first-hand. This module provides an excellent foundation for further study of religion and social sciences, as well as general understanding of issues behind media headlines, and critical awareness of social change affecting our society.

    20 credits
    Cities, Places and People

    The aim of this module is to provide students with an introduction to Sheffield with a particular focus on place, people, the local economy and urban change. You will be introduced to some of the theories, techniques and data  that planners use in their efforts to understand and create better places and the module will develop your skills of analysis for assessing the social, economic and environmental qualities of urban places. Through a series of site visits, students will gain an understanding of several different areas in Sheffield so that they develop a broader appreciation of the city's strengths and some of the contemporary challenges that it faces.

    10 credits
    Politics, Economy and Society in Japan

    This module explores what it means to study Japan at university level, and considers how ‘area studies’ research on Japan fits within disciplines such as political economy, international relations, anthropology, sociology and geography. We will work on a combination of new and established research to explore core topics in contemporary Japan: including how Japanese society has changed; how researchers use different conceptual frameworks and types of primary evidence to understand change and its wider impact; and, how to use the different types of work published in the field and evaluate competing arguments in key debates. You will finish this module with a deeper understanding of our core topic and the disciplinary approaches that frame it, and a foundation in critical research and writing skills that you can apply and develop in further study.

    20 credits
    Histories of Education

    This unit introduces students to a range of historical perspectives on education. It takes a critical historical approach to understanding the development of educational ideas, systems and practices by drawing attention to different cultural and historical contexts. In helping students question and challenge dominant ideas about education and its purposes, it will engage with and critique the philosophy of history to explore possible links between historical investigation and present day understandings of education. Topics include: the nature of history, early conceptions of education, education in pre-modern and modern contexts, development of mass schooling, histories of education, social justice and meritocracy.

    20 credits
    Child Psychology

    This module explores the relationship between psychological theory and educational policy and practice, considering some of the ways in which Education and Local Authority services have been influenced by ideas about children developed in psychological research. Some of the core concepts of Psychology are introduced such as cognitive psychology (intelligence, language and learning), behaviourism (including modification techniques), social and emotional development (including family and attachment, trauma) as well as the study of individual differences (with reference to psychopathologies such as autism, attention deficit/hyperactivity disorder).

    20 credits
    Making Sense of Education: Facts, Fiction and Data

    Politics, practices and media discourses related to Education, frequently invoke 'evidence' or statistical reasoning in an attempt to persuade. These approaches can be deliberately misused or accidentally misleading. This module will equip you with the knowledge you need to become a discerning data user and critic through a mix of active learning, seminars and computer workshops. You will develop practical skills to support your engagement with 'evidence' throughout your studies, explore a range of issues in qualitative and quantitative research design, and create a foundation for your future development as a critical researcher.

    20 credits
    History of English

    What is English? Taking this question as a point of departure, this module introduces students to the exceptionally dynamic linguistic history of English(es), with a specific focus on morpho-syntax and lexical semantics. Changing linguistic forms and functions are contextualized within their historical moments, and language external factors such as language contact, imperialism and racism are also discussed as they pertain to periods of English. The module begins with linguistic prehistory and the beginnings of Old English and finishes with a consideration of Creoles and the future and/or end of English. To be clear: this is not just a module about old language (although there is plenty of that!) - it's about gaining historical linguistic perspective on current Englishes and their place within a much bigger story.

    20 credits
    The Long View: an introduction to archaeology

    This module traces the development of modern humans through to the modern era. It introduces the wide range of materials and methods that archaeologists use to study the past.  The practical laboratory-based classes and field classes provide experience in the basic identification, investigation and interpretation of archaeological evidence. They are supported by lectures that introduce archaeological methods, theories and worldwide case studies. From field to laboratory using examples from throughout the world, you will learn about how archaeology shapes knowledge about the deep and recent human past.

    Through this module students will be introduced to debates on the formation and development of archaeological thought through a world-wide perspective from the Palaeolithic to the present. They will be presented with techniques and ideas used by archaeologists to explore the human record and understand the past. It offers an opportunity to explore and discover the archaeological record through practical engagement, using field and laboratory methods, while also highlighting the importance of selecting analytical techniques appropriate to the question posed and the data available. The module will enable students to develop core skills in decoding and critically understanding literature, observation, recording, analysis and interpreting archaeological evidence.

    20 credits
    Empire: From the Ancient World to the Middle Ages

    Covering the period from the 4th century BC to the 15th century AD, this module invites students to explore the ancient and medieval worlds through the lens of 'empire'. It provides an introduction to ancient and medieval types of empire, their contacts with and legacies to each other, and the connectedness between East and West in this period. Using a wealth of primary evidence and drawing on corresponding historiographical debates, students explore what it meant to live in ancient and medieval empires, what kind of social, cultural and religious encounters they engendered, and whether there was any space for resistance.

    20 credits
    The Making of the Twentieth Century

    This module considers the twentieth century as a time that transformed the social and political order in the world, calling into question the role of the European powers in global contexts, and dramatically reorienting the relationship between states and societies. You will engage with case studies representing key themes in twentieth-century global history: imperialism and the processes of decolonisation; the challenges of building the postcolonial nation; revolutions and the emergence of new states; war, genocide and conflict; and the institutions of international order.

    In addressing these themes, The Making of the Twentieth Century has a particular aim of counteracting prevailing tendencies towards Eurocentrism.  You will gain a considerable body of knowledge on the histories of Asia, Africa and Latin America especially.  At the same time, emphasis is placed on the empirical and theoretical grounds upon which competing interpretations rest in order to encourage you to develop critical awareness of the character of historical analysis.  More generally, this module aims to develop analytical, conceptual and literary skills through class discussion and written assignments.  Communication skills will also be emphasised in weekly seminars that will allow specific issues to be discussed in more depth, often with reference to primary source material.  Above all, the module seeks to stimulate an interest in history and an appreciation of cultural diversity.

    20 credits
    The Transformation of the United Kingdom, 1800 to the Present

    This module explores the central political, social, economic, cultural and diplomatic developments that have transformed Britain since 1800. Unlike most of its European neighbours, Britain did not experience dramatic moments of revolution, constitution-building, invasion or military defeat; indeed the belief that the nation was set on a course of gradual evolutionary progress was central to many versions of British identity. This course examines how, when and why change occurred in Britain. Key themes include the transition to mass democracy; the impact of industrialisation; shifts in social relationships based on class, gender and ethnicity; and the rise and fall of Britain as an imperial power.

    20 credits
    Popular Music Studies

    This module provides an introduction to the academic study of popular music. You will explore the various definitions of 'popular music' in relation to their socio-cultural context, and investigate some of the major issues and debates of popular music studies.

    Lecture materials and in-class tasks will engage with approaches to the analysis of popular music and media, issues of representation, and the relationship between popular musicians and their audiences. Assessments involve critical engagement with the themes of the module in relation to a popular music artist or piece of your choosing.

    10 credits
    Introduction to Comparative Politics

    This module examines the utility of the comparative approach to politics with a particular focus on democracies, dictatorships, and semi-democratic regimes. The key features of each regime type are considered and these are used to explain the nature of the comparative method, its strengths and weaknesses. This course also applies a comparative lens to processes such as democratisation, modernisation, and mobilisation. This course will draw on a wide range of examples from democratic, authoritarian, and semi-democratic countries.

    20 credits
    British Politics

    This module will introduce students to key concepts and debates in British politics through an examination of post-1976 British political history. Each lecture will take as its starting-point one day in recent British history and will describe what happened on that day and what happened as a result of that day. Each of the seminars will then follow that discussion: paying particular attention to concepts and ideas within the study of politics which can help us make sense of those events.

    20 credits
    Gender, Sexuality and Society

    This unit intends to address the following questions regarding gender and sexuality and their interaction with society: What do we mean by gender and sexuality? How do we do gender and sexuality? How do we see gender and sexuality? How do we control gender and sexuality?

    10 credits
    Climate Action

    Humans are altering the climate, with significant impacts on livelihoods, wellbeing, equality, and the environment across the globe.  While international organisations and governments are crucial in mitigating and adapting to these threats, individual and small group collective action are also essential in creatively exploring how the necessary changes can be realistically and equitably implemented.


    This module uses the community linked to the University as a Living Lab.  Focusing on one aspect of daily life in which there is potential for more mitigation or better adaptation, you will identify and plan an investigation or intervention (a 'project') to take a step towards more or better climate action.  You will need to justify your choices by elaborating what you would consider success, how you would deliver it, as well as assessing the impact of its wider implementation.

    10 credits
    Urban Economics

    This module provides an introduction to economic concepts and theories and to the way in which they are applied to the analysis of property markets and policy challenges. The module seeks to offer an economic perspective on planning issues by focusing on land market and urban development. The overall aim of the module is to develop students' understanding of the economic environment within which planners and other urban professions operate and to enhance understanding of economic theory and the property market in general.

    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


    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


    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:
    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:
    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 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

    School of History, Philosophy and Digital Humanities

    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 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

    School of History, Philosophy and Digital Humanities

    In the School of History, Philosophy and Digital Humanities, we interrogate some of the most significant and pressing aspects of human life, offering new perspectives and tackling globally significant issues.

    As a philosophy student at Sheffield you will benefit from the diversity of our modules and the high quality of our teaching which draws on the research expertise of our staff to ensure your lectures and seminars are informed, relevant and exciting.

    Our staff engage in cutting-edge research across a wide range of philosophical disciplines including epistemology, ethics, social, political and environmental philosophy, metaphysics and philosophy of the mind among others.

    Our supportive and inclusive community will also provide you with opportunities to use your philosophical knowledge to engage with real world problems and make a difference in the community through projects like our award-winning Philosophy in the City programme, which enables students to teach philosophy in the local community to audiences of all ages. Our students also run a thriving Philosophy Society and an 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. Their events are open to all students and there are opportunities to get involved in event planning and delivery.

    Philosophy students are 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 scholars of History, English, East Asian Studies and Languages & Cultures.


    Our students get to make the most of the University's facilities across campus. Explore some of the teaching, library and social spaces you'll be able to visit as an arts and humanities student.

    Department of Philosophy

    University rankings

      Number one in the Russell Group
    National Student Survey 2024 (based on aggregate responses)

      University of the Year and best for Student Life 
    Whatuni Student Choice Awards 2024

      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 2024, 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

    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


    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


    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.


    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


    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:

    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


    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:

    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.