Mathematics and Philosophy BSc
School of Mathematics and Statistics
Department of Philosophy
You are viewing this course for 2021-22 entry. 2022-23 entry is also available.
Mathematics and philosophy is a challenging, rewarding combination. Both subjects require careful, rigorous reasoning as well as imagination.
Your maths study will include core mathematics, pure mathematics, applied mathematics and probability and statistics. You can specialise later in the course.
The philosophy side of the course is flexible. There are no compulsory modules. You can develop your understanding of key areas such as ethics, philosophy of mind, theory of knowledge, political philosophy, metaphysics and logic.
We also teach courses on major figures in the history of philosophy such as Plato, Aristotle, Descartes and Hegel.
The modules listed below are examples from the last academic year. There may be some changes before you start your course. For the very latest module information, check with the department directly.
Choose a year to see modules for a level of study:
UCAS code: VG51
- Mathematics Core 1
The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.20 credits
- Mathematics Core II
The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.20 credits
- Numbers and Groups
The module provides an introduction to more specialised Pure Mathematics. The first half of the module will consider techniques of proof, and these will be demonstrated within the study of properties of integers and real numbers. The second semester will study symmetries of objects, and develop a theory of symmetries which leads to the more abstract study of groups.20 credits
- Matters of Life and Death
This course will look at the value of life and the wrongness of killing. We will look at various issues of important practical concern, such as abortion, euthanasia, capital punishment, war, as well as the case of allowing people to die from need whom we could have saved. We will look at how best to understand the principles that guide, and ought to guide, our judgements about what to do when confronted with these issues. Students will gain a better understanding of how to think about these issues, and in particular will be introduced to the benefit of thinking about them philosophically.20 credits
- Mind, Brain and Personal Identity
What is it to have a mind? Is your mind a physical thing, such as your brain? Or is it a non-physical soul? Do human beings have free will¿the ability to freely choose their own actions¿and, if so, how? What makes you the same person you were when you were a young child? Do non-human animals have minds? Could computers or robots have artificially created minds? If animals or computers had minds would they have souls? Could they have free will? This course examines these issues and some historical and contemporary attempts to understand them.20 credits
- Self and Society
This course introduces students to central questions in political philosophy: Do we need a state, and if so, must we obey its laws? When, why and how may states punish citizen for failing to obey the law? What is freedom, and when are we free? Is equality a moral value, and if so, what are its implications for how governments ought to act? What is justice, and how does it relate to freedom, equality, and punishment? Should states be organised democratically, and what does it mean to live in a democracy? The course encourages students to think carefully and clearly about the relationship they have, as citizens, to each other and the state, and to develop their analytical and critical skills in the process. Readings will include influential, historical and contemporary discussions of the state, equality, freedom, justice, and democracy.20 credits
- 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 readings20 credits
This module is mainly about death itself [whereas PHI125 is mainly about killing}. 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
- Elementary Logic
The course will provide students with knowledge of the fundamental parts of formal logic. It will also teach them a range of associated formal techniques with which they can then analyse and assess arguments. In particular, they will learn the languages of propositional and first-order logic, and they will learn how to use those languages in providing formal representations of everyday claims. They will also learn how to use truth-tables and truth-trees.10 credits
- History of Ethics
How should we live? What is the right thing to do? This module offers a critical introduction to the history of western ethical thought, examining some of the key ideas of Plato, Aristotle, Hume, Kant, Wollstonecraft, Douglass, Bentham, Mill, Taylor Mill, Nietzsche, Rawls and Gilligan. It provides a textual introduction to some of the main types of ethical theory: the ethics of flourishing and virtue; rights-based approaches; utilitarianism; contractualism. We explore the close interconnections between ethics and other branches of philosophy (e.g. metaphysics, epistemology, aesthetics), as well as the connections between ethics and other disciplines (e.g. psychology; anthropology).10 credits
- Knowledge, Justification and Doubt
In our age of post-truth politics and fake news, this course aims to introduce students to philosophy by investigating some basic problems in epistemology (i.e. the philosophical study of knowledge). We will address questions such as: what knowledge is and why it is important; what truth is; what kinds of things can be known and how; if and how perceptual experience gives us knowledge of an external world; whether all knowledge has to be grounded in experience; whether knowledge is socially constructed (and if so whether that is necessarily problematic); what role justice plays in our epistemic practices.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
- Philosophy of 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
- 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
- Reason and Argument
Arguments are everywhere - in our newspapers, on our television screens and radios, in books and academic papers, on blogs and other websites. We argue with our friends, families, teachers and taxi drivers. These arguments are often important; they help us to decide what to do, what to believe, whom to vote for, what car to buy, what career path to follow, or where we should attend university (and what we should study). The ability to recognise, evaluate and produce arguments is therefore immeasurably valuable in every aspect of life. This course will teach you how to recognise an argument, how to understand it, how to evaluate and criticise it, and how to produce your own. Students in this module will learn how to extract an argument from a complex text, how to uncover hidden assumptions, and how to recognise and critique bad reasoning10 credits
- Advanced Calculus and Linear Algebra
Advanced Calculus and Linear Algebra are basic to most further work in pure and applied mathematics and to much of statistics. This course provides the basic tools and techniques and includes sufficient theory to enable the methods to be used in situations not covered in the course. The material in this course is essential for further study in mathematics and statistics.20 credits
This unit continues the study of abstract algebra begun in MAS114, going further with the study of groups, and introducing the concepts of a ring, which generalises the properties of the integers, and a vector space, which generalises the techniques introduced in linear algebra to many more examples. As well as demonstrating the interest and power of abstraction, this course is vital to further studies in most of pure mathematics, including algebraic geometry and topology, functional analysis and Galois theory.20 credits
This course is a foundation for the rigorous study of continuity, differentiation and integration of functions of one real variable. As well as providing the theoretical underpinnings of calculus, we develop applications of the theory and examples that show why the rigour is needed, even if we are focused on applications. The material in this course is vital to further studies in metric spaces, measure theory, parts of probability theory, and functional analysis.20 credits
How should we live? How should we conduct ourselves? What duties do we owe t9 other people? Are there certain things we should never do in any circumstances? If so what things are they? Do questions like the foregoing have determinate, correct answers? If so can we know what they are? If so, how? These questions and questions like them are the subject matter of ethics. We will be studying and thinking about such questions by engaging with classical and/or contemporary texts.20 credits
- Ethics: Theoretical and Practical
There are some things we morally ought to do, ways we ought to live. Those of us who are not moral sceptics will agree so far. Indeed, we may even agree extensively about what we ought to do or how we ought to live. But why? Ethicists don¿t just ask what we ought to do. They also try to work out, as systematically as possible, what explains the demands, obligations and requirements that stem from morality. That is what this module will explore. Is morality all about promoting the well-being of humans and other creatures? Does it stem from the requirements of rationality? Is it aimed at achieving the distinctive kinds of excellence that creatures like us can attain?20 credits
Feminists have famously claimed that the personal is political. This module takes up various topics with that methodological idea in mind: the family, cultural critique, language. We examine feminist methodologies - how these topics might be addressed by a feminism that is inclusive of all women - and also turn attention to social structures within which personal choices are made - capitalism, and climate crisis .20 credits
- Formal Logic
The course will start by introducing some elementary concepts from set theory; along the way, we will consider some fundamental and philosophically interesting results and forms of argumentation. It will then examine the use of 'trees' as a method for proving the validity of arguments formalised in propositional and first-order logic. It will also show how we may prove a range of fundamental results about the use of trees within those logics, using certain ways of assigning meanings to the sentences of the languages which those logics employ.20 credits
This course is an introduction to metaphysics. It will focus on two general themes: whether we are material things, and the nature of time. Readings will be drawn mainly from recent and contemporary sources.20 credits
- Philosophy of Education
What is education? And what is it for? These are the questions at the heart of this course. To begin to try to answer them, students will engage in: (1) a theoretical exploration of the central philosophical problems related to education and schooling; and (2) a practical task focusing on learning how philosophy can be taught effectively to secondary school pupils. The theoretical exploration will be taught in a similar way to other philosophy modules (through a weekly lecture and seminar) and a mid-term coursework essay will assess this component (counting for 50% of the module grade). The practical element will be taught through workshops, engagement with reflective practice, observations at a secondary school, and actual experience of running seminars with secondary school pupils at the University during a three-day conference at the end of the course. The practical part of the course will be assessed by a teaching portfolio (which counts for 50% of the module grade) composed of lesson plans and a reflection. Teaching is a special kind of challenge, but students on the course are not expected to have any previous experience in teaching or in planning lessons. Help and support will be provided throughout the module to make the delivery of lessons to secondary school pupils a realistic goal for all motivated students.20 credits
- Philosophy of Mind
This module provides a survey of philosophical theories of the mind, looking at such questions as: How is consciousness possible? Why is it that vibrations in the air around us produce conscious experiences of particular auditory experiences in our minds? Why is it that electromagnetic waves hitting our retinas produce particular visual experiences in our minds? What makes our thoughts represent things in the world? What is it about your thought that cats have whiskers that makes it about cats and whiskers? What is it about your thought that there are stars in the universe too far away for any human to have perceived them that makes it about such stars? What is the relation between thoughts and conscious experiences and brain states? We'll look at a variety of answers to these and related questions and examine some of the most important and influential theories that contemporary philosophers have to offer.20 credits
- Philosophy of Science
It is virtually impossible to overstate the importance that science has in our everyday life. Here is a brief list of things that would not exist without modern science: computers, phones, internet, cars, airplanes, pharmaceutical drugs, electric guitars. Imagine your life without these things. It looks very different doesn't it? Science, however, is not important only in virtue of its practical applications. in fact, many would agree that the the primary value of science is that of being the best available source of knowledge about the world. Indeed, it seems fair to say that we made more discoveries after the 17th century scientific revolution [e.g. the laws of planetary motion, the principles underlying biological evolution, the laws governing quantum phenomena, the structure of DNA, the cellular architecture of the brain] than in all the previous millenia. This raises important philosophical questions. First, what is science? What are the criteria that demarcate science from non-science? For example, what is the difference between science and religion? Second, how does science work? What are the methods and eplanatory strategies that make it so successful? Is there such a thing as the scientific method, and what counts as a scientific explanation? Third, is science objective? That is, is science a form of rational and unbiased inquiry, or does it reflect ethical, political, and social factors? Finally, is science the fundamental source of knowledge about the world? Does science tell us how things really are? These are some of the questions that we will tackle in this course.20 credits
- Philosophy of the Arts
This module introduces students to a broad range of issues in the philosophy of art. The first half asks 'What is art?'. It examines three approaches: expression theories, institutional accounts, and the cluster account. This is followed by two critiques focusing on the lack of women in the canon and problems surrounding 'primitive' art. The evolutionary approach to art is discussed , and two borderline cases: craft and pornography. The second half examines four issues: cultural appropriation of art, pictorial representation, aesthetic experience and the everyday, and the nature of artistic creativity.20 credits
- Political Philosophy
We are citizens in a democratic capitalist society, we vote and choose our representatives and our government, our representatives make laws that we must then follow. We do not only obey the laws only for fear of being punished; we believe that our system of government is just, and that it is just for us to obey the laws. We believe that - by and large - we live in a just society. Do we? What justifies our system of government? Are there alternative possible relations, alternative forms of citizenship; alternative forms of government, alternative ways of organising a society? Is ours the only just one? We will look at the history of political philosophy and explore various systems of citizenship, government and economic arrangements. Our main aim will be to understand how these different systems justify or legitimise the existence of government and its authority to make and enforce laws. We will also look at the more general notion of 'justice' that accompanies and grounds these systems of government. Two side concerns will be:- 1. The relation between a philosopher's view of ethics and her political philosophy. 2. The relation between a philosopher's view of human nature and her political philosophy.20 credits
- Reference and Truth
This module is an introductory course in the Philosophy of Language. The overall focus of the course will be on the notion of meaning. The first part of the course will attempt to shed light on the notion of meaning by investigating different accounts of the meanings of some types of linguistic expressions, in particular names (for instance 'Nelson Mandela') and definite descriptions (for instance 'the inventor of the zip', 'the first minister of Scotland'). We will then look at an influential approach to understanding what it is for words to have meaning and for people to mean things by their words, one due to Paul Grice. And we will examine the role and understanding of conventions and how someone can say something and yet communicate something very different from its conventional meaning. We will also explore the phenomena of “implicature” where people can communicate more (or something different from) what they literally say.20 credits
- Religion and the Good Life
What, if anything, does religion have to do with a well-lived life? For example, does living well require obeying God's commands? Does it require atheism? Are the possibilities for a good life enhanced or only diminished if there is a God, or if Karma is true? Does living well take distinctive virtues like faith, mindfulness, or humility as these have been understood within religious traditions? In this module, we will examine recent philosophical work on questions like these while engaging with a variety of religions, such as Buddhism, Christianity, Confucianism, Daoism, Islam, and Judaism.20 credits
- The Rationalists
This module is an introduction to the major works of Descartes, Spinoza, Leibniz, and Kant. Their work is both fascinating in itself and enormously influential today. The emphasis will be on topics in metaphysics and epistemology, such as whether there is a god, whether you and I are material or immaterial, whether the physical or even the mental world is real or apparent, whether anything could have been otherwise than it is, and what it is possible to know. Readings will be mainly from primary sources. Discussion will focus on philosophical problems rather than on historical context.20 credits
- Theory of Knowledge
The aim of the course is to provide an introduction to philosophical issues surrounding the knowledge. We will be concerned with the nature and extent of knowledge. How must a believer be related to the world in order to know that something is the case? Can knowledge be analysed in terms of more basic notions? Must our beliefs be structured in a certain way if they are to be knowledge? In considering these questions we will look at various sceptical arguments that suggest that the extent of knowledge is much less than we suppose. And we will look at the various faculties of knowledge: perception, memory, introspection, and testimony.20 credits
- Ancient Chinese Philosophy
This course will introduce students to ancient Chinese Philosophy through a study of some of it classical texts.20 credits
Feminists have famously claimed that the personal is political, and argued against traditional understandings of the public/private distinction. This module will be devoted to examining a wide variety of areas not traditionally considered to be of political relevance, which feminists have argued are in fact crucial to politics. We will discuss such issues as family structure, feminine appearance, sexual behaviour, science, culture and language.20 credits
- Free Will & Religion
This module focuses on philosophical questions about the relationship between free will and theistic religions. It has often been claimed that adherents of these religions have significant motivations to affirm an incompatibilist conception of free will according to which free will is incompatible with determinism. Incompatibilist conceptions of free will, it has been argued, have benefits for the theist such as enabling them to better account for the existence of moral evil, natural evil, divine hiddenness, and traditional conceptions of hell. Yet, on the other hand, it has been argued that there is a significant tension between theistic religions and incompatibilist conceptions of free will. For example, there are tempting arguments that an incompatibilist conception of free will makes trouble for affirming traditional views about God’s omniscience, freedom, and providence. We will engage in a critical examination of these and related arguments.20 credits
- Global Justice
What are the demands of justice at the global level? On this module we will examine this question from the perspective of analytic Anglo-American political philosophy. We will start by looking at some debates about the nature of global justice, such as whether justice demands the eradication of global inequalities. We will then turn to various questions of justice that arise at the global level, potentially including: how jurisdiction over territory might be justified; whether states have a right to exclude would-be immigrants; whether reparations are owed for past international injustices such as colonialism; and how to identify responsibilities for combatting global injustice.20 credits
- Language, Speakers and the World
This module explores in depth some of the most important notions in 20th and 21st century Philosophy of Language, an area of study which has often been seen as central to analytic philosophy more generally. As well as examining theories of central elements of language, such as names and descriptions, it investigates potentially puzzling phenomena such as fiction and the vagueness of language. And it explores issues in Applied Philosophy of Language including questions about lying and misleading, about forms of silencing, and about language and power. Language is at the heart of much distinctively human activity, and so study of language provides insight into us – its users/speakers – and also into how we relate to each other and to the world.20 credits
Update short/full description: The course will focus on metaphysical themes of perennial interest such as parts and wholes, the nature of people, and the passage of time. Readings will be drawn mainly from recent and contemporary sources. Lectures are shared with PHI225, and students who have taken that module may not take this one.20 credits
- Moral Theory and Moral Psychology
This course examines the relationship of moral theory and moral psychology. We discuss the relationship of science and ethics, examine the nature of self-interest, altruism, sympathy, the will, and moral intuitions, explore psychological arguments for and against familiar moral theories including utilitarianism, virtue ethics, deontology and relativism, and confront the proposal that understanding the origins of moral thought ¿debunks¿ the authority of ethics. In doing so, we will engage with readings from historical philosophers, including Hobbes, Butler, Hume, Smith, Kant, Mill, Nietzsche and Moore, as well as contemporary authors in philosophy and empirical psychology.20 credits
- Pain, Pleasure, and Emotions
Affective states like pain, pleasure, and emotions have a profound bearing on the meaning and quality of our lives. Chronic pain can be completely disabling, while insensitivity to pain can be fatal. Analogously, a life without pleasure looks like a life of boredom, but excessive pleasure seeking can disrupt decision-making. In this module, we will explore recent advances in the study of the affective mind, by considering theoretical work in the philosophy of mind as well as empirical research in affective cognitive science. These are some of the problems that we will explore: Why does pain feel bad? What is the relation between pleasure and happiness? Are emotions cognitive states? Are moral judgments based on emotions? Can we know what other people are feeling?20 credits
This module introduces students to Phenomenology - a philosophical tradition in continental European philosophy, which is closely related to Existentialism. Phenomenology seeks to understand the human condition. Its starting-point is everyday experience, where this includes both mundane and less ordinary forms of experience such as those typically associated with conditions such as schizophrenia. Whilst Phenomenology encompasses a diverse range of thinkers and ideas, there tends to be a focus on consciousness as embodied, situated in a particular physical, social, and cultural environment, essentially related to other people, and existing in time. (This is in contrast to the disembodied, universal, and isolated notion of the subject that comes largely from the Cartesian tradition.) There is a corresponding emphasis on the world we inhabit as a distinctively human environment that depends in certain ways on us for its character and existence. Some of the central topics addressed by Phenomenology include: embodiment; ageing and death; the lived experience of oppression; human freedom; our relations with and knowledge of, other people; the experience of time; and the nature of the world. In this module, we will discuss a selection of these and related topics, examining them through the work of key figures in the Phenomenological Movement, such as Edmund Husserl, Simone de Beauvoir, Maurice Merleau-Ponty, Frantz Fanon, and Edith Stein.20 credits
- Philosophical Project 1
A variety of topics will be set. For each topic, a short list of key readings is provided. Having chosen a topic, a short list of key readings is provided. Having chosen a topic, students are expected to master the readings, and the supplement them with at least two other pieces of relevant literature and they have used the available library and web resources to uncover. They then, having agreed a title with a tutor assigned to them for the module, write an extended essay that identifies the central issue (or issues) under discussion, relates the various responses to that issue found in the literature, evaluates those contributions, and goes some way to identifying a satisfactory resolution of the issue.20 credits
- Philosophical Project 2
A variety of topics will be set. For each topic, a short list of key readings is provided. Having chosen a topic, students are expected to master the readings, and to supplement them with at least two other pieces of relevant literature that they have used the available library and web resources to uncover. They then, having agreed a title with the tutor assigned to them for the module, write an extended essay that identifies the central issue (or issues) under discussion, relates the various responses to that issue found in the literature, evaluates those contributions, and goes some way to identifying a satisfactory resolution of the issues.20 credits
- Philosophy of Cognitive Science
Cognitive science is the multidisciplinary study of the mind. It involves contributions from philosophy, psychology, linguistics, computer science, neuroscience, and other fields. This module will investigate a number of topics within the cognitive sciences themselves as they attempt to understand the mind and some of the philosophical issues that arise when we reflect on the cognitive sciences as a scientific discipline. Some of the questions to be investigated include: how do we adjudicate disagreements in theory and methodology between the branches of the cognitive sciences, how does biology and neuroscience influence our thinking about the mind, and what is the relationship between observation and theory in the cognitive sciences. This module will address these topics by focusing on historical and current literature on specific topics. Representative topics include: what is the self, what is memory, how does consciousness fit in the biological world, and is the mind a computer. This module is equal parts cognitive science, philosophy of mind, and philosophy of science20 credits
- Philosophy of Law
Law is a pervasive feature of modern societies and governs most aspects of our lives. This module is about some of the philosophical questions raised by life under a legal system. The first part of the module investigates the nature of law. Is law simply a method of social control? For example, the group calling itself Islamic State issued commands over a defined territory and backed up these commands with deadly force. Was that a legal system? Or is law necessarily concerned with justice? Do legal systems contain only rules or do they also contain underlying principles? Is “international law” really law? The second part of the module investigates the relationship between law and individual rights. What kinds of laws should we have? Do we have the moral right to break the law through acts of civil disobedience? What is the justification of punishment? Is there any justification for capital punishment? Are we right to legally differentiate between intended crimes (like murder) and unintended crimes (like manslaughter), or does this involve the unjustified punishment of “thought crime”? Are we right to legally differentiate between murder and attempted murder, despite the fact that both crimes involve the same intent to kill?20 credits
- Philosophy of Psychology
This course provides an in-depth look at a selection of issues in contemporary philosophy of psychology. Philosophy of psychology is concerned with such questions as : What is the structure and organisation of the human mind? Is the mind one big homogenous thing, or is it made up of smaller interacting components? If it has components, what sort are they and how are they interrelated? What aspects of our minds are uniquely, or distinctively human? What is the cognitive basis for such capacities as our capacity for language, rationality, science, mathematics, cultural artefacts, altruism, cooperation, war, morality and art? To what extent are the concepts, rules, biases, and cognitive processes that we possess universal features of all human beings and to what extent are they culturally (or otherwise) variable? Do infants (non-human) animals, and individuals with cognitive deficits have minds, and if so, what are they like? To what extent are these capacities learned as opposed to innately given? How important is evolutionary theory to the study of the mind? What is the Self? What are concepts? Is all thought conceptual? Is all thought conscious? What is consciousness? This course will discuss a selection of these and related issues by looking at the work of philosophers, psychologists, and others working within the cognitive sciences more generally.20 credits
- Plato's Symposium
The Symposium is a vivid, funny and moving dramatic dialogue in which a wide variety of characters - orators, doctor, comic poet, tragic poet, soldier-cum-statesman, philosopher and others - give widely differing accounts of the nature or erotic love (eros) at a banquet. Students should be willing to engage in close textual study, although no previous knowledge of either ancient philosophy or ancient Greek is required. We will be exploring the origins, definition, aims, objects and effects or eros, and asking whether it is viewed as a predominantly beneficial or harmful force. Are some manifestations or eros better than others? Is re-channelling either possible or desirable, and if so, how and in what contexts? What happens to eros if it is consummated? We will in addition explore the issues that the dialogue raises about relations between philosophy and literature, and the influence it has had on Western thought (e.g. Freud). The edition we will use is Rowe, C . J., 1998, Plato Symposium. Oxford: Aris and Phillips Classical texts.20 credits
- Sources of Normativity
The module will present some fundamental debates in meta-ethics concerning the foundations of norms, obligations and reasons. We will read parts of Korsgaard's book 'The Sources of Normativity' and more recent literature grappling with the question Korsgaard has raised. We will try to understand what it means to ground a norm, whether norms must be grounded, what could possibly ground them and whether the grounding process has a terminus point.20 credits
- The Political Philosophy of Climate Change
Why is climate change a problem of global justice and how could the international community address this problem fairly? In this course we will look at various questions of justice that climate change raises and examine how political philosophers have attempted to answer them. Topics to be considered may include: historical responsibility for climate change, duties regarding future generations, the problem of allocating the burdens of addressing climate change, natural resource justice, the rights of indigenous peoples, moral issues concerning territorial loss or displacement, and the politics of geoengineering the planet.20 credits
- Undergraduate Ambassadors Scheme in Mathematics
This module provides an opportunity for Level Three students to gain first hand experience of mathematics education through a mentoring scheme with mathematics teachers in local schools. Typically, each student will work with one class for half a day every week for 11 weeks. The classes will vary from key stage 2 to sixth form. Students will be given a range of responsibilities from classroom assistant to the organisation and teaching of self-originated special projects. Only a limited number of places are available and students will be selected on the basis of their commitment and suitability for working in schools.20 credits
- Utopia, Reform and Democracy
Humanity faces a recurrent political challenge: the task of steering itself towards a sustainable and just future. A crucial part of this challenge involves developing a vision of change, of an achievable good society: a vision of the harbour we are aiming for as we sail through these troubled waters. But how are those visions to be enacted in the world? What theories of change lay at the heart of various philosophical visions? This module will introduce students to some of the major schools of thought - historical and contemporary - regarding the relationship between social theory and political practice.20 credits
- Codes and Cryptography
The word `code' is used in two different ways. The ISBN code of a book is designed in such a way that simple errors in recording it will not produce the ISBN of a different book. This is an example of an `error-correcting code' (more accurately, an error-detecting code). On the other hand, we speak of codes which encrypt information - a topic of vital importance to the transmission of sensitive financial information across the internet. These two ideas, here labelled `Codes' and `Cryptography', each depend on elegant pure mathematical ideas: codes on linear algebra and cryptography on number theory. This course explores these topics, including the real-life applications and the mathematics behind them.10 credits
Combinatorics is the mathematics of selections and combinations. For example, given a collection of sets, when is it possible to choose a different element from each of them? That simple question leads to Hall's Theorem, a far-reaching result with applications to counting and pairing problems throughout mathematics.10 credits
- Complex Analysis
It is natural to use complex numbers in algebra, since these are the numbers we need to provide the roots of all polynomials. In fact, it is equally natural to use complex numbers in analysis, and this course introduces the study of complex-valued functions of a complex variable. Complex analysis is a central area of mathematics. It is both widely applicable and very beautiful, with a strong geometrical flavour. This course will consider some of the key theorems in the subject, weaving together complex derivatives and complex line integrals. There will be a strong emphasis on applications. Anyone taking the course will be expected to know the statements of the theorems and be able to use them correctly to solve problems.10 credits
- Differential Geometry
What is differential geometry? In short, it is the study of geometric objects using calculus. In this introductory course, the geometric objects of our concern are curves and surfaces. Besides calculating such familiar quantities as lengths, angles and areas, much of our focus is on how to measure the 'curvature' of a geometric object. The story is relatively simple for curves, but naturally becomes more involved for surfaces - and more interesting too.10 credits
A field is a set where the familiar operations of arithmetic are possible. It often happens, particularly in the theory of equations, that one needs to extend a field by forming a bigger one. The aim of this course is to study the idea of field extension and various problems where it arises. In particular, it is used to answer some classical problems of Greek geometry, asking whether certain geometrical constructions, such as angle trisection or squaring the circle, are possible.10 credits
- Game Theory
The module will give students the opportunity to apply previously acquired mathematical skills to the study of Game Theory and to some of the applications in Economics.10 credits
- Graph Theory
.A graph is a simple mathematical structure consisting of a collection of points, some pairs of which are joined by lines. Their basic nature means that they can be used to illustrate a wide range of situations. The aim of this course is to investigate the mathematics of these structures and to use them in a wide range of applications.10 credits
- History of Mathematics
The course aims to introduce the student to the history of mathematics. The topics discussed are Egyptian and Babylonian mathematics, early Greek mathematics, Renaissance mathematics, and the early history of the calculus.10 credits
- Knots and Surfaces
The course studies knots, links and surfaces in an elementary way. The key mathematical idea is that of an algebraic invariant: the Jones polynomial for knots, and the Euler characteristic for surfaces. These invariants will be used to classify surfaces, and to give a practical way to place a surface in the classification. Various connections with other sciences will be described.10 credits
- Measure and Probability
The module will give students an additional opportunity to develop skills in modern analysis as well as providing a rigorous foundation for probability theory. In particular it would form a useful precursor or companion course to the Level 4 courses MAS436 (Functional Analysis) and MAS452 (Stochastic Processes and Finance), the latter of which is fundamentally dependent on measure theoretic ideas10 credits
- Metric Spaces
This unit explores ideas of convergence of iterative processes in the more general framework of metric spaces. A metric space is a set with a distance function which is governed by just three simple rules, from which the entire analysis follows. The course follows on from MAS207 `Continuity and Integration', and adapts some of the ideas from that course to the more general setting. The course ends with the Contraction Mapping Theorem, which guarantees the convergence of quite general processes; there are applications to many other areas of mathematics, such as to the solubility of differential equations.10 credits
- Operations Research
Mathematical Programming is the title given to a collection of optimisation algorithms that deal with constrained optimisation problems. Here the problems considered will all involve constraints which are linear, and for which the objective function to be maximised or minimised is also linear. These problems are not continuously differentiable; special algorithms have to be developed. The module considers not only the solution of such problems but also the important area of post-optimality analysis; i.e. given the solution can one answer questions about the effect of small changes in the parameters of the problem (such as values of the cost coefficients)?10 credits
- Topics in Number Theory
In this module we study intergers, primes and equations. Topics covered include linear and quadratic congruences, Fermat Little Theorem and Euler's Theorem, the RSA cryptosystem, Quadratic Reciprocity, perfect numbers, continued fractions and others.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. We are no longer offering unrestricted module choice. If your course included unrestricted modules, your department will provide a list of modules from their own and other subject areas that you can choose from.
Learning and assessment
You'll learn through lectures, seminars, problems classes in small groups and research projects. Some modules also include programming classes.
This tells you the aims and learning outcomes of this course and how these will be achieved and assessed.
With Access Sheffield, you could qualify for additional consideration or an alternative offer - find out if you're eligible
The A Level entry requirements for this course are:
including A in Maths
The A Level entry requirements for this course are:
including A in Maths
A Levels + additional qualifications | ABB, including A in Maths + B in a relevant EPQ; ABB, including A in Maths + B in Further Maths ABB, including A in Maths + B in a relevant EPQ; ABB, including A in Maths + B in Further Maths
International Baccalaureate | 34, 6 in Higher Level Mathematics (Analysis and Approaches) 33 with 6 in Higher Level Mathematics
BTEC | DDD in a relevant subject with Distinctions in Maths units DDD in a relevant subject with Distinctions in Maths units
Scottish Highers + 1 Advanced Higher | AAABB + A in Maths AAABB + A in Maths
Welsh Baccalaureate + 2 A Levels | B + AA, including Maths B + AB, including A Maths
Access to HE Diploma | 60 credits overall in a relevant subject with Distinctions in 36 Level 3 credits, including Mathematics units, + Merits in 9 Level 3 credits 60 credits overall in a relevant subject with Distinctions in 30 Level 3 credits, including Mathematics units, + Merits in 15 Level 3 credits
Mature students - explore other routes for mature students
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
We will give your application additional consideration if you have passed the Sixth Term Examination Paper (STEP) at grade 3 or above or the Test of Mathematics for University Admissions (TMUA) at grade 5 or above
If you have any questions about entry requirements, please contact the department.
School of Mathematics and Statistics
Staff in the School of Mathematics and Statistics work on a wide range of topics, from the most abstract research on topics 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.
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.
Why choose Sheffield?
The University of Sheffield
A Top 100 university 2021
QS World University Rankings
Top 10% of all UK universities
Research Excellence Framework 2014
No 1 Students' Union in the UK
Whatuni Student Choice Awards 2019, 2018, 2017
School of Mathematics and Statistics
National Student Survey 2019
Department of Philosophy
National Student Survey 2019
National Student Survey 2019
School of Mathematics and Statistics
There will always be a place for maths graduates in banking, insurance, pensions, and financial districts from the City of London to Wall Street. Big engineering companies still need people who can crunch the numbers to keep planes in the sky and trains running on time too. But the 21st century has also created new career paths for our students.
Smartphones, tablets, social networks and streaming services all use software and algorithms that need mathematical brains behind them. In the age of ‘big data’, everyone from rideshare apps to high street shops is gathering information that maths graduates can organise, analyse and interpret. The same technological advances have created new challenges and opportunities in cybersecurity and cryptography.
If the maths itself is what interests you, a PhD can lead to a career in research. Mathematicians working in universities and research institutes are trying to find rigorous proofs for conjectures that have challenged pure mathematicians for decades, or are doing the calculations behind major experiments, like the ones running on the Large Hadron Collider at CERN.
What if I want to work outside mathematics?
A good class of degree from a top university can take you far, whatever you want to do. We have graduates using their mathematical training in everything from teaching and management to advertising and publishing.
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.
Fees and funding
The annual fee for your course includes a number of items in addition to your tuition. If an item or activity is classed as a compulsory element for your course, it will normally be included in your tuition fee. There are also other costs which you may need to consider.
Funding your study
Depending on your circumstances, you may qualify for a bursary, scholarship or loan to help fund your study and enhance your learning experience.
Use our Student Funding Calculator to work out what you’re eligible for.
University open days
There are four open days every year, usually in June, July, September and October. You can talk to staff and students, tour the campus and see inside the accommodation.
At various times in the year we run online taster sessions to help Year 12 students experience what it is like to study at the University of Sheffield.
If you've received an offer to study with us, we'll invite you to one of our applicant open days, which take place between November 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 run regularly throughout the year, at 1pm every Monday, Wednesday and Friday.
Apply for this course
Make sure you've done everything you need to do before you apply.
The awarding body for this course is the University of Sheffield.
Recognition of professional qualifications: from 1 January 2021, in order to have any UK professional qualifications recognised for work in an EU country across a number of regulated and other professions you need to apply to the host country for recognition. Read information from the UK government and the EU Regulated Professions Database.