Mathematics and Philosophy BSc

Core modules:

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

Optional modules:

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 readings

20 credits

Death

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

10 credits

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

History of Philosophical Ideas

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

10 credits

Philosophy of 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 reasoning

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

LGBTQ (Lesbian, Gay, Bisexual, Trans* and Queer) Studies

This module introduces students to study of genders and sexualities, and LGBTQ scholarship, both historical and contemporary. It examines genders and sexualities in society, culture, media, and their academic study, as well as contemporary issues of inequality affecting sexual minorities in different global contexts. The module is team taught by experts in different departments at the University of Sheffield, who will introduce students to a wide range of theoretical and methodological perspectives, such as philosophy, history, social sciences, psychology, evolutionary biology, education, cultural studies, and critical study of religion. The module is assessed by a coursework portfolio, where students answer a number of short questions on different topics in the syllabus.

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

Core modules:

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

Algebra

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

Analysis

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

Optional modules:

Ethics

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

Feminism

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

Metaphysics

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

Ethnography and Lived Religion

The course begins with pioneering empirical studies on religion to introduce students to methods and issues in ethnography of religion. We will then move on to more contemporary perspectives in ritual study, and examine religious experience, mindfulness and yoga, as well as lived religion, and intersections of religion, ethnicity, class, gender and sexuality. The students will be able to undertake their own ethnography project as part of their portfolio to examine 21st century faith in its rich variety. The module will equip students with understanding of sociological and anthropological approaches on religion and contemporary religious diversity and intersectionality of embodied and lived religion.

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

Topics in Political Philosophy

This module will investigate a broad range of topics and issues in political philosophy and through doing so provide students with a broad understanding of those. It will include both historical and foundational matters and recent state of the art research.

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

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

Optional modules:

Ancient Chinese Philosophy

This course will introduce students to ancient Chinese Philosophy through a study of some of it classical texts.

20 credits

Advanced Political Philosophy

This module will investigate a broad range of topics and issues in political philosophy and explore these questions in some detail. It will include both historical and foundational matters and recent state of the art research.

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

Philosophical Problems 1

The detailed content of this course will vary from year to year depending upon the member of staff teaching it. For details contact the Department of Philosophy.

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

Phenomenology

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 Problems II

The detailed content of this course will vary from year to year depending upon the member of staff teaching it. For details contact the Department of Philosophy.

20 credits

Advanced Logic

This module will build upon PHI203 Formal Logic It will examine some philosophically important areas of formal logic, and it will also consider some philosophical debates concerning foundational aspects of logic. The unit will be assessed by means of a coursework essay on a philosophical topic [worth 50% of the final mark] and an unseen exam [worth the remaining 50% of the final mark]

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 science

20 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

The Radical Demand in Logstrup's Ethics

The biblical commandment 'to love your neighbour as yourself' still has great resonance with people, as does the story of the Good Samaritan who helps the injured traveller he encounters on the road. But what exactly does this love require, and what it its basis? Do we have an obligation to care for others, or is it beyond the call of duty? How can love be a matter of obligation at all? If you help the neighbour, can you demand something in return? Should we help them by giving them what they want, or instead what they need? How far do our obligations to others extend - who is the 'neighbour', and might it include 'the enemy' ? And does the requirement to help the other come from God's command, or from some sort of practical inconsistency given we all need help ourselves, or from their right to be helped - or simply from the fact they are in need? But can our needs be enough on their own to generate obligations of this sort?
We will consider these sorts of questions in relation to the work of K.E. Logstrup [1905-1981], a Danish philosopher and theologian, who discussed them in his key work The Ethical Demand [1956] in which he characterized this relation between individuals as involving a 'radical demand' for care, involving important commitments about the nature of life, value, and human interdependency. We will compare his ideas to related themes in Kant, Kierkegaard, Levinas, and contemporary care ethics.

20 credits

Gender and Religion

This module applies feminism and queer studies in analysis of gender and sexuality in religious traditions and cultures around the world. We will examine deities and goddesses, gendered language in religions, cisheteropatriarchy, and LGBTQIA life in eg. Hinduism, Buddhism, Christianity, Judaism and Islam, as well as Chinese and Japanese cultures. We will discuss genders, rituals, spirituality, sexual practices, procreation, abstinence, and asexuality, reading a range of feminist and queer philosophical works and texts ranging from the Karma Sutra to Confucius and the Vatican documents.

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

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

Fields

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 ideas

10 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

Groups and Symmetry

Groups arise naturally as collections of symmetries. Examples considered include symmetry groups of Platonic solids. Groups can also act as symmetries of other groups. These actions can be used to prove the Sylow theorems, which give important information about the subgroups of a given finite group, leading to a classification of groups of small order.

10 credits