Mathematics and Philosophy BSc

Core maths modules:

Mathematics Core

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

40 credits

Foundations of Pure Mathematics

The module aims to give an overview of basic constructions in pure mathematics; starting from the integers, we develop some theory of the integers, introducing theorems, proofs, and abstraction.  This leads to the idea of axioms and general algebraic structures, with groups treated as a principal example.  The process of constructing the real numbers from the rationals is also considered, as a preparation for “analysis”, the branch of mathematics where the properties of sequences of real numbers and functions of real numbers are considered.

20 credits

You must take at least 40 credits of Philosophy modules. You must take:

Writing Philosophy (20 credits, details TBC)

And at least one other core Philosophy module (20 credits) from the list below:

Ethics & Society (20 credits, details TBC)
Mind & World (20 credits, details TBC)
Reason and Argument (20 credits, details TBC)

Maths options:

Mathematical modelling

Mathematics is the language of science.  By framing a scientific question in mathematical language, it is possible to gain deep insight into the empirical world.  This module aims to give students an appreciation of this astonishing phenomenon.  It will introduce them to the concept of mathematical modelling via examples from throughout science, which may include biology, physics, environmental sciences, and more.  Along the way, a range of mathematical techniques will be learned that tend to appear in empirical applications.  These may include (but not necessarily be limited to) difference and differential equations, calculus, and linear algebra.

20 credits

Probability and Data Science

Probability theory is branch of mathematics concerned with the study of chance phenomena. Data science involves the handling and analysis of data using a variety of tools: statistical inference, machine learning, and graphical methods. The first part of the module introduces probability theory, providing a foundation for further probability and statistics modules, and for the statistical inference methods taught here. Examples are presented from diverse areas, and case studies involving a variety of real data sets are discussed. Data science tools are implemented using the statistical computing language R.

20 credits

Mathematical Investigation Skills

This module introduces topics which will be useful throughout students’ time as undergraduates and in employment. These skills fall into two categories: computer literacy and presentation skills.  One aim of this module is to develop programming skills within Python to perform mathematical investigations.  Students will also meet the typesetting package LaTeX, the web design language HTML, and Excel for spreadsheets.  These will be used for making investigations, and preparing reports and presentations into mathematical topics.

20 credits

Philosophy options:

Death

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

10 credits

Philosophy of Sex

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

10 credits

Philosophy of Religion

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

10 credits

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 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

Core maths module:

Mathematics Core II

Building on Level 1 Mathematics Core, Mathematics Core II will focus on foundational skills and knowledge for both higher mathematics and your future life as a highly skilled, analytically-astute worker.  Mathematical content will focus on topics that are vital for all areas of the mathematical sciences (pure, applied, statistics), such as vector calculus and linear algebra.  This will help develop your analytic and problem solving skills.  Alongside this, you will continue to develop employability skills, building on Level 1 Core.  Finally, there will be opportunities to learn and reflect on social, ethical, and historical aspects of mathematics, which will enrich your understanding of the importance of mathematics in the modern world.

30 credits

Maths options:

Differential equations

Differential equations are perhaps the most important tool in applied mathematics.  They are foundational for modelling all kinds of physical and natural phenomena, including fluids and plasmas, populations of animals or cells, cosmological objects (via relativity), subatomic particles (via quantum mechanics), epidemics, even political and social opinions have been modelled using differential equations.  This module will build on the tools learned at Level 1 for analysing differential equations, extending them in a variety of ways.  This may include topics such as bifurcation analysis, partial differential equations (which are particularly valuable for modelling things that vary in both space and time), and the effects of boundaries on the dynamics of differential equations.  It will provide the foundation for essentially all applied maths modules taught at Levels 3 and 4.

20 credits

Analysis and Algebra

This module will build on the theory built in Level 1 'Foundations of Pure Mathematics', focusing on the twin pillars of analysis and algebra.  These are not only fundamental for pure mathematics at higher levels, but provide rigorous theory behind core concepts that are used throughout the mathematical sciences.  Whilst to some extent you have been doing analysis and algebra since you were at school, here you will be going much deeper.  You will examine why familiar tools, like differentiation and integration, actually work.  Familiar objects, such as vectors, differential operators, and matrices, will be unpacked; powerful, formal properties of these objects proved.  Ultimately, this rigorous foundation will enable you to extend these tools and concepts to tackle a far greater set of problems than before.

20 credits

Statistical Inference and Modelling

Statistical inference and modelling are at the heart of data science, a field of rapidly-growing importance in the modern word.  This module develops methods for analysing data, and provides a foundation for further study of probability and statistics at higher Levels.  You will learn about a range of standard probability distributions beyond those met at Level 1, including multivariate distributions. You will learn about sampling theory and summary statistics, and their relation to data analysis. You will discover how to parametrise various types of statistical model, learn techniques for determining whether one model is 'better' than another for understanding a dataset, and learn how to ascertain how good a statistical model is at explaining trends in data. The software package R will be used throughout.

20 credits

Additional options to be taken from this group:

Stochastic Modelling

Many things about life are unpredictable.  Consequently, it often makes sense to incorporate some randomness in mathematical models of natural and physical processes. Such models are called 'stochastic models' and are the study object of this module.  We will learn about a number of general models for processes where the state of a system is fluctuating randomly over time. Examples might include the length of a queue, the size of a reproducing population, or the quantity of water in a reservoir. We will cover various techniques for analysis of such models, setting the student up for further study of stochastic processes and probability at levels 3 and 4.

10 credits

Vector Calculus and Dynamics

Vector calculus is a fundamental tool for modelling the dynamics of all kinds of objects, both solid and fluid.  In this module, you will build on the tools of vector calculus from Mathematics Core II, combining them with tools of differential equations from the L1 Mathematical Modelling module, and applying them to understand the dynamics of physical systems.  Possible examples might include liquid, gases, plasmas, and/or planetary motion.  The tools developed here will build valuable knowledge for the study of fluid dynamics and other applied mathematics modules at higher levels.

10 credits

Group Theory

A group is one of the most foundational objects in mathematics.  It just consists of a set, together with a way of combining two objects in that set to create another object in an internally-consistent fashion.  Familiar examples abound: integers with addition, real numbers with multiplication, symmetries of the square, and so on.  In this module, you will learn about formal properties of groups in general, including famous results like the orbit-stabiliser theorem.  You will also learn about important foundational examples, such as number, matrices, and symmetries.  You will learn how the general framework of groups allows you to prove theorems that pertain to all these examples in one go.  This provides a great example of the power and beauty of abstraction, a feature of pure mathematics that underlies the entire module.

10 credits

Mathematics and Statistics in Action

In this project module, you will investigate one or more case studies of using mathematics and statistics for solving empirical (i.e. 'real world') problems. These case studies will illustrate the process of mathematical and statistical modelling, whereby real-world questions are translated to mathematical and/or statistical questions. Students will see how techniques learned earlier in their degree can be used to explore these problems. There will be a mix of individual and group projects to choose from, and some projects may  involve the use of R or Python, but 'MAS116 Mathematical Investigations Skills' is not a prerequisite. Students will be expected to work independently (either individually or in a small group). However, the topic and scope of each piece of project work will be clearly defined by the lecturer in charge of the topic.

10 credits

Scientific Computing

The ability to programme is a central skill for any highly-numerate person in the 21st century.  This module builds on skills learned at Level 1 in 'Mathematical Investigation Skills' by developing skills in computer programming and independent investigation. You will learn how to solve various mathematical problems in programming languages commonly-used by mathematicians, for example Python. You will learn basic computational and visualisation methods for exploring numerical solutions to equations (including differential equations), and then apply this knowledge to explore the behaviour of example physical systems that these equations might model.

10 credits

Analysis

This module will build on the theory built in Level 1 'Foundations of Pure Mathematics', focusing specifically on analysis.  This provides rigorous theory behind core concepts that are used throughout the mathematical sciences.  Whilst to some extent you have been doing analysis since you were at school, in the form of calculus, here you will be going much deeper.  You will examine why familiar tools, like differentiation and integration, actually work.  This allows powerful, formal properties of these objects to be proved.  Ultimately, this rigorous foundation will enable you to extend these tools and concepts to tackle a far greater set of problems than before.

10 credits

Philosophy options:

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

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

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

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

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

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

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

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

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

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

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

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

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

Environmental Justice

This module will introduce students to contemporary philosophical discussions of environmental justice at the global level. Topics to be covered may include: The nature of global environmental injustices; responsibility for global environmental problems; the relationship between global environmental challenges and other historical and contemporary injustices; fair international sharing of the costs of environmental action; the justifiability of environmental activism; the rights of indigenous peoples; fairness in global environmental decision-making; and the politics of ‘geoengineering’ the planet.

20 credits

Optional modules - students will select half of their credits in mathematics modules and half in philosophy.

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

Ancient Chinese Philosophy

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

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.

30 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

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

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

Feminist and Queer Studies in Religion, Global Perspectives

This module applies feminism, queer studies and trans philosophy in analysis of genders and sexualities in religious traditions and cultures around the world. We will examine deities and goddesses, gendered language in religions, cisheteropatriarchy, and LGBTQIA life in e.g. Hinduism, Buddhism, Christianity, Judaism and Islam, as well as in Chinese, and Japanese cultures. We will discuss genders, rituals, spirituality, sexual practices, procreation, abstinence, and asexuality, reading a range of feminist, queer and trans philosophical works, and texts ranging from the Kama Sutra to Confucius and the Vatican documents, Scriptures, and empirical research. Assignments allow students in Philosophy, Humanities, and Social Sciences develop their expertise using their preferred methods and topics, on religions of their choice.

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

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

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

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

Time Series

Time series are observations made in time, for which the time aspect is potentially important for understanding and use. The course aims to give an introduction to modern methods of time series analysis and forecasting as applied in economics, engineering and the natural, medical and social sciences. The emphasis will be on practical techniques for data analysis, though appropriate stochastic models for time series will be introduced as necessary to give a firm basis for practical modelling. Appropriate computer packages will be used to implement the methods.

10 credits

Machine Learning

Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.

10 credits

Topics in Mathematical Biology

This module focuses on the mathematical modelling of biological phenomena.  The emphasis will be on deterministic models based on systems of differential equations.  Examples will be drawn from a range of biological topics, which may include the spread of epidemics, predator-prey dynamics, cell biology, medicine, or any other biological phenomenon that requires a mathematical approach to understand.  Central to the module will be the dynamic consequences of feedback interactions within biological systems.  In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used.  If you did not take Scientific Computing at Level 2, you may still be able to enrol on this module, but you will need to obtain permission from the module leader first.

10 credits

Medical Statistics

This course comprises sections on Clinical Trials and Survival Data Analysis. The special ethical and regulatory constraints involved in experimentation on human subjects mean that Clinical Trials have developed their own distinct methodology. Students will, however, recognise many fundamentals from mainstream statistical theory. The course aims to discuss the ethical issues involved and to introduce the specialist methods required. Prediction of survival times or comparisons of survival patterns between different treatments are examples of paramount importance in medical statistics. The aim of this course is to provide a flavour of the statistical methodology developed specifically for such problems, especially with regard to the handling of censored data (eg patients still alive at the close of the study). Most of the statistical analyses can be implemented in standard statistical packages.

10 credits

Mathematical modelling of natural systems

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

10 credits

Work Place Learning

This module involves a work placement of 35-70 hours with a local organisation (voluntary or commercial sector). You will experience firsthand the practical challenges and problems facing the organisation. You will learn about the organisation's overall aims, and the various methods and strategies employed to accomplish those aims. You will draw on the concepts and theoretical frameworks studied in your other philosophy modules to identify a philosophical issue relevant to the organisation's work or goals, and to write a piece or pieces of coursework addressing that issue; or you will be able to use the skills and knowledge you have gained in your other philosophy modules to analyse a problem of philosophical interest faced by the organisation or encountered in the course of your employment. You will have two meetings together with other students in the module to discuss your work placement and formulate ideas for your written coursework. You will have a further individual meeting with the module convener or an appropriate supervisor from the Department of Philosophy to discuss the progression of the coursework.

At the end of the module, you should have:

the ability to apply ideas from your other philosophy modules in rigorously assessing the challenges facing organisations like the one you worked for, and interrogating potential solutions to them

insight into the practical application of theoretical issues in philosophy

practical experience that will make you a strong candidate for jobs in the sector you worked in.

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