Mathematics and Philosophy BSc

Core modules:

Introduction to University Mathematics

This core module is designed to consolidate A-level material and explore topics in mathematics that you'll use throughout your degree. You'll also be introduced to core skills, such as mathematical literacy, communication and problem-solving.  

Throughout this module you'll develop a strong foundation in core mathematics. You'll consider techniques for solving equations, special functions, calculus, vectors, complex numbers, and finite and infinite series.

20 credits

Geometry, Matrices and Multivariate Calculus

This core module is designed to further develop your knowledge of the core mathematics you'll use across your degree.

You'll learn about two-dimensional coordinate geometry, discussing the theory of matrices geometrically and algebraically. You'll also define and evaluate derivatives and integrals for functions that depend on more than one variable, with an emphasis on functions of two variables.

Throughout this module you'll continue to develop your employability skills, exploring the career options open to mathematics graduates. You'll also work with your coursemates to undertake a group project on sustainability.

20 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

Writing Philosophy

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

20 credits

Reason and Argument

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

20 credits

Optional modules:

You'll take 20 credits (one module) from this group.

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

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

Mind and World

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

20 credits

Religion, Reason and Reality

Religious traditions typically understand reality as involving more than just the tangible physical world.  This module tackles philosophical questions about religion and reality.  These include questions about different conceptions of God and the justification for religious beliefs, such as belief in God, supernatural forces and an afterlife.  And questions about the nature of religious 'beliefs': are these the same kind of thing as mundane 'beliefs'?   They also include questions about reality, raised by potential technological advances, like the question of whether we are living in a simulation, and how we should think about God if we think we are.  And the question of whether technologies like virtual reality can offer what people have long sought from religion.

20 credits

Bodies, Sex and Desires

This module introduces students to some key topics in the Philosophy of Sex and Queer Theory. We will begin with the surprisingly difficult questions of what sex is, and what a sexual orientation is, examining these questions from the perspective of contemporary philosophy, and also the history of sexuality and desire. We will consider a range of issues around the nature of embodiment, for example, whether there are only two biological sexes (male and female), as well as social and political implications of these categorisations. We will also discuss the nature of intimacy and relationships, including asexuality, aromanticism, polyamory; 'sexual racism'; how we should understand consent; and whether having power over someone makes it impermissible to have sex with them. Finally, we will think about some issues surrounding sex work, focusing on whether or not it is inherently different from other jobs, and whether there is anything morally problematic about pornography.The readings and perspectives covered in this module are diverse, and include examples from empirical studies, media and popular culture. You can develop knowledge of your favourite topics in the portfolio assessment, engaging with module readings in Philosophy of Sex, and Queer theory.

20 credits

Ethics and Society

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

20 credits

Science, Medicine and Society

This is a module on the relationship between science, society, and values and serves as an introduction to the philosophy of science and bioethics.

Science plays an essential role in modern society. We trust science, and its results, on a day to day basis as we navigate our worlds and interact with each other. Yet, what is it about science, or scientific methodology, that makes it so trustworthy? We will investigate a range of questions that concern the epistemology and social structure of science. These include: What is the relationship between evidence, observation, and theory? Is there a distinctive scientific methodology? Does the social structure of science help or hinder scientific research? After considering these theoretical questions, we will turn to questions of value and a range of problems that arise with the application of science. Some of these problems are historic but many have emerged as we move through the 21st century. In a pandemic, for example, how should we balance concerns for liberty and protecting the vulnerable? Should we try to 'enhance' human beings, or should we be happy with the way we are? How might the use of artificial intelligence impact trust in the healthcare system? This module thus moves from the theoretical to the practical.

20 credits

Death and Killing

This module introduces students to some key philosophical questions about life and death. What is death? What happens to us when we die? Could there be an afterlife? Would it be a good thing if there were? Is it rational to fear death? Do we have moral duties towards the dead? If death is usually bad for us then killing someone, or allowing them to die, is usually wrong. But it is not always wrong. There are exceptions. The module looks at a range of life-and-death situations that may include euthanasia, abortion, killing non-human animals, war and capital punishment.

20 credits

History of Philosophy

In Philosophy the past can be a guide to the present.  The ideas that shape and guide philosophical thought can be understood by examining their historical development.  This module will introduce students to key debates and the thought of key figures from the history of philosophy. The focus will be on a number of selected readings covering topics of central philosophical importance from philosophy's long past.

20 credits

Core modules:

Core Mathematics I

Linear algebra and calculus are fundamental to most advanced work in pure and applied mathematics and to much of statistics.

This module will provide you with basic tools and techniques from linear algebra and calculus. You'll also develop an understanding of the theory underpinning these, enabling you to use these methods in a variety of situations beyond the module.

Building on your first year, you'll also continue to develop employability skills throughout this module.

20 credits

Core Mathematics II

This module will develop your understanding of theory covered in first year modules. 

You'll explore analysis, which underpins core concepts across the mathematical sciences.  You'll examine why familiar tools, like differentiation and integration, actually work, allowing us to prove their formal properties. This rigorous foundation in analysis will enable you to tackle more complex problems in the future.

You'll extend your understanding of ideas from calculus to higher dimensions, considering differentiation of functions of many variables as linear transformations.

You'll also have opportunities to reflect on social, ethical, and historical aspects of mathematics, enriching your understanding of the importance of mathematics in the modern world.

20 credits

Formal Logic

The birth of modern philosophy is intimately linked to major developments in logic that began at the end of the 19th century, and logical ideas have continued to shape philosophy during the 150 or so years since that time. Indeed, formal logic is one of the crucial sources of the greatest role that modern philosophy has played in shaping the modern world, via its influence on the development of computers. The module will start by introducing some elementary concepts from set theory; along the way, we will consider some fundamental and philosophically important 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 show how we may prove a range of fundamental 'metalogical' 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

Knowing and Being

Knowing and Being tackles questions about the nature of things and about our knowledge of things. The first set of questions are metaphysical. They ask about the world independent of thought. What, for example, is the nature of possibility, objects, numbers, colour and time? The second set of questions are epistemological. They ask how thought can have access to how things are. For example, we seem to know about objects and colour by perception, so how does perception support knowledge? Similar questions can be asked about reason, introspection and communication. 

In discussing these questions, and others, you will gain an understanding of the nature of things, the nature of possibility of knowledge, and how knowledge is related to ethics and power.

20 credits

Optional modules:

You'll take 40 credits (two modules) from this group.

Algebra

This module will further develop your understanding of abstract algebra. The theory of groups, met at Level 1, will be developed in more generality, with further theory as well as applications to combinatorial problems.

You'll also meet the abstract concepts of rings and fields.  A ring is similar to a group, but where we have two operations, of addition and multiplication, like the integers, while a field also has a division operation.  You'll see concrete examples of both, realising that a number of particular situations you've previously encountered are examples of this more general concept, and that results you've seen before are examples of abstract results that hold in wider generality.  Finally, you will see that the results about vectors that you have seen in core modules can be generalised to the setting of vector spaces over arbitrary fields.

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

Stochastic Modelling

This module examines stochastic processes. These are models of natural and physical processes that incorporate randomness, to reflect the way that life can change unpredictably over time. 

You'll explore a number of general models for processes where the state of a system is fluctuating randomly. This might include the length of a queue, the size of a reproducing population, or the amount of payouts on insurance policies. 

You'll learn various techniques for the analysis of these models, preparing you for further study of stochastic processes and probability in later years.

20 credits

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

Mind and Language

This module will take place on the moon. The previous sentence was false, yet you understood its meaning. And it had meaning although it was just a bunch of marks on a page or pixels on a screen. One key question this module investigates is then: What it is that makes such arrangements of matter meaningful. One suggestion is that we give meaning to language by thinking. But this seems to merely move the problem. Thinking depends on what goes on in our brains, and our brains are also arrangements of matter. In fact, brains do more than thinking: they are also responsible for our conscious experiences. And this is even more mysterious. This is another key question of this module: How can a bunch of little grey cells give rise to our subjective feelings?

In discussing these questions, and others, you will gain an understanding of the nature of language, of the mind, and of their relations, and philosophers theorise about how meaning, thinking, and consciousness are possible in a material world.

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 Philosophy of AI and Robotics

This module will investigate a range of philosophical  issues pertaining to current developments in AI and  robotics. Example topics might include relationships with  AI and robots, responsibility concerns in regard to  autonomous technology such as self-driving cars, the rise of data ethics, and the rights of cyborgs and future  artificial beings. By studying these topics and others,  students will gain a broad knowledge of the philosophical  questions pertaining to contemporary and near-future  technology, develop their ability to critically assess and  discuss philosophy in regards to real world uses and  developments in AI and robotics, as well as improve their  understanding of how theoretical philosophical theories  can be applied and used to tackle practical challenges  posed by modern technology.

20 credits

Science and the Search for Reality

Where would we be without science?  There would be no computers, phones, internet, cars, pharmaceutical drugs, or electric guitars.  However science doesn't just allow us to produce practical technologies; science is also arguably our best tool for uncovering the fundamental nature of reality.

In this module we will investigate some of the philosophical questions that arise concerning the role that science has in uncovering reality, and the use of science to understand the mind.  In considering these questions, you will gain an understanding of the nature of scientific theories, explanation laws and evidence, and an understanding of what scientific research tells us about the mind.

20 credits

Life Worth Living

What does it mean for a life to go well? How does one live life well? What is a flourishing life? These questions have shaped intellectual endeavour for millennia. Life Worth Living explores approaches to these questions through engagement with diverse traditions/thinkers including classical Greek philosophy, Buddhism, Judaism, Christianity, Islam, Confucianism, Existentialism, Marx, and Nietzsche. The module includes historical analysis of these traditions, visits from individuals whose lives are shaped by them, fieldwork to discuss the ideas beyond the classroom, and assessments to help students develop their own vision of a life worth living.

20 credits

Political Philosophy

In this module we will discuss and engage with a selection of those topics, each of which invites you to participate in important debates in political philosophy. Key questions include: Should we obey the state? Who has a right to rule? How should we decide who has such a right? What does justice require? What is injustice? What is democracy? What is the value of equality? What is liberty? Should borders exist? Do people have a right to live in any country they want? Should minority groups benefit from protections against the majority group? By considering these questions, and examining crucial political concepts and debates, you will gain an understanding of the fundamental topics in political philosophy. In doing so you will develop your own capacities to discuss and critically assess both traditional debates and real-world issues. Ultimately, this module will help you understand how theoretical and conceptual considerations have or sometimes fail to have practical implications in real politics.

20 credits

Global History of Philosophy

This module will explore a range of key concepts concerning the self, the world, and our relations to it and to each other, as these have been understood in different philosophical schools from the ancient world until the present. We will ask questions such as: how did the world come about? Is our will free? Can we ever really know the world? Some topics under discussion could include: Ubuntu understandings of community and liberation, or Buddhist no-self approaches. The module will focus on a selection of texts and thinkers from different geographical regions, cultures and traditions, such as Africa, China, Europe, India, Islam, Judaism, South America. In studying this global history of philosophy, you will gain an understanding of diverse philosophical approaches.

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

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

Social Justice Today

In this module, you will engage with key political questions and learn about contemporary social justice debates, including as they arise in medical ethics. Key questions include: Should there be a limit on personal wealth? Does everyone have an equal obligation to protect the climate? Should we lower the voting age, or even get rid of an age limit altogether? How should we allocate medical resources when we cannot give everyone the treatment they need? Is private education just a personal choice or an assault on equality? And do crises (like wars and pandemics) justify suspending civil liberties? All of these questions ask of us what social justice is and what it requires. By considering these questions, you learn about the political and ethical concepts that undergird our social world. This will give you an understanding of political philosophy, ethics, and medical ethics, and develop your capacity to discuss and critically assess real-world debates.

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

- Ethics: from Theory to Practice (20 credits)

Core module:

Mathematical and Physical Sciences Projects and Professional Skills

Through this module you'll hone the skills and knowledge required of a graduate-level professional.

You'll undertake extended project work, which will include relating project work to the literature, setting project aims and objectives, planning and carrying out the work, and reporting it using disciplinary conventions.

You'll investigate how your academic studies relate to either research, society, or industry. You'll develop an understanding of where your degree could lead you and reflect on your career ambitions.You'll also undertake activities to develop the professional skills needed to complete applications for employment or further study.

40 credits

Optional modules:

You'll take 80 credits (four modules) from this group:

Metric Spaces, Topology and Measure

This module will explore how the notion of the metric allows measuring distances on sets of functions, matrices, or even graphs and networks. 

You'll learn to generalise the concepts of convergence and continuity. You'll see how this theory has far-reaching implications, from existence of solutions to differential equations, to equilibria in financial markets.

You'll study open, closed, and compact sets, first relying on metrics, before exploring how objects can be defined in the more general setting of a topological space. You'll also develop an understanding of a consistent theory of 'size' (or volume) and probability.

Through this module, you'll gain the knowledge needed to tackle advanced topics in analysis, while content on topological spaces theory will also prepare you for topics in algebraic topology and differential geometry.

20 credits

Fields and Galois Theory

The main goal of this module is to prove the wonderful classification of Galois of those polynomials whose roots can be expressed by radicals, that is, in terms of square, cube and higher roots.

You'll first enhance your understanding of fields, met in your second year, with some further theoretical results, such as studying ruler-and-compass constructions, and the classical problems of antiquity: doubling the cube and trisecting an angle. Next, you'll consider extensions of fields, where one field contains another. The Galois group of a field extension is a sort of symmetry group: if the roots of a polynomial can be expressed by radicals, then the Galois group of the field extension containing the roots of the polynomial has to have a particular structure, and you'll see that this is not generally true for quintic polynomials.

20 credits

Stochastic Processes and Finance

A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.

20 credits

Medical and Actuarial Statistics

This module covers statistical ideas that are important in medicine and the actuarial sector. 

You'll learn about the design and statistical analysis of clinical trials used to license new drugs. These trials have their own distinct methodology, due to ethical and regulatory constraints involved in experimentation on human subjects.

You'll develop an understanding of survival analysis, which involves analysing 'time-to-event' data. An example of this could include how long an individual lives and the factors that may increase or decrease life expectancy.

You'll also explore statistical methods with actuarial applications, such as extreme value theory (EVT), which considers the likelihood and magnitude of rare events.

Throughout the module you'll implement statistical methodologies using packages in the programming language R.

20 credits

Bayesian and Computational Inference

This module will develop your understanding of the Bayesian approach to statistical inference, which is fundamentally different to the approach taken in earlier statistics modules.

The Bayesian method is more general and more powerful. While widely used, it relies on modern computers for much of its implementation.  It's based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model.

Through this module, you'll explore the foundations of Bayesian statistics and the incorporation of prior beliefs. You'll study the computational tools important in modern applied statistics, including those important for Bayesian inference such as Markov Chain Monte Carlo. You'll also learn to implement computational methods using R and Python.

20 credits

Time Series and Generalised Linear Models

This module introduces two important areas of modern statistics.

Time series are observations made in time, for which the time aspect is potentially important for understanding and use. You'll be introduced to modern methods of time series analysis and forecasting, as applied in economics and finance, environmental sciences, medical and social sciences. You'll gain practical techniques for data analysis and a firm basis for practical modelling.

Generalised linear models extend linear models, such as regression-type models, in order to accommodate non-normal (non-Gaussian) observations. Through this module, you'll be introduced to generalised linear models and explore inference, including model building and goodness of fit. 

You'll also learn to implement computational methods using a programming language such as R.

20 credits

Mathematical Biology

This module focuses on the mathematical modelling of biological phenomena.

You'll learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning.

You'll focus 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.

You'll investigate the dynamic consequences of feedback interactions within biological systems. In cases where explicit solutions are not readily obtainable, you'll learn to use techniques that give a qualitative picture of the model dynamics (including numerical simulation).

20 credits

Waves and Fluid Dynamics

This module will introduce you to the mathematical ideas used to describe waves and fluids, which play a central role in many physical systems. 

You'll explore wave motion in nature, to illustrate wave propagation, dispersion, and energy transport in fluids. You'll consider shock wave solutions to simple nonlinear partial differential wave equations, learning how basic differential equations can be used to model real-life phenomena. 

Starting from basic conservation principles, you'll also see how simple mathematical models arise for fluid flows, introducing  Euler's equations and Navier-Stokes equations. You'll learn how to identify the dominant physical effects in different situations and choose suitable models.Through this module, you'll develop analytical techniques and modelling skills that are used in applied mathematics and beyond, in areas such as engineering, climate and finance.

20 credits

Game Theory and Optimisation

In this module, you'll study two topics in operations research, which involve developing strategies to make decisions about the optimal ways to respond to certain situations. 

You'll explore game theory, learning about optimal responses to competitive situations.

You'll also study optimisation, by finding and analysing optimal solutions to certain kinds of mathematical problems.

Through this module, you'll develop an understanding of strategies with far-reaching applications, from engineering and computing to economics and business management.

20 credits

Combinatorics and Graph Theory

In this module, you'll investigate the mathematics of combinatorics and graph theory, and use them in a wide range of applications.

Combinatorics is the mathematics of selections and combinations. You'll explore counting and pairing problems from across mathematics, developing a toolbox of techniques to solve problems, such as the inclusion-exclusion principle and binomial coefficients.

Graph theory involves the study of graphs, which are a simple mathematical structure consisting of a collection of points, some pairs of which are joined by lines. You'll develop an understanding of their basic nature and explore how they can be used to illustrate a wide range of situations.

20 credits

Number Theory and Cryptography

This module will develop your understanding of number theory, which involves the study of integers, primes and equations.

You'll explore topics such as linear and quadratic congruences, Fermat's Little Theorem and Euler's Theorem, the RSA cryptosystem, quadratic reciprocity, perfect numbers, and continued fractions.

You'll also study codes and cryptography. Codes are used to store information reliably, while cryptography is used to transmit information securely.

In addition to the RSA cryptosystem, you'll also see other examples where number theory is used in the construction of cryptographic protocols.

20 credits

Geometry, Knots and Surfaces

This module explores various ways that mathematicians model shapes like curves and surfaces in two and three dimensions.

You'll study differential geometry, considering curves in the plane and surfaces in three-dimensional space as rigid things. You'll look at how we can model how 'curved' they are and learn mathematical notions of curvature. You'll also look at the interplay between geometric intuition of curvature and the formal mathematical definition.

You'll consider knotted curves and surfaces in three-dimensional space as 'floppy' rather than 'rigid' and consider the notion of algebraic invariants (analogous to curvature), which can be used to distinguish shapes. You'll also meet the Jones polynomial of knots and the Euler characteristic of surfaces.

20 credits

Machine Learning

This module provides a practical toolkit for modelling and understanding complex datasets by integrating modern AI tools. 

Bridging computer science, statistics, and physics, you'll learn to implement industry-standard algorithms, from linear models to deep neural networks, using Python and modern libraries like Keras and scikit-learn.

You'll not only learn to code, but also effectively co-pilot with AI agents for debugging and code generation, preparing you for the future of technical work.

We'll focus on intuition and implementation. You'll learn to understand when to use a method, how to implement it, and why it works, enabling you to solve real-world problems in science, finance, and business.

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

Ethics and Belief

We know things as individuals, but we also know things collectively. And what we know individually can depend on our relation to other knowers and collective knowledge. These relations are not merely epistemic, they are also practical and ethical. Knowledge can, for instance, be based on trust, while a failure to recognize someone as a knower can be a matter of injustice. Knowledge thereby has a social character and an ethical dimension. This course will introduce a broad range of topics in epistemology that explore this social and ethical turn.

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

People, Organisations and Technology

This module addresses some of the most important moral and political questions faced by human beings in our relation to each other, to organizations and to technology.  The aim of the module is to understand some of our  basic moral concepts as they apply in the context of organisational life as mediated by technology; including truthfulness, trustworthiness, integrity, manipulation, freedom, responsibility and complicity. 

Can organisations be held morally responsible for the effects they have on the world, or is moral responsibility restricted to individuals? What about the effects of technology, such as artificially intelligent machines? 

Does it make sense  to hold a machine morally responsible for its behaviour? Is information technology a threat to human freedom or flourishing  in virtue of its ability to predict, manipulate or control human thought and behaviour? And to what extent do current technological development reinforce existing injustice, oppression or prejudice, as opposed to presenting us with new form

of emancipation, protection or control? In this module these and related questions are addressed both theoretically and by applying them to actual example in the present.

20 credits

Memory and the Self

Our memories of our personal past (i.e. our episodic memories) play an important role in our lives. They help us perform mundane tasks like finding our keys, but they arguably also form the foundation of our sense of self and personal identity. They let us know who we are by recording what we've done and experienced. In this module we will try to better understand what episodic memory is and to what extent it grounds our understanding of the self. This module will introduce students to the cognitive science of memory and to core issues in the philosophical foundations of cognitive science.In the first part of the module, we will look at methodological issues that arise when we attempt to describe the mind's structure within philosophy, psychology, and neuroscience. In the second part of the module, we will look towards the cognitive sciences to better understand what sort of thing episodic memory is. In the final part of the module, we will consider the relationship between episodic memory and our sense of the self. This is an interdisciplinary module. Understanding how the mind is structured is a complex project. In order to make progress we need to appeal to both empirical and philosophical work (and work that blurs this distinction). We'll read scientific and philosophical papers; however, no prior knowledge of cognitive science (or neuroscience) will be presumed.

20 credits

The Science of Consciousness

Consciousness is at once both something incredibly familiar and something utterly mysterious. Consciousness seems to be a subjective phenomenon to which we have a privileged first-person access Yet, this very subjective nature of consciousness makes it hard, if not impossible, to scientifically study. In this module we'll look at recent developments in the study of consciousness from across the cognitive sciences (including philosophy, psychology, neuroscience, and biology). This module will also serve as an introduction to some core issues in the philosophical foundations of cognitive science.In the first part of the module, we will look at various theories of consciousness from across different disciplines. In the second part of the module, we'll look at specific methodological issues that arise in studying consciousness in human and non-human animals.This is an interdisciplinary module. Understanding how the mind is structured is a complex project. In order to make progress we need to appeal to both empirical and philosophical work (and work that blurs this distinction). We'll read scientific and philosophical papers; however, no prior knowledge of cognitive science (or neuroscience) will be presumed.

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

Free Will and 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

Work Place Learning

Philosophy as a discipline is defined by its very general subject matter, and also by the skills that philosophers deploy in getting to grips with philosophical problems: skills that the Workplace Learning module gives you the opportunity to apply in the workplace.

For this module, you will do a work placement, either self-organised or with the help of University employability specialists, or otherwise have some work placed skill development opportunity. Through work or practical activity, you will be able to deploy and enhance some of the skills you have gained during your studies, such as communications skills, analytical and problem solving skills, and project management skills. The graded coursework for Workplace Learning will then either take the form of a philosophical essay tackling a question relevant to the goals or methods of a particular organisation or type of work, or to work in general. Given the generality of the subject matter of Philosophy this can be a question in any of the traditional subfields of Philosophy; or it can (wholly or partly) take the form of a diagnostic report addressing a problem facing the organisation you worked for or a problem you encountered in your work. This coursework will be individually supervised. And there will also be group sessions to consider the philosophical relevance of your work experiences, to further hone your critical and communications skills, and to provide peer feedback.

20 credits

Feminist and Queer Studies in Religion

This module uses feminist, queer, and trans philosophical frameworks to examine the constructions of gender, sexuality and social norms within diverse religious and cultural contexts. You will apply critical insights to a variety of questions including the nature of deities, gender roles (from masculinity to the 'trad-wife' phenomenon, and LGBTQ+). You will engage with a broad range of sources—from the Kama Sutra and Vatican documents to scriptures and theologies,  developing a sophisticated understanding of religious hermeneutics, gender and sexuality. Flexible assignment options allow students across Philosophy, Humanities, and Social Sciences to specialize in their preferred traditions and research interests, working with real life questions, empirical data or literary sources to formulate arguments for justice and liberation.

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

Bodies and Souls

Descartes is famous for his view that all mental activity takes place in an immaterial substance, so that what we call a human being is really two things: a thinking soul and an unthinking body. Aristotle thought that every living thing, whether conscious or not, was a compound of matter and form, and he called this form a 'soul'. This view, 'hylomorphism', dominated European philosophy throughout the middle ages. Both views are currently the subject of renewed interest. This module will examine them from a contemporary perspective.

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

Ancient Chinese Philosophy

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

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

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

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

- The Philosophy of Psychology (20 credits)
- Ethical Scepticism (20 credits)
- Social Philosophy (20 credits)
- Utopia, Reform and Democracy (20 credits)