Mathematics and Philosophy BSc

Core modules:

Writing Philosophy

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

20 credits

Mathematics Core

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

40 credits

Foundations of Pure Mathematics

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

20 credits

Optional modules:

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

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

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

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

Optional modules:

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

Philosophy of Religion

Religious teachings and practices raise many philosophical questions. For example, how should we understand the nature of God for purposes of evaluating evidence for and against God's existence? Are there persuasive arguments for believing God does exist, or for believing God doesn't? Could the universe itself in some sense be divine? Is there any evidence for thinking that people can survive the death of their physical bodies? Does the pervasiveness of religious disagreement provide support for suspending judgment about religious claims in general? Does it make any sense to follow a religion without believing what it teaches? This module will interrogate philosophical work bearing on questions such as these.

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

History of Philosophical Ideas

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

10 credits

Truth, Reality and Virtual Reality

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

10 credits

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

Ethics in Antiquity: East and West

How should we live? What are the right values and principles by which we should guide our lives? What weight should we give to considerations of morality and justice? Are there fixed truths about these matters or are they just determined by choice or convention? Ethics is concerned with questions such as these. This course will engage with such questions by examining some important and influential texts from the ancient world, both Western and Eastern, including key writings by the Greek philosopher Plato and the Chinese philosopher Zhuangzi.

10 credits

Optional modules:

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

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

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

Optional modules:

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

Social and Historical Constructions of Childhood

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

20 credits

Varieties of English

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

20 credits

The Sounds of English

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

10 credits

The Structures of English

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

10 credits

Early Englishes

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

20 credits

Contemporary Literature

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

20 credits

Cities, Places and People

The aim of this module is to provide you with an introduction to the central concept of place through a focus on the city of Sheffield, its communities and its people. In developing this understanding of place, you will be introduced to some of the theories, techniques and data  that planners use in their efforts to understand and create better places and the module will develop your skills of analysis for assessing the social, economic and environmental qualities of urban places. Through lectures, site visits and computer-based workshops, you will gain an understanding of several different areas in Sheffield so that you develop a broader appreciation of the city's strengths and some of the contemporary challenges that it faces.

10 credits

Empire: From the Ancient World to the Middle Ages

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

20 credits

Religion in Britain

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

20 credits

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

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

20 credits

Music Psychology

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

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

10 credits

History and Culture in China

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

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

20 credits

Technologies for Music

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

10 credits

Music in a Global Context

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

20 credits

History and Culture in Japan

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

20 credits

Histories of Education

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

20 credits

Child Psychology

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

20 credits

Making Sense of Education: Facts, Fiction and Data

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

20 credits

History of English

What is English? Taking this question as a point of departure, this module introduces students to the exceptionally dynamic linguistic history of English(es). Changing linguistic forms and functions are contextualized within their historical moment, and language external factors such as language contact, imperialism and racism are also discussed as they pertain to periods of English. To be clear: this is not just a module about old forms of language (although there is plenty of that!) - it's about gaining historical linguistic perspective on current Englishes (including related Creoles) and their place within a much bigger story.

20 credits

Urban Economics

This module is designed to introduce you to key economic concepts and theories and show how they are applied to real estate markets and policy challenges. You'll gain an economic perspective on planning issues, focusing on real estate markets and urban development.

This module is designed to help you understand the economic environment that planners and other urban professionals operate in and deepen your knowledge of economic theory and how it relates to the real estate market.



This module is designed to enable you to:

- Understand and critically assess a range of economic ideas and their relative merits.

- Gain insight into how markets operate, including their strengths and weaknesses.

- Develop a solid understanding of key economic issues in real estate and planning.

- Learn to analyse data using basic descriptive statistics effectively.

10 credits

Climate Action

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



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

10 credits

The Making of the Twentieth Century

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

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

20 credits

The Transformation of the United Kingdom, 1800 - 2000

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

20 credits

Politics, Economy and Society in Japan

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

20 credits

Popular Music Studies

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

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

10 credits

Gender, Sexuality and Society

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

10 credits

Introduction to Comparative Politics

Comparative politics is the systematic study and comparison of the diverse political systems in the world. 

Throughout the module you will examine the utility of the comparative approach to politics, focusing particularly on types of political regimes (democracies, dictatorships, and electoral authoritarian), and their implications for fascinating outcomes such as development (why some countries are more affluent than others), and conflict (why some countries are more prone to civil war than others). We will also discuss the role that colonialism plays in this interaction between regimes and consequences.

You will consider the key features of each regime type to be able to explain the nature of the comparative method, its strengths and weaknesses. You will also have the opportunity to learn useful skills which will help you design and come up with potential data to answer your research questions.

20 credits

British Politics

You will be introduced to the key concepts and debates that have shaped British politics with an emphasis on history, institutions and culture.

Each lecture will focus on a specific element of British politics, with subsequent and linked seminars providing an opportunity to deepen this knowledge by looking at critical case studies or official reviews.

This module provides key employability skills and practice based knowledge through a focus on the theory and practice of political decision-making processes and the challenges of implementing policy.

20 credits

Core 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

Optional modules:

A student will take 20 credits (one module) from this group.

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

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

Optional modules:

A student will take 10 credits (one module) 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

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

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

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

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 'MPS115 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

Optional modules:

A student will take a minimum of 40 credits (two modules) and a maximum of 60 credits (three modules) from this group.

Ethics: From Theory to Practice

Ethical values shape our world and the lives we lead - from how we relate to our friends and community, to our social and political attitudes, to the aspirations and goals that guide our life choices. But ethics is also challenging. When our values clash, or we face unfamiliar problems, or we reflect on the objectionable values of people in the past, it becomes unclear what to do. Ethical theories attempt to help us solve these problems by giving a precise, unified and systematic account of moral values, ideals and duties.

This module introduces students to a range of contemporary and historical ethical theories. We discuss six broad approaches to ethical theorising, each centred on a core unifying value: altruism, relationships, freedom, agreements, rights and excellence. In doing so we will encounter theories such as Utilitarianism, Contractualism and Feminist Care Ethics, and the ideas of philosophers including JS Mill, Harriet Taylor, Simone de Beauvoir, Immanuel Kant, Thomas Hobbes, Mary Wollestonecraft, Aristotle and Freidrich Nietzsche.

Students will learn how to articulate the key concepts and theories in philosophical ethics, and to evaluate, compare and criticise different approaches to ethical theorising. They will also learn to employ philosophical concepts to uncover and analyse the ethical values and presuppositions made in contemporary moral and social debates.

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

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

History of 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

Religion and the Good Life

What, if anything, does religion have to do with a well-lived life? For example, does living well require obeying God's commands? Does it require atheism? Are the possibilities for a good life enhanced or only diminished if there is a God, or if Karma is true? Does living well take distinctive virtues like faith, mindfulness, or humility as these have been understood within religious traditions? In this module, we will examine recent philosophical work on questions like these while engaging with a variety of religions, such as Buddhism, Christianity, Confucianism, Daoism, Islam, and Judaism.

20 credits

Theory of Knowledge

The aim of the course is to provide an introduction to philosophical issues surrounding the knowledge. We will be concerned with the nature and extent of knowledge. How must a believer be related to the world in order to know that something is the case? Can knowledge be analysed in terms of more basic notions? Must our beliefs be structured in a certain way if they are to be knowledge? In considering these questions we will look at various sceptical arguments that suggest that the extent of knowledge is much less than we suppose. And we will look at the various faculties of knowledge: perception, memory, introspection, and testimony.

20 credits

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 Science

It is virtually impossible to overstate the importance that science has in our everyday life. Here is a brief list of things that would not exist without modern science: computers, phones, internet, cars, airplanes, pharmaceutical drugs, electric guitars. Imagine your life without these things. It looks very different doesn't it? Science, however, is not important only in virtue of its practical applications. in fact, many would agree that the the primary value of science is that of being the best available source of knowledge about the world. Indeed, it seems fair to say that we made more discoveries after the 17th century scientific revolution [e.g. the laws of planetary motion, the principles underlying biological evolution, the laws governing quantum phenomena, the structure of DNA, the cellular architecture of the brain] than in all the previous millenia. This raises important philosophical questions.

First, what is science? What are the criteria that demarcate science from non-science? For example, what is the difference between science and religion? Second, how does science work? What are the methods and eplanatory strategies that make it so successful? Is there such a thing as the scientific method, and what counts as a scientific explanation? Third, is science objective? That is, is science a form of rational and unbiased inquiry, or does it reflect ethical, political, and social factors? Finally, is science the fundamental source of knowledge about the world? Does science tell us how things really are? These are some of the questions that we will tackle in this course.

20 credits

Bioethics

Bioethics arose in response to the moral challenges thrown up by technological advances of the twentieth century. As we move through the 21st century, new moral problems are emerging, even as old one still concern us.

How should we allocate resource for medical care and research? Are there limits to what can be done to our bodies, or does consent permit everything? In a pandemic, 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?

This module will introduce a range of practical bioethical problems, as well as some methods for approaching them. Our emphasis will be on doing philosophy practically, with a view to the implications of philosophical argument in the real world of healthcare, research and bioscience.

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

Metaphysics

This course is an introduction to metaphysics. It will focus on two general themes: whether we are material things, and the nature of time. Readings will be drawn mainly from recent and contemporary sources.

20 credits

Philosophy of 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

Political Philosophy Today

This module will investigate a broad range of contemporary topics and issues in political philosophy. Example topics include the political rights of animals and children, how we should allocate scarce health resources, whether we should ban private education, and the limits of free speech in the workplace. By studying these topics and others, students will gain a broad knowledge of the state of contemporary political philosophy, develop their ability to critically assess and discuss real-world issues, and improve their understanding of how theoretical topics in political philosophy can be applied in practical ways.

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

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

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

Theories of Value : Aesthetics and Ethics

This module will introduce students to a range of 

topics relating to the nature of value in aesthetics and

ethics, including relations between the two. 

20 credits

Optional modules:

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

Psychology and Learning Communities

This module explores learning as conceptualised by different approaches within the broad umbrella of psychology. It examines how and why these different approaches emerged, how they compare to one another, and how they have come to inform different understandings of what learning is, how it happens and how it might be facilitated. It also explores how these different conceptualisations have come to impact individual learners, and particular learning communities. Critical attention is drawn to the way in which language facilitates social practices including those involved in the construction of different kinds of knowledge. In this sense, knowledge relates to formal conceptualisations of learning provided by developments in scientific disciplines (e.g. psychology) and the social sciences (e.g. education and sociology). It is also concerned with informal understandings such as the continual constitution of learner's identities through social engagement. The module aims to challenge notions of learning as an individual enterprise and to support students in critical reflection upon their own learning experiences in connection to the approaches discussed.

20 credits

Phonetics

The first year module Sounds of English will be expanded upon in order to give a practical knowledge of a much broader range of speech sounds, how they are produced and how they can be analysed by careful listening and by examination of their acoustic properties. A working knowledge of phonetics is fundamental to the wider study of linguistics, both theoretical and applied. You will be given straightforward access to other bodies of knowledge which are often denied to students of the humanities but which inform the study of phonetics, such as the biological and physical sciences. The module has a practical as well as a theoretical component which involves learning to recognise, produce and transcribe the sounds of the International Phonetic Alphabet.

20 credits

Urban Analytics

This module will serve as an introduction to quantitative and spatial analytical methods, with a specific focus on understanding, interpreting and presenting secondary data in urban contexts. It will expose students to a variety of substantive issues surrounding the use of data in practice and enhance their understanding of methods used in real world policy settings. Students will access and use a range of different datasets, covering demographics, property, and land use and will analyse them using both spatial and aspatial methods. They will be required to demonstrate competence in accessing, analysing and presenting such data using both aspatial and spatial methods in order to gain a deeper understanding of key issues facing urban settings.

20 credits

Urban Theory

At the heart of every discipline lie the ideas, concepts and frameworks that help its students and researchers to make sense of its object of study. In planning, geography and urban studies there are numerous perspectives, concepts and key thinkers who have shaped the development of these disciplines. This course introduces you to a series of key concepts and thinkers and helps them to make sense of urban life as a result.

Urban Theory aims to develop your imaginative engagement with the nature of urban life and human settlement. Urban theory refers to writing and thinking devoted to 'seeing' and understanding urban life. Concepts and ideas are critical to how we engage with the key features and problems of the urban world, shape the process of conducting research and help us to make sense of and understand many of the key challenges in cities today. Theory is therefore critical to our understanding of how cities work in practice and how we understand and view urban life subsequently informs the development of cities and efforts to make them more socially just, sustainable and better places to live. Urban Theory introduces a range of ideas and key concepts in urban studies with a view to understanding how cities have developed and how they 'work' in broad terms. The module considers a range of thinkers, concepts and perspectives. The aims of the module are:

1. To introduce and extend your knowledge of different ways of seeing city life. This includes a wide range of perspectives, thinkers and concepts relating to urban social and political life, the economies of cities, the range of communities and groups living in cities and, their built and natural environments

2. To provide you with an armoury of critical ideas and concepts that will deepen their understanding of the fundamental power relations, inequalities and divisions that characterise cities and which structure localities, particularly in relation to questions of class, race and gender.

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

Gender and Identities in East Asia

This module offers an overview of the study of gender and its connection to social, cultural, political and economic discourses across East Asia. Covering key issues related to the structures and dynamics of gender in East Asia, we learn to situate these dynamics in their historical and cultural context using case studies drawn from across the region.

20 credits

Contemporary Chinese Society and Culture

This module introduces students to different ways of thinking about Chinese society and culture. In particular, we focus on sociological, anthropological and geographical approaches to contemporary Chinese society and culture, showing why and how China is important to current theoretical debates in these disciplines.

20 credits

Dynamics of Social Change and Policy

This module will present you with a 'sociological perspective on social policy' to provide a macro perspective on contemporary social and economic transformations in the UK and globally. Particular emphasis will be placed on the challenges posed for social policy theory and practice, as well as the potential to imagine alternative social policy scenarios.

Some of the issues you will consider include: globalisation, neoliberalism, falling fertility and ageing societies, precarious labour markets and migration, and mobility. You will be encouraged to take a comparative and international/global perspective, emphasising not only the perspectives of International Organisations, but also the challenges faced by other types of welfare regimes. 

The module will equip you with a deep understanding of key socio economic challenges faced by postindustrial societies while also reflecting on how these challenges are received and responded to by Global South countries. You will also develop your skills in policy report writing, an essential tool most will use in their professional careers.

20 credits

Children and Digital Cultures

Digital technology has transformed the lives of many, impacting on culture and society. Many young people have quickly seen ways of extending and deepening social networks through their uses of technology, and immersed themselves in Virtual Worlds, Facebook etc and enjoyed browsing on shopping sites. This module examines new technologies and associated social practices impacting on children's lives, considering the nature of new digital practices and how these affect identity, society and culture. Educational implications of new technologies is a developing field of research and students will engage critically with debates within the field alongside examining websites and new practices.

20 credits

First Language Acquisition

This second-year module is aimed at students who have already taken Linguistic Theory in Level 1. In this course, we focus specifically on the first language acquisition of phonetic, phonological, and morpho-syntactic knowledge. Addressing both theoretical and methodological issues, the course explores the relationship between the logical problem of language acquisition -- how very young children manage to acquire quite abstract and subtle properties of their target grammars in the absence of clear positive evidence -- and the developmental problem of acquisition -- how children recover from systematic errors, and acquire subtle language-specific properties. We also explore the related tension between nativist vs. emergentist explanations for language acquisition and development.

20 credits

Phonology

This module examines phonological theories and the data on which they are constructed, exploring how languages across the world organise their systems of speech sounds, and critically interrogating how their phonological processes can be analysed. Sound-based and prosodic (e.g. syllable-based) phenomena will be investigated, using rule- and constraint-based frameworks. Problem-solving, data-handling, and critical thinking are key skills developed in this module, and by treating all languages equally in terms of what they can tell us about human communication, the module is inherently diverse and inclusive. As well as being a core part of theoretical linguistics, an understanding of phonology is essential to the studies of historical linguistics, sociolinguistics, psycholinguistics, speech pathologies, language acquisition, and computerised speech synthesis and recognition technologies.

20 credits

Cities, Violence and Security

Urban violence, insecurity and crime are features of the everyday and crisis moments of city life in many nations around the world. Warfare touches life in many cities today, questions of narco-terror and violence affect many others. Meanwhile, the role of the climate emergency in driving migration and instability, forms of economic crisis and precarity, alongside other forms of disturbance lead to forms of injustice, violence and victimisation. The course seeks to develop student understanding of the political, economic and social drivers of human insecurity in urban settings.

This course has been designed to develop student's engagement with and responses to multiple forms of urban insecurity. It discusses the diverse kinds of responses to insecurity by states, armies, police and citizens, many of which bring further rounds of insecurity and violence to marginalised and excluded populations. 

The primary aim of the course is to find answers to the question: how can peace and security be enjoyed by all citizens in cities around the world today?

Cities, Violence and Security introduces students to a range of examples of violence, conflict and insecurity in urban contexts around the world. The course develops awareness of the programs and policies being pursued to make better and safer places. Examples of urban violence and crime, policing, forced evictions, domestic violence, terrorism, gangs and the rise of gated communities and other modes of design and control to produce securitised urban spaces are discussed and analysed in their effectiveness.

The aims of the course are:

1. To develop students' awareness of the political, social and economic context in which urban violence and insecurity are embedded in different global contexts

2. To develop students' understanding of core debates relating to urban insecurity in both the global North and South

3. To develop students' critical understanding of the role of these debates in informing policies and initiatives to try and reduce violence and insecurity in cities

20 credits

City makers

Drawing on cities from different contexts, this module provides an introduction to the administrative, economic and socio-political contexts in which city making takes place, as well as the role that different groups and interests play in mediating and affecting urban transformation. In doing so, the module will explore questions around the agency of built environment professionals  and how the relationships between stakeholders, development projects, finance, activists, and trade-offs in agendas impact the ability of planners and other built environment professionals to pursue the public interest.

20 credits

Modern Chinese History: Beyond Revolution

This module will examine key themes in the histories of China's short twentieth century, with a primary focus on interpretations of 'modernity' and 'progress', explanations of revolution, and the ways in which new approaches in scholarship have influenced our understanding of China's recent past. While the structure of the module is loosely chronological, the emphasis is not on the detail of events but on the critical analysis of broad social and political changes, and we will examine these through recent historical writing on China and a range of primary textual and visual sources.

20 credits

Solidarity: Politics, Law, and Society across the Globe

In this interdisciplinary module, we explore how solidarity has been understood, practised, and contested across the globe. From Cuban solidarity for African liberation struggles to cross-species solidarity in climate activism today, we explore the possibilities of solidarity in action. In doing so, we will look at the wide-ranging impact that solidarity has had from individual survival to regime change. Taking a critical approach to the topic, we will also explore situations in which acts of solidarity can amplify forms of exclusion and injustice.

20 credits

Social Problems: Policy and Practice

Drawing on current examples and comparative references, you will explore social and ideological constructions of social problems and the role of the state and other agencies in responses to them. This module is team taught which means sessions are delivered by a range of leading experts on different social problems.

Some of the key concepts and themes in social policy and practice that you will cover include inequality, justice and fairness, individual versus collective responsibility, and welfare versus social control. The content of this module mainly focuses on major contemporary issues, including welfare and work, housing and homelessness, and community participation.

By the end, you will be equipped with the necessary critical perspective and skills to understand and explore social problems.

20 credits

Students can also select Languages for All modules.

Optional modules:

A student will take a minimum of 40 credits (two modules) and a maximum of 60 credits (three modules) from this group.

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 School of History, Philosophy and Digital Humanities 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

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

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

Dissertation Project 1

A variety of topics including an independent choice will be set  For each topic, a short list of key readings is provided. Having chosen a topic, students are expected to master the readings, and then supplement them with at least two other pieces of relevant literature having used the available library and web resources to research. They then, having agreed a title with a supervisor assigned to them for the module, write an extended essay that identifies the central issue (or issues) under discussion, relates the various responses to that issue found in the literature, evaluates those contributions, and goes some way to identifying a satisfactory resolution of the issue.

20 credits

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

Ancient Chinese Philosophy

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

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

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

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

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

Dissertation Project 2

A variety of topics including an independent choice will be set  For each topic, a short list of key readings is provided. Having chosen a topic, students are expected to master the readings and then supplement them with at least two other pieces of relevant literature, having used the available library and web resources to uncover research. They then, having agreed a title with a supervisor assigned to them for the module, write an extended essay that identifies the central issue (or issues) under discussion, relates the various responses to that issue found in the literature, evaluates those contributions, and goes some way to identifying a satisfactory resolution of the issue.

20 credits

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

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

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

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

Political Resistance

This course examines various dimensions of political resistance in the face of injustice. 



The course begins with a basic examination of some key texts discussing concepts such as individuals' natural duties, political authority and political legitimacy. Here, the goal is to figure out the bases of citizens' obligation to comply with the law, in order to specify the conditions in which those obligations might be void, unenforceable, or overridden. This is crucial for understanding the conditions in which political resistance or even disobedience of the law could be permissible.

We will also examine various justifications for political resistance and disobedience. Is the point of resistance to communicate one's principled disagreements with, or objection to, some law or public policy? Or is it to make an appeal to the sense of justice of the community, in the hopes of stirring democratic action to remedy injustices? Or might resistance and disobedience be justifiable in a more direct fashion, as a form of defensive action which eliminates or at least mitigates injustice? Following this, we turn to the question of whether there might be principles that can even impose duties on individuals to engage in resistance or disobedience.

We will also examine the distinctions between different forms of political resistance and disobedience. How do we differentiate among legal protests and marches, illegal sit-ins or occupation of public or private spaces, property damage, rioting, among others? Why should we be interested in differentiating among these forms of political action? How can those who engage in political protest against injustice differentiate themselves from non-politically motivated criminals? A related goal is to critically examine the arguments for and against each of these forms of political action. We shall also consider the weight of pragmatic or strategic considerations, relative to those of normative considerations. 

We will also examine how the state should respond to political resistance and disobedience which disrupts social norms or breaks the law. How should law-enforcement decide whether and how to intervene? How should prosecutors decide whether and when to file charges against protestors? How should judges and juries decide whether to convict, and how much to punish? 



Throughout the course, the discussions are anchored in a variety of historical and contemporary cases of political resistance and disobedience, and in a variety of contexts. We will examine environmental activism, animal rescue, hacktivism, facilitating illegal migration, anti-colonial resistance, civil rights movements, independence and liberatory struggles, among others. Students should expect to develop their ability to critically analyse and assess these cases with reference to the philosophical ideas discussed in the course.

20 credits

Optional modules:

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

What is Learning?

The module explores understandings about how people learn, and implications that these understandings have for how we conduct key social practices, including teaching, caring for children, assessing learning, and on educating generally. We will also look 'beneath' understandings of learning to the worldviews on which they stand, particularly 'realist' and 'constructivist' positions. This matters because 'realism' and 'constructivism' carry implications for how we conceptualise things we take for granted: the nature of truth, the process and products of science, the basis for ethics, the outcomes of research, and assumptions about what is. The module will explore these challenging issues.

20 credits

Philosophies of Education

This module will explore the importance of philosophy to the study of education. It covers key moments in the history of Western philosophy, focusing on the question of modernity (What is modernity? What are its ramifications for education?). The module will investigate the consequences of late modernity for present day education, a period in which the aims and purposes of education have become increasingly unclear, leaving education open to the rise of instrumentalism and the forces of capital. Overall the module offers a critique of common assumptions in education, provoking questioning about its nature and purposes.

20 credits

Language and Religion

This module examines the ways in which people talk about what they hold sacred, both in overtly religious and 'secular' contexts. This module takes a critical, functional approach to language, first asking, what does religious language do for us? Among the topics that will be covered are definitions of religion and religious language, a three-dimensional approach to studying religious language and common discursive strategies and linguistic features used to perform religion. The module will be of particular interest to students interested in language and power as well as language and ideology, but we will also be looking at language and religion as it enacts and represents the full range of human experience.

There will be opportunities each week to examine religious language in a variety of contexts, using specific analytic tools within three levels of critical discourse analysis (text, discourse practice and sociocultural practice). In the assessments, you will have the freedom to develop these skills further by analysing texts of your choice, taken from contexts that suit your interests. The tutor will provide support in finding and selecting these texts.Overall, this module aims to examine the porous boundaries between the sacred and the secular. In so doing, we will consider the language not just of those looking to a sacred supernatural but those who articulate ultimate significance to values and priorities without adherence to organized religion.

20 credits

Future Cities

This module will introduce students to conceptual and policy debates that frame possible urban futures.  It will develop students' understanding of the emerging contemporary practices and challenges that are transforming cities, such as smart cities, fantasy urban planning, eco-cities, cities and technology and cities and the super rich.  It will also expose students to a range of case studies that present urban issues and processes from both the Global North and the Global South.

20 credits

Children, Families and Welfare States

This module examines welfare state support and services for children, parents and families, informed by sociological and social policy theories, concepts and research. Adopting a comparative approach, the module critically reviews different approaches to, and configurations of, welfare state support and services for children, parents and families across the UK and Western/Northern European welfare states. Four policy and provision domains are examined, namely cash support for children and families; childcare and early years' services; parental leave and work-family balance policies; and child welfare and family support services.

20 credits

Education@Sheffield

In Education@Sheffield students are invited to explore and evaluate the rich and diverse research taking place within the School of Education. Through a series of seminars presented by active researchers, students are encouraged to critically engage with research - and the researchers themselves - in the fields of educational and childhood studies. The Education@Sheffield module enables students to acquire a critical understanding of various themes, settings and methodologies which shape contemporary educational research.

20 credits

Globalising Education

This module considers the extent to which education might be viewed as a global context with a shared meaning. Moving outwards from the dominant concepts, principles and practices which frame 'our own' national, or regional responses to education, the module explores other possible ways of understanding difference. By examining 'other ways of seeing difference', in unfamiliar contexts, students are able to examine the implications of globalisation for education and explore the opportunities and obstacles for the social justice agendas within a range of cultural settings.

20 credits

Housing and Urban Inequalities

The aims of this module are to build on substantive knowledge, theory and skills about housing. Emphasis is placed on policy, practice, strategy analysis and understanding the links between housing, planning, social policies and outcomes at national, regional and local levels. The module further aims to: increase understanding of contemporary issues and debates in housing and housing policy and strategies; understand the causes and manifestations of problems, dilemmas and conflicts in housing systems and policy processes; and to develop abilities to synthesise and apply knowledge by understanding and critically assessing potential policy approaches to addressing housing problems.

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

Optional modules:

A student will take a minimum of 50 and a maximum of 60 credits from this group.

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

Financial Mathematics

The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance.

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

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

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 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

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

Bayesian Statistics

This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is 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. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python.

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

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

Introduction to Relativity

Einstein's theory of relativity is one of the corner stones of our understanding of the universe. This course will introduce some of the ideas of relativity, and the physical consequences of the theory, many of which are highly counter-intuitive. For example, a rapidly moving body will appear to be contracted as seen by an observer at rest. The course will also introduce one of the most famous equations in the whole of mathematics: E=mc^2.

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

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

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

Sampling Theory and Design of Experiments

The results of sample surveys through opinion polls are commonplace in newspapers and on television. The objective of the Sampling Theory section of the module is to introduce several different methods for obtaining samples from finite populations. Experiments which aim to discover improved conditions are commonplace in industry, agriculture, etc. The purpose of experimental design is to maximise the information on what is of interest with the minimum use of resources. The aim of the Design section is to introduce some of the more important design concepts.

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

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

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

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

Mathematical Physics

Linear algebra: matrices and vectors; eigenvalue problems; matrix diagonalisation; vector spaces; transformation of basis; rotation matrices; tensors; Lie groups; Noether's theorem. Complex analysis: analytic functions; contour integration; Cauchy theorem; Taylor and Laurent series; residue theorem; application to evaluating integrals; Kronig-Kramers relations; conformal mapping; application to solving Laplace's equation.

10 credits

Probability with Measure

Probability is a relatively new part of mathematics, first studied rigorously in the early part of 20th century. This module introduces the modern basis for probability theory, coming from the idea of 'measuring' an object by attaching a non-negative number to it. This might refer to its length or volume, but also to the probability of an event happening. We therefore find a close connection between integration and probability theory, drawing upon real analysis. This rigorous theory allows us to study random objects with complex or surprising properties, which can expand our innate intuition for how probability behaves. The precise material covered in this module may vary according to the lecturer's interests.

10 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

Skills Development in Mathematics and Statistics

This module consolidates skills development across a number of areas of the mathematics curriculum, allowing students choice from a range of application areas in mathematics and statistics.  Students will complete a portfolio, comprising a range of outputs from project work, group work, and evidence of professional skills development.  Possible areas of mathematics include statistical investigations, history of mathematics, mathematical modelling, and sustainability, while the outputs might take the form of written projects, for example.  The module will involve considerable independent study, but staff will be available to guide you in your work.

20 credits

Optional modules:

A student will take up to 10 credits (one module) from this group.

Evolution of Terrestrial Ecosystems

This module examines the evolution of terrestrial ecosystems, from the invasion of the land by plants and animals in the Ordovician (475 million years ago) up to the present day. All of the major events will be covered: the origin of land plants; the invasion of the land by invertebrate animals (worms, insects, etc); the first forests; the origin of amphibians, reptiles, mammals and birds; beginnings of phytogeographical differentiation; origin of the flowering plants etc. Throughout the course the evolution of terrestrial ecosystems will be considered in light of: (i) the interrelationships between global change and evolving terrestrial ecosystems; (ii) plant-fungal-animal interactions and coevolution.

10 credits

Sustainable Agro-Ecosystems

This module highlights the threats to global sustainability, with a particular focus on food production and ecosystem functioning, being caused by human impacts on the environment. The module considers how we have got into the present unsustainable mess: of poor land and natural resource management, under valuing of farmers, life-threatening soil degradation causing flooding, pollution of fresh water and soil insecurity, as well as large numbers of people overconsuming and wasting food whilst others don't have enough. It shows that how we sustainably manage agro-ecosystems now, and in the immediate future, will determine the fate of humanity. Soils are the foundations of terrestrial ecosystems, food and biofuel production, but are amongst the most badly abused and damaged components of the ecosphere. Climate change, agricultural intensification, biofuels and unsustainable use of fertilizers and fossil fuels pose critical threats to global food production and sustainable agro-ecosystems - and their impacts on soil ecosystems are central to these threats. The module considers soil ecosystems function in nature and the lessons that we can then apply to develop more sustainable agriculture and ecosystem management.

10 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

Topics in Evolutionary Genetics

This course aims to provide the opportunity for students to develop (i) their knowledge of current leading-edge research areas in evolutionary genetics and (ii) their skills in accessing, interpreting and synthesising the primary scientific literature in this field. This will be achieved by examining three areas of current research activity in evolutionary genetics though detailed analysis of the questions, methods and interpretations in groups of recent publications.

10 credits

Globalising Education

This module considers the extent to which education might be viewed as a global context with a shared meaning. Moving outwards from the dominant concepts, principles and practices which frame 'our own' national, or regional responses to education, the module explores other possible ways of understanding difference. By examining 'other ways of seeing difference', in unfamiliar contexts, students are able to examine the implications of globalisation for education and explore the opportunities and obstacles for the social justice agendas within a range of cultural settings.

20 credits

Students can also select Languages for All modules.