Students in a maths lecture

Mathematics and Philosophy BSc

School of Mathematics and Statistics

Department of Philosophy

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You are viewing this course for 2021-22 entry. 2022-23 entry is also available.

Key details

Course description

Students in a maths lecture

Mathematics and philosophy is a challenging, rewarding combination. Both subjects require careful, rigorous reasoning as well as imagination.

Your maths study will include core mathematics, pure mathematics, applied mathematics and probability and statistics. You can specialise later in the course.

The philosophy side of the course is flexible. There are no compulsory modules. You can develop your understanding of key areas such as ethics, philosophy of mind, theory of knowledge, political philosophy, metaphysics and logic.

We also teach courses on major figures in the history of philosophy such as Plato, Aristotle, Descartes and Hegel.

Dual and combined honours degrees

Modules

The modules listed below are examples from the last academic year. There may be some changes before you start your course. For the very latest module information, check with the department directly.

Choose a year to see modules for a level of study:

Title: Mathematics and Philosophy BSc course structure
UCAS code: VG51
Years: 2021

Core modules:

Mathematics Core 1

The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.

20 credits
Mathematics Core II

The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.

20 credits
Numbers and Groups

The module provides an introduction to more specialised Pure Mathematics. The first half of the module will consider techniques of proof, and these will be demonstrated within the study of properties of integers and real numbers. The second semester will study symmetries of objects, and develop a theory of symmetries which leads to the more abstract study of groups.

20 credits

Optional modules:

Matters of Life and Death

This course will look at the value of life and the wrongness of killing. We will look at various issues of important practical concern, such as abortion, euthanasia, capital punishment, war, as well as the case of allowing people to die from need whom we could have saved. We will look at how best to understand the principles that guide, and ought to guide, our judgements about what to do when confronted with these issues. Students will gain a better understanding of how to think about these issues, and in particular will be introduced to the benefit of thinking about them philosophically.

20 credits
Mind, Brain and Personal Identity

What is it to have a mind? Is your mind a physical thing, such as your brain? Or is it a non-physical soul? Do human beings have free will¿the ability to freely choose their own actions¿and, if so, how? What makes you the same person you were when you were a young child? Do non-human animals have minds? Could computers or robots have artificially created minds? If animals or computers had minds would they have souls? Could they have free will? This course examines these issues and some historical and contemporary attempts to understand them.

20 credits
Self and Society

This course introduces students to central questions in political philosophy: Do we need a state, and if so, must we obey its laws? When, why and how may states punish citizen for failing to obey the law? What is freedom, and when are we free? Is equality a moral value, and if so, what are its implications for how governments ought to act? What is justice, and how does it relate to freedom, equality, and punishment? Should states be organised democratically, and what does it mean to live in a democracy? The course encourages students to think carefully and clearly about the relationship they have, as citizens, to each other and the state, and to develop their analytical and critical skills in the process. Readings will include influential, historical and contemporary discussions of the state, equality, freedom, justice, and democracy.

20 credits
Writing Philosophy

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

20 credits
Death

This module is mainly about death itself [whereas PHI125 is mainly about killing}. What is death? What happens to us when we die? Could there be an afterlife? Would it be a good thing if there were? What is it about death that we dislike so much, or that makes it bad? Is it rational, or even possible to fear death? What is the right attitude towards our own death? Do we have moral duties towards the dead? The course will clarify these questions and attempt to answer them. Readings will be taken from both historical and contemporary sources.

10 credits
Elementary Logic

The course will provide students with knowledge of the fundamental parts of formal logic. It will also teach them a range of associated formal techniques with which they can then analyse and assess arguments. In particular, they will learn the languages of propositional and first-order logic, and they will learn how to use those languages in providing formal representations of everyday claims. They will also learn how to use truth-tables and truth-trees.

10 credits
History of Ethics

How should we live? What is the right thing to do? This module offers a critical introduction to the history of western ethical thought, examining some of the key ideas of Plato, Aristotle, Hume, Kant, Wollstonecraft, Douglass, Bentham, Mill, Taylor Mill, Nietzsche, Rawls and Gilligan. It provides a textual introduction to some of the main types of ethical theory: the ethics of flourishing and virtue; rights-based approaches; utilitarianism; contractualism. We explore the close interconnections between ethics and other branches of philosophy (e.g. metaphysics, epistemology, aesthetics), as well as the connections between ethics and other disciplines (e.g. psychology; anthropology).

10 credits
Knowledge, Justification and Doubt

In our age of post-truth politics and fake news, this course aims to introduce students to philosophy by investigating some basic problems in epistemology (i.e. the philosophical study of knowledge). We will address questions such as: what knowledge is and why it is important; what truth is; what kinds of things can be known and how; if and how perceptual experience gives us knowledge of an external world; whether all knowledge has to be grounded in experience; whether knowledge is socially constructed (and if so whether that is necessarily problematic); what role justice plays in our epistemic practices.

10 credits
Philosophy of Religion

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

10 credits
Philosophy of Science

Science plays an important role in modern society. We trust science on a day to day basis as we navigate our worlds. What is about science that makes it so trustworthy? Why is science a good guide for understanding the world? The aim of this half-module is to introduce some of the philosophical issues that arise in science and through reflecting on science. Most of the questions considered concern the epistemology of scientific knowledge and methodology: what are scientific theories, what counts as evidence for these theories, what is the relationship between observation and theory, is there a scientific method, what distinguishes science from other ways of understanding the world, and how does the social structure of science help or hinder science in studying the world. This module aims to introduce these questions as philosophical issues in their own right and within in the context of the history of the philosophy of science.

10 credits
Philosophy of Sex

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

10 credits
Reason and Argument

Arguments are everywhere - in our newspapers, on our television screens and radios, in books and academic papers, on blogs and other websites. We argue with our friends, families, teachers and taxi drivers. These arguments are often important; they help us to decide what to do, what to believe, whom to vote for, what car to buy, what career path to follow, or where we should attend university (and what we should study). The ability to recognise, evaluate and produce arguments is therefore immeasurably valuable in every aspect of life. This course will teach you how to recognise an argument, how to understand it, how to evaluate and criticise it, and how to produce your own. Students in this module will learn how to extract an argument from a complex text, how to uncover hidden assumptions, and how to recognise and critique bad reasoning

10 credits

The content of our courses is reviewed annually to make sure it's up-to-date and relevant. Individual modules are occasionally updated or withdrawn. This is in response to discoveries through our world-leading research; funding changes; professional accreditation requirements; student or employer feedback; outcomes of reviews; and variations in staff or student numbers. In the event of any change we'll consult and inform students in good time and take reasonable steps to minimise disruption. We are no longer offering unrestricted module choice. If your course included unrestricted modules, your department will provide a list of modules from their own and other subject areas that you can choose from.

Learning and assessment

Learning

You'll learn through lectures, seminars, problems classes in small groups and research projects. Some modules also include programming classes.

We invest to create the right environment for you. That means outstanding facilities, study spaces and support, including 24/7 online access to our online library service.

Study spaces and computers are available to offer you choice and flexibility for your study. Our five library sites give you access to over 1.3 million books and periodicals. You can access your library account and our rich digital collections from anywhere on or off campus. Other library services include study skills training to improve your grades, and tailored advice from experts in your subject.

Learning support facilities and library opening hours

Programme specification

This tells you the aims and learning outcomes of this course and how these will be achieved and assessed.

Find programme specification for this course

Entry requirements

With Access Sheffield, you could qualify for additional consideration or an alternative offer - find out if you're eligible

Standard offer
Access Sheffield offer

The A Level entry requirements for this course are:
AAB
including A in Maths

The A Level entry requirements for this course are:
ABB
including A in Maths

A Levels + additional qualifications | ABB, including A in Maths + B in a relevant EPQ; ABB, including A in Maths + B in Further Maths ABB, including A in Maths + B in a relevant EPQ; ABB, including A in Maths + B in Further Maths

International Baccalaureate | 34, 6 in Higher Level Mathematics (Analysis and Approaches) 33 with 6 in Higher Level Mathematics

BTEC | DDD in a relevant subject with Distinctions in Maths units DDD in a relevant subject with Distinctions in Maths units

Scottish Highers + 1 Advanced Higher | AAABB + A in Maths AAABB + A in Maths

Welsh Baccalaureate + 2 A Levels | B + AA, including Maths B + AB, including A Maths

Access to HE Diploma | 60 credits overall in a relevant subject with Distinctions in 36 Level 3 credits, including Mathematics units, + Merits in 9 Level 3 credits 60 credits overall in a relevant subject with Distinctions in 30 Level 3 credits, including Mathematics units, + Merits in 15 Level 3 credits

Mature students - explore other routes for mature students

English language requirements

You must demonstrate that your English is good enough for you to successfully complete your course. For this course we require: GCSE English Language at grade 4/C; IELTS grade of 6.5 with a minimum of 6.0 in each component; or an alternative acceptable English language qualification

Equivalent English language qualifications

Visa and immigration requirements

Other requirements
  • We will give your application additional consideration if you have passed the Sixth Term Examination Paper (STEP) at grade 3 or above or the Test of Mathematics for University Admissions (TMUA) at grade 5 or above

We also accept a range of other UK qualifications and other EU/international qualifications.

If you have any questions about entry requirements, please contact the department.

School of Mathematics and Statistics

Students in a maths lecture

Staff in the School of Mathematics and Statistics work on a wide range of topics, from the most abstract research on topics like algebraic geometry and number theory, to the calculations behind animal movements and black holes. They’ll guide you through the key concepts and techniques that every mathematician needs to understand and give you a huge range of optional modules to choose from.

The department is based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces for our students. It’s right next door to the Students' Union, and just down the road from the 24/7 library facilities at the Information Commons and the Diamond.

School of Mathematics and Statistics

Department of Philosophy

We pride ourselves on the diversity of our modules and the high quality of our teaching. Our staff are among the best in the world at what they do. They're active researchers so your lectures and seminars are informed, relevant and exciting. We'll teach you how to think carefully, analytically and creatively.

Our staff and students use philosophy to engage with real world issues. You will be able to use what you learn to make a difference in the community, through projects like Philosophy in the City, an innovative and award-winning programme that enables students to teach philosophy in schools, homeless shelters and centres for the elderly.

Our students run a thriving Philosophy Society and the only UK undergraduate philosophy journal. Our Centre for Engaged Philosophy pursues research into questions of fundamental political and social importance, from criminal justice and social inclusion to climate ethics, all topics that are covered in our teaching.

Philosophy changes our perspective on the world, and equips and motivates us to make a difference.

The Department of Philosophy is based at 45 Victoria Street at the heart of the University campus. We're close to the Diamond and the Information Commons, as well as Jessop West, which houses our fellow Arts & Humanities departments of History, English and Languages & Cultures.

Department of Philosophy

Why choose Sheffield?

The University of Sheffield

  A Top 100 university 2021
QS World University Rankings

  Top 10% of all UK universities
Research Excellence Framework 2014

  No 1 Students' Union in the UK
Whatuni Student Choice Awards 2019, 2018, 2017


School of Mathematics and Statistics

3rd in the Russell Group for overall satisfaction

National Student Survey 2019


Department of Philosophy

96% overall student satisfaction

National Student Survey 2019

3rd in the Russell Group for student satisfaction

National Student Survey 2019


Graduate careers

School of Mathematics and Statistics

There will always be a place for maths graduates in banking, insurance, pensions, and financial districts from the City of London to Wall Street. Big engineering companies still need people who can crunch the numbers to keep planes in the sky and trains running on time too. But the 21st century has also created new career paths for our students.

Smartphones, tablets, social networks and streaming services all use software and algorithms that need mathematical brains behind them. In the age of ‘big data’, everyone from rideshare apps to high street shops is gathering information that maths graduates can organise, analyse and interpret. The same technological advances have created new challenges and opportunities in cybersecurity and cryptography.

If the maths itself is what interests you, a PhD can lead to a career in research. Mathematicians working in universities and research institutes are trying to find rigorous proofs for conjectures that have challenged pure mathematicians for decades, or are doing the calculations behind major experiments, like the ones running on the Large Hadron Collider at CERN.

What if I want to work outside mathematics?

A good class of degree from a top university can take you far, whatever you want to do. We have graduates using their mathematical training in everything from teaching and management to advertising and publishing.

Department of Philosophy

Studying philosophy will develop your ability to analyse and state a case clearly, evaluate arguments and be precise in your thinking. These skills will put you in a strong position when it comes to finding employment or going on to further study.

Our graduates work in teaching, law, social work, computing, the civil service, journalism, paid charity work, business, insurance and accountancy. Many also go on to study philosophy at postgraduate level.

Sonia Nayyar in her graduation gown holding her degree certificate

"My degree in maths has given me an excellent grounding in mathematical concepts which I am able to use in my everyday work"

Sonia Nayyar Mathematics BSc

After graduating from Sheffield with a BSc in Mathematics, Sonia went on to work for a financial, actuarial and business consultancy, putting the analytic and logical thinking skills she learned during her degree to daily use.

Matt sat at a desk in an office with lots of plants in the background

"I use skills from Maths in my job every single day"

Matthew Jenkins BSc Mathematics

After graduating, Matthew used the University Careers Service to help him find a job, and he now develops software in the marine navigation industry.

A profile image of Rachael Batteson smiling in front of a yellow background

"I analyse the cost-effectiveness of new drugs, to see if they are viable to be accepted within the NHS, or other countries' health care systems"

Rachael Batteson BSc Mathematics

Rachael works in health economics, using the analysis and problem solving skills she got from her maths degree to assess the viability of new drugs.

Fees and funding

Fees

Additional costs

The annual fee for your course includes a number of items in addition to your tuition. If an item or activity is classed as a compulsory element for your course, it will normally be included in your tuition fee. There are also other costs which you may need to consider.

Examples of what’s included and excluded

Funding your study

Depending on your circumstances, you may qualify for a bursary, scholarship or loan to help fund your study and enhance your learning experience.

Use our Student Funding Calculator to work out what you’re eligible for.

Visit us

University open days

There are four open days every year, usually in June, July, September and October. You can talk to staff and students, tour the campus and see inside the accommodation.

Open days: book your place

Taster days

At various times in the year we run online taster sessions to help Year 12 students experience what it is like to study at the University of Sheffield.

Upcoming taster sessions

Applicant days

If you've received an offer to study with us, we'll invite you to one of our applicant open days, which take place between November and April. These open days have a strong department focus and give you the chance to really explore student life here, even if you've visited us before.

Campus tours

Campus tours run regularly throughout the year, at 1pm every Monday, Wednesday and Friday.

Book your place on a campus tour

Apply for this course

Make sure you've done everything you need to do before you apply.

How to apply When you're ready to apply, see the UCAS website:
www.ucas.com

The awarding body for this course is the University of Sheffield.

Recognition of professional qualifications: from 1 January 2021, in order to have any UK professional qualifications recognised for work in an EU country across a number of regulated and other professions you need to apply to the host country for recognition. Read information from the UK government and the EU Regulated Professions Database.

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Explore this course:

    2021-2022