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Mathematics and Philosophy

Mathematics and Philosophy

BSc
  • UCAS code GV15
  • Option 3 years full time
  • Year of entry 2021

This programme is currently under development and may be subject to change

The course

This three-year course combines two of the most fundamental and intellectually stimulating forms of human enquiry. It is perfect for those students wishing to benefit from gaining advanced skills in mathematics alongside critical thinking skills, with the flexibility and freedom to choose philosophical subjects of interest to them, from contemporary analytic philosophy to ancient Stoic thought.

By studying both subjects you will not only master the skills of handling complex data and finding creative solutions to problems, but you will also be introduced to the beautiful world of abstract ideas, and encouraged to analyse challenging issues, question your assumptions and communicate your thoughts with clarity. You will gain a unique insight into the world of logic that bridges the two disciplines and you will open doors to a diverse range of career opportunities.

Our modular structure gives you the flexibility to tailor your studies to your own interests, and we offer a friendly and motivating learning environment, with a strong focus on small group teaching. Mathematics is one of the oldest academic disciplines and yet it sits at the heart of modern science and technology. Led by experts in the field, our core modules will give you a grounding in the key methods and concepts that underpin the subject, as well as practical skills that are widely transferable in the world of work. Our curriculum covers pure and applied mathematics, practical quantitative and statistical skills, the mathematics of information, financial markets, and more.

You'll also learn about the fundamentals of ancient and modern philosophy, the philosophy of politics, and the art of argument and persuasion. We address some of the most important political, cultural and ethical issues in the world today and tackle fundamental questions about knowledge, reasoning, our views on the universe and the impacts they have on our lives. As well as training in core philosophical areas: epistemology, metaphysics, ethics, political philosophy, and the history of philosophy, you will benefit from a diverse range of modules on gender, the environment, mental health and quantum difference. We also have a vibrant Philosophy Society.

Your mathematical studies will make up 50% of your overall degree, and philosophy will contribute the remaining 50%.

Our flexible degree courses enable you to apply to take a Placement Year, which can be spent studying abroad, working or carrying out voluntary work. You can even do all three if you want to (minimum of three months each)! To recognise the importance of this additional skills development and university experience, your Placement Year will be formally recognised on your degree certificate and will contribute to your overall result. Please note conditions may apply if your degree already includes an integrated year out, please contact the Careers & Employability Service for more information. Find out more

  • Study two of the world’s oldest and most widely applicable academic subjects.
  • Learn from renowned mathematicians and inspirational philosophy teachers, with the flexibility to tailor your studies to your own interests.
  • Benefit from our strong focus on small group teaching.
  • Balance detailed knowledge of cutting-edge mathematical practices with gaining philosophical skills and expertise

Core Modules

Year 1

You will take the following modules in Mathematics:

  • In this module, you will develop an understanding of the key concepts in Calculus, including differentiation and integration. You will learn how to factorise polynomials and separate rational functions into partial fractions, differentiate commonly occurring functions, and find definite and indefinite integrals of a variety of functions using substitution or integration by parts. You will also examine how to recognise the standard forms of first-order differential equations, and reduce other equations to these forms and solve them.

  • In this module you will develop an understanding of the calculus functions of more than one variable and how it may be used in areas such as geometry and optimisation. You learn how to manipulate partial derivatives, construct and manipulate line integrals, represent curves and surfaces in higher dimensions, calculate areas under a curve and volumes between surfaces, and evaluate double integrals, including the use of change of order of integration and change of coordinates.

  • In this module you will develop an understanding of the fundamental algebraic structures, including familiar integers and polynomial rings. You will learn how to apply Euclid's algorithm to find the greatest common divisor of two integers, and use mathematical induction to prove simple results. You will examine the use of arithmetic operations on complex numbers, extract roots of complex numbers, prove De Morgan's laws, and determine whether a given mapping is bijective.

  • In this module you will develop an understanding of basic linear algebra, in particular the use of matrices and vectors. You will look at the basic theoretical and computational techniques of matrix theory, examining the power of vector methods and how they may be used to describe three-dimensional space. You will consider the notions of field, vector space and subspace, and learn how to calculate the determinant of an n x n matrix.

You will take the following modules in Philosophy:

  • Introduction to Modern Philosophy
  • Knowledge is often thought to be the highest achievement of rational creatures, the thing that distinguishes us from other animals and is the basis of our ability to predict and control our environment. Beginning with the most Platonic of questions—‘what is knowledge?’—this course introduces you to basic topics in contemporary epistemology. Among the questions it goes on to address are: why is knowledge valuable?; how do we acquire knowledge and how do we pass it on to others?; how do we become better knowers?; is there such a thing as collective knowledge?; do animals have knowledge?; is there such a thing as knowledge at all?

     

  • In every aspect of our lives we are inundated by information and misinformation, claims and counter-claims: some people tell us we should believe this; others that we should believe that. Decisions have to be made; possible evidence has to be sifted; reasons have to be given; arguments have to be propounded; risks evaluated. All this requires the ability to reason critically: to distinguish between bad arguments and good ones, supporting evidence from mere distraction. Everybody has the basic ability to do this, but it is not always as developed we need it to be: and in this complex world being able to present your point forcefully and rationally is vitally important. The aim of this module is to help you develop the skills required to get the most out of their degree and beyond. 

  • In this module you will develop an understanding of ancient philosophical ideas and the ways in which philosophical arguments are presented and analysed. You will look at the thought and significance of the principal ancient philosophers, from the Presocratics to Aristotle, and examine sample texts such as Plato's 'Laches' and the treatment of the virtue of courage in Aristotle, 'Nicomachean Ethics' 3.6-9.

Year 2

You will take the following modules in Mathematics:

  • In this module you will develop an understanding of the concepts of scalar and vector fields. You examine how vector calculus is used to define general coordinate systems and in differential geometry. You will learn how to solve simple partial differential equations by separating variables, and become familiar with how these concepts can be appield in the field of dynamics of inviscid fluids.

  • In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to forumulate an explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.

  • In this module you will develop an understanding of vectors and matrices within the context of vector spaces, with a focus on deriving and using various decompositions of matrices, including eigenvalue decompositions and the so-called normal forms. You will learn how these abstract notions can be used to solve problems encountered in other fields of science and mathematics, such as optimisation theory.

You will choose one of the following:

  • The module looks at key texts by Immanuel Kant which are the foundation of Modern European Philosophy. These texts raise questions concerning the status of human knowledge and the nature and justification of human action that have concerned philosophers ever since. The module considers Kant's Critique of Pure Reason. The core theme of the module is how philosophy responds to the situation in which it can no longer rely on theological support for its claims about truth and morality. This raises questions about the nature of the human subject that are evident in the conjunction of the massive success of the modern natural sciences with an abiding worry as to whether sceptical objections to establishing true knowledge can be overcome. Kant sees these issues in terms of 'transcendental philosophy' establishing the limits of knowledge by seeing what the necessary conditions of knowledge are.

     

  • This module will explore the central developments in modern philosophy occurring between the foundation of modern empiricism and rationalism by Locke and Descartes in the 17th century, and the emergence of Kant’s philosophical system in the late 18th century. The module will look at three of the key figures from the two traditions, exploring the key theories they expound, and the arguments used to support these theories. The figures covered will depend on the research specialisms of the module convenor, but a typical syllabus would involve reading works by Spinoza, Leibniz, and Hume. Looking at these philosophers over a number of weeks will allow you to develop your close reading skills, and to see how the arguments put forward by these philosophers work together to produce a systematic metaphysical worldview.

You will take the following module in Philosophy:

  • In this module you will develop an understanding of how the rationalist and empiricist traditions in philosophy influence contemporary thought in the philosophy of mind. You will look at the continuing relevance of the mind-body problem to the question of what it is to be a human being and consider the connections between the analytic and European traditions in philosophy with respect to language, subjectivity, and the phenomenology of experience. You will also examine the importance of consciousness to contemporary debates in philosophy, psychology and cognitive science.

Year 3
  • All modules are optional

Optional Modules

There are a number of optional course modules available during your degree studies. The following is a selection of optional course modules that are likely to be available. Please note that although the College will keep changes to a minimum, new modules may be offered or existing modules may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.

Year 1
  • All modules are core
Year 2
  • In this module you will develop an understanding of the concepts of scalar and vector fields. You examine how vector calculus is used to define general coordinate systems and in differential geometry. You will learn how to solve simple partial differential equations by separating variables, and become familiar with how these concepts can be appield in the field of dynamics of inviscid fluids.

  • In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to forumulate an explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.

  • There has been a sharp revival of interest in fundamental questions relating to knowledge in recent years. These include the status of testimonial knowledge; the extent to which possession of knowledge requires one or more virtues; the suggestion that knowledge can be a group rather than an individual achievement; the idea that it is unjust to place people in positions where they cannot acquire knowledge that might empower them; the relationship between knowing how to do something and that something is the case; the role of bias, discrimination and presupposition. Building on the first year module on epistemology, this module focusses on one or more of these and investigates them in depth.

  • This module will introduce ancient Greek ethics, primarily focusing on the ideas of Socrates (as presented in Plato’s early dialogues) and Aristotle. The first part will look at key themes in Socratic-Platonic ethics, examining material from a range of Platonic dialogues, including (but not limited to) the Protagoras, Gorgias, and Euthydemus. It will consider topics such as virtue, knowledge, ignorance, and weakness of will. The second part will focus on Aristotle’s ethics, as presented in his Nicomachean Ethics, and will look at topics such as happiness, character, virtue, pleasure, and the ideal life. Subsequent developments in ancient Greek ethics (i.e. Epicureanism, Stoicism) will be covered in the companion module ‘PY2218/PY3218 Hellenistic Philosophy’, although each module is designed to stand without the other. Where relevant, aspects of ancient ethics from other traditions (Indian, Chinese) may also be incorporated in order to broaden and diversify the curriculum. Although focused on historical texts, the module will be primarily concerned with the philosophical problems that they raise.

  • In this module you will develop an understanding of the key developments of the Twentieth Century French philosophical tradition. You will look at how the French tradition developed as an alternative approach to philosophical problems on the basis of the perceived failure of classical analytical approaches. You will engage with a number of theorists, studying key texts in depth, further developing your ability to express, question, and justify theories, both dialogically, and in writing. You will assess arguments presented by Jacques Derrida, Jean-Francois Lyotard and Gilles Deleuze.

  • We will draw on issues in philosophy of science and ethics to understand and attempt to solve conceptual problems arising in medicine and the biomedical sciences. Among other things, we will consider what a disease is, whether we own our bodies (and body parts), what is involved in informed consent, and what is properly involved in decision-making in medicine.

  • This module will examine a range of key thinkers and themes in medieval philosophy, from the fourth to the fourteenth century, telling the story of the development and transmission of philosophical ideas along the way. It will begin in late antiquity, showing the ways in which medieval thought was built on the ancient Greek philosophical tradition. It will outline the transmission of Greek thought to the Arabic-speaking world, examine a number of Arabic philosophers, and consider the impact of Arabic thought on medieval philosophy in Paris. It will conclude with Duns Scotus, active in fourteenth century Paris and Oxford. Topics discussed will focus on problems in metaphysics, such as the nature of existence, universals, the mind, and time. The relationship between philosophy and theology (or reason and faith) will be a continuing theme. The primarily metaphysical content will make this module a companion to ‘PY2217/PY3217 Ancient Metaphysics’, although each module is designed to stand without the other. It will examine (in translation) texts originally written in Greek, Arabic, and Latin.

Year 3
  • In this module you will develop an understanding of quantum theory, and the development of the field to explain the behaviour of particles at the atomic level. You will look at the mathematical foundations of the theory, including the Schrodinger equation. You will examine how the theory is applied to one and three dimensional systems, including the hydrogen atom, and see how a probabilistic theory is required to interpret what is measured.

  • You will carry out a detailed investigation on a topic of your choosing, guided by an academic supervisor. You will prepare a written report around 7,000 words in length, and give a ten-minute presentation outlining your findings.

  • In this module you will develop an understanding of how prime numbers are the building blocks of the integers 0, ±1, ±2, … You will look at how simple equations using integers can be solved, and examine whether a number like 2017 should be written as a sum of two integer squares. You will also see how Number Theory can be used in other areas such as Cryptography, Computer Science and Field Theory.

  • This module will focus on the metaphysics of Plato and Aristotle, concentrating on Plato’s theory of Ideas and Aristotle’s response to it. The first part will look at Plato’s theory of Ideas as developed in his middle period dialogues and his own criticisms of it in his later works, drawing on dialogues such as the Republic, Sophist, and Parmenides. The second part will look at Aristotle’s criticisms of Plato and his own theory of hylomorphism, developed in response (in the Metaphysics, Physics, and elsewhere). Central philosophical themes will include the ontological status of ideas, the role of universals, causation, the nature of matter, and problems relating to knowledge. The metaphysics of Plato and Aristotle are foundational for the subsequent history of philosophy, some of which will be explored in the companion module ‘PY2219/PY3219 Medieval Philosophy’, although each module is designed to stand without the other. Although focused on historical texts, the module will be primarily concerned with the philosophical problems that they raise. 

  • Philosophy and Literature
  • The aim of this module is to consider the main directions of eighteenth-century and post-Kantian aesthetics, in particular the issues that have arisen about what it means to consider objects—whether art or nature—aesthetically, and an analysis of concepts bound up with this “aesthetic attitude”, such as disinterestedness, beauty and the sublime. Each week will focus on one issue surrounding the question of taste, of judgements of beauty and the sublime and of the aesthetic experience, from Hume, through Kant, to the present day. Particularly attention will be paid to non-artistic aesthetic experiences, such as those of the natural world, and, as much as feasible, attention will also be paid to art and aesthetics produced outside the modern European tradition, such as aesthetics in the Islamic world. 

  • The module will provide the opportunity for you to apply theoretical skills developed in relation to philosophy of art and aesthetics to practical problems in some of the following domains: curating, gallery education, artistic practice, art criticism and the management of cultural institutions. After an initial five weeks of theoretical discussions around historical and contemporary art, you will work closely with the curators of Royal Holloway's art collection to gain familiarity with and apply knowledge and skills to the exhibition of and reflection on situated artworks.

  • German idealism sets itself the task of satisfying three main aims: systematizing Kant’s philosophy by finding necessary premises for its conclusions; providing a rigorous demonstration of the laws of thought; and ensuring that satisfying these aims satisfies the third aim of proving that reason is not the product of a purposeless, mechanistic world, but is itself an absolutely free purposive activity. This module investigates Hegel’s Phenomenology of Spirit as an attempt to satisfy these aims. We will explore Hegel’s distinctive and influential criticisms of Kant, his development of dialectic as a method of deriving the laws of thought, and his argument that reason is absolutely free. We will pay special attention to his successive, unfolding theses for the essentially self-conscious character of consciousness, the essentially recognitive character of self-consciousness, and the essentially historical character of recognition.

  • You will demonstrate your skills as an independent learner by embarking upon a substantial piece of written work of between 8,000 and 10,000 words in length. You will be guided by a dissertation supervisor, but will choose your own topic, approach, and philosophical sources.

You will be assigned a Personal tutor in Mathematics and designated staff liaison in Philosophy.

We use a variety of teaching methods and there is a strong focus on small group teaching. Our mathematics courses are delivered through lectures, seminars, group tutorials, statistics and IT classes, and problem solving workshops. You will also be expected to work on worksheets, revision and project work in your own time. In year 2, much of our mathematics teaching is delivered through lectures, workshops and practical classes, and in year 3, mostly through relatively small group lectures and supervised project work. Philosophy is taught through a combination of lectures, large and small seminars and occasionally through one-to-one tutorials. Outside of class time you will work on group projects and wide-ranging but guided independent study. You will be supported in both subjects by the extensive resources available on Moodle, our e-learning facility. Your degree course will comprise 50% modules in Mathematics and 50% modules in Philosophy

Assessment is through a mixture of coursework and end-of-year examinations, depending on the modules you choose to take. 

A Levels: AAB-ABB

Required subjects:

  • A-level in Mathematics at grade A
  • At least five GCSEs at grade A*-C or 9-4 including English and Mathematics.

Where an applicant is taking the EPQ alongside A - levels, the EPQ will be taken into consideration and result in lower A-level grades being required. Socio - economic factors which may have impacted an applicant's education will be taken into consideration and alternative offers may be made to these applicants.

English language requirements

All teaching at Royal Holloway (apart from some language courses) is in English. You will therefore need to have good enough written and spoken English to cope with your studies right from the start.

The scores we require
  • IELTS: 6.0 overall. No subscore lower than 5.5.
  • Pearson Test of English: 61 overall. No subscore lower than 51.
  • Trinity College London Integrated Skills in English (ISE): ISE III.
  • Cambridge English: Advanced (CAE) grade C.

Country-specific requirements

For more information about country-specific entry requirements for your country please visit here.

For international students who do not meet the direct entry requirements, we offer an International Foundation Year, run by Study Group at the Royal Holloway International Study Centre. Upon successful completion, you may progress on to selected undergraduate degree programmes at Royal Holloway, University of London.

Our joint course will equip you with a wide range of transferable skills, including advanced numeracy, data handling and analysis, critical thinking, logical reasoning, creative problem solving, time management and self-discipline. You will also be able to present complex ideas and arguments clearly and coherently and to carry out independent research. We have a strong record of success in helping students progress into work and further study,

Our recent graduates have gone on to enjoy successful careers in a diversity of fields, from teaching, the civil service and the arts, to management and consultancy, computing, law, academic research, accountancy, finance, risk analysis, engineering and the intelligence services. We also offer a wide range of exciting postgraduate opportunities in both mathematics and philosophy. Depending on your choice of courses, you could also be eligible for certain membership exemptions from professional bodies such as the Institute of Actuaries.

We offer a competitive work experience scheme at the end of year 2, with short-term placements available during the summer holidays. You will also attend a CV writing workshop in year 2, and your personal adviser and the campus Careers team will be on hand to offer advice and guidance on your chosen career. Royal Holloway's Careers and Employability Service offers regular, tailored sessions on finding summer internships or holiday jobs and securing employment after graduation.

  • With an advanced understanding of mathematics and philosophy, you will have a wealth of opportunities in the world of work.
  • Take advantage of our summer work placement scheme and fine-tune your CV before you enter your final year.
  • Benefit from a personal adviser who will guide you through your many options.

Home (UK) students tuition fee per year*: £9,250

EU and International students tuition fee per year**: £21,400

Other essential costs***: There are no single associated costs greater than £50 per item on this course.

How do I pay for it? Find out more about funding options, including loansscholarships and bursaries. UK students who have already taken out a tuition fee loan for undergraduate study should check their eligibility for additional funding directly with the relevant awards body.

*The tuition fee for UK undergraduates is controlled by Government regulations. For students starting a degree in the academic year 2020/21, the fee will be £9,250 for that year. The fee for UK undergraduates starting in 2021/22 has not yet been confirmed.

**The Government has confirmed that EU nationals starting a degree in 2020/21 will pay the same fee as UK students for the duration of their course. For EU nationals starting a degree in 2021/22, the UK Government has recently confirmed that you will not be eligible to pay the same fees as UK students, nor be eligible for funding from the Student Loans Company. This means you will be classified as an international student. At Royal Holloway, we wish to support those students affected by this change in status through this transition. For eligible EU students starting their course with us in September 2021, we will award an automatic fee reduction which brings your fee into line with the fee paid by UK students. This will apply for the duration of your course.

Fees for international students may increase year-on-year in line with the rate of inflation. The policy at Royal Holloway is that any increases in fees will not exceed 5% for continuing students. For further information see fees and funding and our terms and conditions. Fees shown above are for 2020/21 and are displayed for indicative purposes only.

***These estimated costs relate to studying this particular degree programme at Royal Holloway. Costs, such as accommodation, food, books and other learning materials and printing etc., have not been included.

Accreditation

Institute of Mathematics and its Applications

This course is accredited by the Institute of Mathematics and its Applications (IMA). On successful completion of the programme, you will to meet, in part, the educational requirements for Chartered Mathematician status.

96% Percentage of our graduates in work or undertaking further study within six months of leaving.

Source: DLHE, 2017

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