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BScMathematics with Philosophy

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Overview

This three-year programme combines two of the most fundamental and intellectually stimulating forms of human enquiry. The idea of using mathematics to describe the universe was first introduced by the philosophers of ancient Greece but it is as relevant as ever today. Questions such as “What is a number?” or “Is mathematics discovered or invented?” are deeply philosophical. 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 transferrable in the world of work. Our curriculum covers pure and applied mathematics, statistics and probability, 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. We also have a vibrant Philosophy Society. We take a uniquely collaborative and interdisciplinary approach to the subject, by looking beyond the confines of the analytic or European tradition to disciplines across the art, humanities and social sciences. You will learn from seasoned philosophers who are published authorities in their field.

Your mathematical studies will make up 75% of your overall degree, while philosophy will contribute the remaining 25%.

Programme structure

Year 1

Mathematics: Calculus
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.

Mathematics: Functions of Several Variables
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.

Mathematics: Number Systems
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 comon 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.

Mathematics: Matrix Algebra
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.

Mathematics: Numbers and Functions
In this module you will develop an understanding of key mathematical concepts such as the construction of real numbers, limits and convergence of sequences, and continuity of functions. You will look at the infinite processes that are essential for the development of areas such as calculus, determining whether a given sequence tends to a limit, and finding the limits of sequences defined recursively.

Epistemology and Metaphysics
In this module you will develop an understanding of some of the key problems that have preoccupied contemporary philosophers. You will look at logical questions relating to the structure of arguments, epistemological questions about the sources and limits of knowledge, and consider metaphysical questions that explore the relationship between minds, bodies, and the possibilities of human freedoms.

Introduction to Logic
In this module you will develop an understanding of the formal study of arguments through the two basic systems of modern logic – sentential or propositional logic and predicate logic. You will learn how to present and analyse arguments formally, and look at the implications and uses of logical analysis by considering Bertrand Russell’s formalist solution to the problem of definite descriptions. You will also examine the the broader significance of findings in logic to philosophical inquiry.

Mind and Consciousness
In this module you will develop an understanding of the relationship between the mind and the brain. You will examine the key theories, from Descartes’ dualist conception of the relationship between mind and body through to Chalmers’s conception of consciousness as ‘the hard problem’ in the philosophy of mind. You will also consider some of the famous thought experiments in this area, including Descartes’s and Laplace’s demons, the Chinese Room and the China Brain, Mary and the black-and-white room, and the problem of zombie and bat consciousness.

Introduction to Aesthetics and Morals
In this module you will develop an understanding of the central problems and debates within moral philosophy and aesthetics. You will look at questions relating to both metaphysical and ethical relativism, including the ways we view our moral commitments within the world, how the individual is related to society, and the value and nature of the work of art. You will also examine approaches from the history of philosophy, including the Anglo-American tradition and recent European philosophy.

Year 2

Mathematics: Linear Alegbra and Project
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. Working in small groups, you will put together different aspects of mathematics in a project on a topic of your choosing, disseminating your findings in writing and giving an oral presentation to your peers.

Mathematics: Complex Variable
In this module you will develop an understanding of the basic complex variable theory. You will look at the definitions of continuity and differentiability of a complex valued function at a point, and how Cauchy-Riemann equations can be applied. You will examine how to use a power series to define the complex expontential function, and how to obtain Taylor series of rational and other functions of standard type, determining zeros and poles of given functions. You will also consider how to use Cauchy’s Residue Theorem to evaulate real integrals.

Introduction to European Philosophy 1 – From Kant to Hegel
In this module you will develop an understanding of the major debates in European and some Anglo-American philosophy. You will look at the key texts by eighteenth and nineteenth century philosophers Immanuel Kant and Georg Wilhelm Friedrich Hegel, examining the continuing significance of their ideas. You will consider the major espistemological, ethical and aesthetical issues their idea raise, and the the problems associated with the notion of modernity. You will also analyse the importance of the role of history in modern philosophy via Hegel’s influence.

Mind and World

Year 3

All modules are optional

Optional modules

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

Career opportunities

Our joint programme will equip you with a wide range of transferrable 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, which puts us in the top ten for graduate career prospects, nationally (Complete University Guide 2015). For instance, 90% of our mathematics graduates are in work or further study within six months of leaving us (Unistats 2015).

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. The University of London Careers Advisory Service offers regular, tailored sessions on finding summer internships or holiday jobs and securing employment after graduation.

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States