Study location	United Kingdom, Egham, Surrey
Type	Bachelor courses, full-time
Nominal duration	3 years
Study language	English
Awards	BA
Course code	GW13

Entry qualification

High school / secondary education (or higher) Required subjects: A in Mathematics and A in Music, if not taken at A-level Grade 8 Music Theory at Pass is accepted At least five GCSEs at grade A*-C or 9-4 including English and Mathematics The entry qualification documents are accepted in the following languages: English. Often you can get a suitable transcript from your school. If this is not the case, you will need official translations along with verified copies of the original.

Language requirements	English IELTS: 6.5 overall (with 7 in writing and a minimum of 5.5 in all other subscore) CAE: 176 overall (with no less than 185 in writing and a minimum of 162 in all other subscore)

Other requirements	At least 1 reference(s) must be provided. A motivation letter must be added to your application.

More information	royalholloway.ac.uk/..atics-and-music.aspx

Overview

Interested? To learn more about this study programme, entry requirements and application process, please contact one of our consultants in a country nearest to you.

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.

Year 2

Mathematics: Graphs and Optimisation
In this module you will develop an understanding of the basic concepts of graph theory and linear programming. You will consider how railroad networks, electrical networks, social networks, and the web can be modelled by graphs, and look at basic examples of graph classes such as paths, cycles and trees. You will examine the flows in networks and how these are related to linear programming, solving problems using the simplex algorithm and the strong duality theorem.

Mathematics: Linear Algebra and Group 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.

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

With a joint Mathematics and Music degree from Royal Holloway, University of London you will be in demand for your wide range of transferrable skills, including: numerical skills, data handling powers, logical thinking and creative problem solving abilities, as well as communication, teamwork, technical, time management, commercial awareness and critical thinking and analysis skills. We have a strong track record of preparing our students for the world of work and research. By combining mathematics with music you will also keep your career options open, with the opportunity to pursue your musical talents in performance, composition, production or musicology after you graduate.

Our recent graduates have gone on to enjoy successful careers in: business management, IT consultancy, computer analysis and programming, teaching, accountancy, law, the civil service, actuarial science, finance, risk analysis, research and engineering, as well as in composition, music technology, publishing and the performing arts. They are working for employers as diverse as: KPMG, Ernst & Young, the Ministry of Defence, Barclays Bank, English National Opera, Surrey County Arts Service, EMI and Slaughter & May. Others go on to establish themselves as successful independent musicians and/or teachers. Our Department of Mathematics is part of the School of Mathematics and Information Security and we enjoy close ties with both the information security sector and industry at large.

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 as part of your core modules in year 2, and your personal adviser and the campus Careers team will be on hand to offer career advice and guidance. The University of London Careers Advisory Service offers tailored sessions on finding relevant summer internships or holiday jobs and securing employment after graduation.