Mathematics and Music

“There is geometry in the humming of the strings. There is music in the spacing of the spheres.” – Pythagoras

Looking to keep your love of music alive whilst exploring the true breadth of mathematical ideas and methods? Since Pythagoras developed his theory of the unity of arithmetic, geometry and music around the fundamental laws of proportion and harmony, in the 6th century BC, the two disciplines have influenced and informed each other. They are both concerned with the creation, appreciation and analysis of abstract patterns and logical ideas. Our joint honours degree allows you to keep your career options open and pursue your mathematical and musical interests in a 50/50 split, under the guidance of inspiring teachers from both departments.

Throughout your course, you will have the flexibility to tailor your studies to your own particular interests. Alongside our core Mathematics modules in year 1, which will give you a thorough grounding in all the key methods and concepts that underpin the subject, we offer a wide range of practical and academic modules from one of UK's top music departments (Complete University Guide 2015). In years 2 and 3 this flexibility increases, allowing you to specialise in the areas of mathematics and music that interest you the most. You will develop your musicianship and mathematical skills to an advanced level, and gain a host of transferable skills such as data handling and analysis, logical thinking, communication, creativity and problem-solving.

Our Department of Mathematics is internationally renowned for its work in pure mathematics, information security, statistics and theoretical physics, and our joint BA programme spans pure and applied mathematics, statistics and probability. It also offers you to chance to carry out project work on chosen topics. Meanwhile, in the Department of Music, you will be able to pursue performance and composition whilst exploring the broader historical, sociological, ethnographic and philosophical elements of music. For keen singers and instrumentalists, we offer a wide range of exciting and diverse performance opportunities and you will have access to our well-equipped studios, practice rooms and recording facilities.

We offer a friendly and motivating learning environment and a strong focus on small group teaching and academic support. You will take part in group tutorials, problem-solving sessions, practical workshops and IT classes, as well as practical music lessons and lectures. You will also benefit from generous staff office hours and a dedicated personal adviser to guide you through your studies, plus a CV writing workshop and competitive work placement scheme.

Combine your love of mathematics and music and benefit from a varied and flexible, modular curriculum.

We are a friendly department with a strong focus on small group teaching.

Course Modules

Core Modules

Year 1

• Calculus

• Calculus II

• Introduction to Pure Mathematics

• Linear Algebra I

• Theory and Analysis

• Fundamentals of Music Theory

• Creative Composition Techniques

• A Very Short History of Music

• Introduction to Historical Musicology

• Introduction to World Music

• Contemporary Debates in Music

• Solo Performance

• Creative Ensemble Performance

• Introduction to Composing with Music Technology

Year 2

• Probability Theory

• Graphs and Optimisation

• Linear Algebra II

• Studies in Music Analysis

• Studies in Composition

• Studies in Music History

• Studies in Ethnomusicology

• Studies in Music, Media and Technology

• Practical Performance I

Year 3

• Special Study: Dissertation

• Special Study: Theory and Analysis

• Special Study: Solo Performance

• Special Study: Composition

Optional Modules

Below is a taster of some of the exciting optional modules that students on the course could choose from during this academic year. Please be aware these do change over time, and optional modules may be withdrawn or new ones added.

Year 1

• All modules are core

Year 2

• Vector Calculus

• Statistical Methods 2

• Probability Theory

• Ordinary Differential Equations and Fourier Analysis

• Ring Theory

• Group Theory

• Further Linear Algebra and Modules

• Complex Analysis

• Solo Performance

• Ensemble Performance

• Composition Portfolio

• Practical and Creative Orchestration

• Practical Conducting (Choral and Orchestral)

• Composing with Technology 1

• Introduction to Jazz: Theory, Practice and Contexts

• Popular Music and Musicians in Post-War Britain and North America

• Korean Percussion Performance

• Musical Aesthetics

• Mozart's Operas

• Issues in Sound, Music and the Moving Image

• Music and Society in Purcell's London

• Contemporary Music Performance

• Music, Power and Politics

• Ideas of German Music from Mozart to Henze

• Music and Gender

Year 3

• Mathematics Project

• Mathematics in the Classroom

• Number Theory

• Computational Number Theory

• Complexity Theory

• Principles of Algorithm Design

• Quantum Theory 1

• Quantum Theory 2

• Dynamics of Real Fluids

• Non-Linear Dynamic Systems

• Inference

• Time Series Analysis

• Channels

• Quantum Information and Coding

• Mathematics of Financial Markets

• Financial Mathematics II

• Combinatorics

• Error Correcting Codes

• Cipher Systems

• Cryptography

• Applications of Field Theory

• Group Theory

• Further Linear Algebra and Modules

• Topology

• Musical Aesthetics

• Mozart's Operas

• Issues in Sound, Music and the Moving Image

• Music and Society in Purcell's London

• Contemporary Music Performance

• Music, Power and Politics

• Ideas of German Music from Mozart to Henze

• Music and Gender

• Practical Performance 2

• Composing with Technology 2

• Group Theory

• Markov Chains and Applications

• Introduction to Optimisation

• Game Theory

https://www.royalholloway.ac.uk/studying-here/undergraduate/mathematics/mathematics-and-music/

The course has a flexible, modular structure and reflects the division of interest of a Joint Honours programme. In addition to our compulsory core modules you will be free to choose between a number of optional modules. 

In year one the mandatory modules in the Department of Mathematics seek to provide a broadly based introduction to mathematics, which will develop manipulative skills, understanding of the key concepts and the ability to construct logical arguments. In year two, you will take modules which continue your study of abstract pure mathematics and its applications. In year three, you take modules from a range of options and are advised on appropriate combinations and pathways depending on your interests, optional modules you've taken in year two, and possible future career paths. You may choose to undertake an extended project and select from a range of optional Music modules to the value of 60 credits in years two and three.

We use a variety of teaching methods and there is a strong focus on small group teaching throughout the course. You will attend 12 to 15 hours of formal teaching in a typical week, including lectures, seminars, group tutorials, statistics and IT classes, problem-solving workshops in mathematics, and instrumental, vocal and compositional classes in music. You will also be expected to work on mathematical worksheets, musical practice and composition, revision and project work outside of these times.

Assessment is through a mixture of coursework, end-of-year examination and a portfolio of practical work, in varying proportions depending on the course units you choose to take. Statistics and computational course units may include project work and tests, and music modules may include performance or coursework components. All students will work in small groups to prepare a report and an oral presentation on a mathematical topic of their choice, which contributes towards one of the core subject marks in year 2, and two of the optional mathematics units in year 3 are examined solely by a project and presentation.

Private study and preparation are essential aspects of every course, and you will have access to many online resources and the University’s Moodle e-learning facility. You will also have a dedicated personal adviser to guide you and help you with any personal or academic issues that arise in the course of your studies.