Mathematics with Philosophy

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 transferable 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%.

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.

Our philosophy courses are taught in a lively international community of students in the Department of Politics and International Relations.

Benefit from our strong focus on small group teaching.

Course Modules

Core Modules

Year 1

• Calculus

• Introduction to Pure Mathematics

• Calculus II

• Linear Algebra I

• Problems of Knowledge

• Statistical Methods 1

• Introduction to Logic

• Mind and Consciousness

• Introduction to Aesthetics and Morals

Year 2

• Linear Algebra II

• Complex Analysis

• Introduction to European Philosophy 1: Kant to Hegel

• Mind and World

• Scientific Programming

• Probability Theory

Year 3

• Advanced Skills in Mathematics

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

• From Euclid to Mandelbrot

• Introduction to Applied Mathematics

• Statistical Methods 1

Year 2

• Vector Calculus

• Statistical Methods 2

• Ring Theory

• Complex Analysis

• Probability Theory

• Graphs and Optimisation

• Ordinary Differential Equations and Fourier Analysis

• Group Theory

• Further Linear Algebra and Modules

• Introduction to European Philosophy 2: The Critique of Idealism

• Varieties of Scepticism

• Philosophy and the Arts

• The Philosophy of Religion

• Philosophy and Literature

• The Good Life in Ancient Philosophy

Year 3

• Mathematics Project

• Number Theory

• Complexity Theory

• Quantum Theory 1

• Non-Linear Dynamic Systems

• Inference

• Time Series Analysis

• Channels

• Mathematics of Financial Markets

• Combinatorics

• Cipher Systems

• Electromagnetism

• Applications of Field Theory

• Mathematics in the Classroom

• Computational Number Theory

• Principles of Algorithm Design

• Dynamics of Real Fluids

• Quantum Theory 2

• Markov Chains and Applications

• Quantum Information and Coding

• Financial Mathematics I

• Financial Mathematics II

• Error Correcting Codes

• Cryptography

• Further Linear Algebra and Modules

• Topology

• Modern European Philosophy 1: Husserl to Heidegger

• Modern European Philosophy 2: Critical Theory and Hermeneutics

• The Varieties of Scepticism

• The Philosophy of Religion

• Philosophy and Literature

• The Good Life in Ancient Philosophy

• Group Theory

• Introduction to Optimisation

• Game Theory

https://www.royalholloway.ac.uk/studying-here/undergraduate/mathematics/mathematics-with-philosophy/

The programme has a flexible, modular structure and you will take a total of 12 course units at a rate of four, 30-credit modules per year. In addition to compulsory modules in years 1 and 2, you will choose from a range of optional courses each year. Some contribute 15 credits to your overall award while others contribute the full 30.

We use a variety of teaching methods and there is a strong focus on small group teaching. You will attend 12 to 15 hours of formal teaching in a typical week. 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.

Assessment is through a mixture of coursework and end-of-year examinations, depending on the courses you choose to take. Statistics and computational courses in mathematics may include project work and tests. 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. The results of the first year assessments qualify you to progress to the second year but do not contribute to your final degree award. The second and final year results do contribute to the final degree result.

You will be required to take a study skills course during year 1, to equip you with and enhance the writing skills you will need to be successful in your degree. This does not count towards your final degree but you are required to pass it to progress to your second year.