General entry requirements

A level:

• A* in Mathematics, A* in Further Mathematics and A in a further subject

IB:

• 39 to include 6, 6, 6 in three Higher Level subjects including Mathematics

BTEC:

• We welcome applications from students taking a BTEC as long as essential subject requirements are met

Additional requirements:

You will also need to meet our English Language requirements.

International Students

We welcome applications from students with other internationally recognised qualifications.

Find out more about international entry requirements.

Contextual data and differential offers

Warwick may make differential offers to students in a number of circumstances. These include students participating in the Realising Opportunities programme, or who meet two of the contextual data criteria. Differential offers will be one or two grades below Warwick’s standard offer (to a minimum of BBB).

Warwick International Foundation Programme (IFP)

All students who successfully complete the Warwick IFP and apply to Warwick through UCAS will receive a guaranteed conditional offer for a related undergraduate programme (selected courses only).

Find out more about standard offers and conditions for the IFP.

Taking a gap year

Applications for deferred entry welcomed.

Interviews

We do not typically interview applicants. Offers are made based on your UCAS form which includes predicted and actual grades, your personal statement and school reference.

Year One

Mind and Reality

Look around. What if all your experiences were the products of dreams, or neuroscientific experiments? Can you prove they aren’t? If not, how can you know anything about the world around you? How can you even think about such a world? Perhaps you can at least learn about your own experience, what it’s like to be you. But doesn’t your experience depend on your brain, an element of the external world? This course will deepen your understanding of the relationship between your mind and the rest of the world.

Logic 1: Introduction to Symbolic Logic

This module introduces you to formal (i.e., symbolic) logic, covering both propositional and first-order logic. You will study formal languages, and learn how they allow for precise definitions of central logical notions such as the logical validity of an argument. You will learn methods for establishing the validity and invalidity of an argument, and also learn how to translate English sentences into formal language ones and vice versa.

Linear Algebra

Linear algebra addresses simultaneous linear equations. You will learn about the properties of vector space, linear mapping and its representation by a matrix. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.

Analysis I/II

Analysis is the rigorous study of calculus. In this module, there will be a considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers, and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. The module will allow you to deal carefully with limits and infinite summations, approximations to pi and e, and the Taylor series. The module ends with the construction of the integral and the Fundamental Theorem of Calculus.

Foundations

It is in its proofs that the strength and richness of mathematics is to be found. University mathematics introduces progressively more abstract ideas and structures and demands more in the way of proof until much of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on calculation, and gradually moving towards abstraction and proof.

This module also looks at algorithms and operational complexity, including cryptographic keys and RSA.

Differential Equations

Can you predict the trajectory of a tennis ball? In this module you cover the basic theory of ordinary differential equations (ODEs), the cornerstone of all applied mathematics. ODE theory proves invaluable in branches of pure mathematics, such as geometry and topology. You will be introduced to simple differential and difference equations and methods for their solution. You will cover first-order equations, linear second-order equations and coupled first-order linear systems with constant coefficients, and solutions to differential equations with one-and two-dimensional systems. We will discuss why in three dimensions we see new phenomena, and have a first glimpse of chaotic solutions.

Geometry and Motion

Geometry and motion are connected as a particle curves through space, and in the relation between curvature and acceleration. In this course you will discover how to integrate vector-valued functions and functions of two and three real variables. You will encounter concepts in particle mechanics, deriving Kepler’s Laws of planetary motion from Newton’s second law of motion and the law of gravitation. You will see how intuitive geometric and physical concepts such as length, area, volume, curvature, mass, circulation and flux can be translated into mathematical formulas, and appreciate the importance of conserved quantities in mechanics.

Introduction to Abstract Algebra

This course will introduce you to abstract algebra, covering group theory and ring theory, making you familiar with symmetry groups and groups of permutations and matrices, subgroups and Lagrange’s theorem. You will understand the abstract definition of a group, and become familiar with the basic types of examples, including number systems, polynomials, and matrices. You will be able to calculate the unit groups of the integers modulo n.

Introduction to Probability

This module takes you further in your exploration of probability and random outcomes. Starting with examples of discrete and continuous probability spaces, you’ll learn methods of counting (inclusion-exclusion formula and multinomial coefficients), and examine theoretical topics including independence of events and conditional probabilities. Using Bayes’ theorem you’ll reason about a range of problems involving belief updates, and engage with random variables, learning about probability mass, density and cumulative distribution functions, and the important families of distributions. Finally, you’ll study variance and co-variance, including Chebyshev’s and Cauchy-Schwarz inequalities. The module ends with a discussion of the celebrated Central Limit Theorem.

Year Two

Logic II: Metatheory

In this module, you will learn about the metatheory of propositional and first-order logic; to understand the concept of a sound and complete proof system similar to that of Logic I. You will study elementary set theory and inductive definitions and then consider Tarski's definitions of satisfaction and truth, proceeding to develop the Henkin completeness proof for first-order logic. You will learn to appreciate the significance of these concepts for logic and mathematics, with the ability to define them precisely.

Algebra I: Advanced Linear Algebra

On this course, you will develop and continue your study of linear algebra. You will develop methods for testing whether two general matrices are similar, and study quadratic forms. Finally, you will investigate matrices over the integers, and investigate what happens when we restrict methods of linear algebra to operations over the integers. This leads, perhaps unexpectedly, to a complete classification of finitely generated abelian groups. You will be familiarised with the Jordan canonical form of matrices and linear maps, bilinear forms, quadratic forms, and choosing canonical bases for these, and the theory and computation of the Smith normal form for matrices over the integers.

Analysis III

In the first half of this module, you will investigate some applications of year one analysis: integrals of limits and series; differentiation under an integral sign; a first look at Fourier series. In the second half you will study analysis of complex functions of a complex variable: contour integration and Cauchy’s theorem, and its application to Taylor and Laurent series and the evaluation of real integrals.

Year Three

Set Theory

Set theoretical concepts and formulations are pervasive in modern mathematics. They provide a highly useful tool for defining and constructing mathematical objects as well as casting a theoretical light on reducibility of knowledge to agreed first principles. You will review naive set theory, including paradoxes such as Russell and Cantor, and then encounter the Zermelo-Fraenkel system and the cumulative hierarchy picture of the set theoretical universe. Your understanding of transfinite induction and recursion, cardinal and ordinal numbers, and the real number system will all be developed within this framework.

Year Four†

Dissertation OR Third Year Maths Essay

†(BSc with Specialism in Logic and Foundations only)

Examples of optional modules/options for current students

• Commutative Algebra
• Knot Theory
• Logic III: Incompleteness and Undecidability
• Philosophy of Mathematics
• Metaphysics
• Computability Theory

Tuition fees

Find out more about fees and funding

Additional course costs

There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course. Students who choose to complete a work placement or study abroad will pay reduced tuition fees for their third year.

Warwick Undergraduate Global Excellence Scholarship 2021

We believe there should be no barrier to talent. That's why we are committed to offering a scholarship that makes it easier for gifted, ambitious international learners to pursue their academic interests at one of the UK's most prestigious universities. This new scheme will offer international fee-paying students 250 tuition fee discounts ranging from full fees to awards of £13,000 to £2,000 for the full duration of your Undergraduate degree course.

Find out more about the Warwick Undergraduate Global Excellence Scholarship 2021

Your career

Graduates from our Philosophy single and joint honours degrees have gone on to pursue careers as:

• Authors, writers and translators
• Legal professionals
• Marketing professionals
• Management consultants and business analysts
• Chartered and certified accountants
• Teaching and educational professionals

Helping you find the right career

Our department has a dedicated professionally qualified Senior Careers Consultant to support you. They offer impartial advice and guidance, together with workshops and events throughout the year. Previous examples of workshops and events include:

• Philosophy Orienteering/Scavenger Hunt
• Identifying Your Skills, Strengths and Motivators for Philosophy Students
• Thinking about Work Experience for Philosophy Students
• Careers in the Public Sector
• Warwick careers fairs throughout the year

Find out more about careers support at Warwick.

"If I could sum up the Philosophy course at Warwick in one word it would be...modern. I found that unlike some institutions that tend to focus only on the typical Plato and Aristotle type modules, Warwick gives you the opportunity to intertwine philosophy with your everyday life.

One of my favourite modules was ‘Philosophy through film’ which involved investigating whether films could actually do philosophy. Although we didn’t get to swap lectures for film screenings, we had fun movie nights, thoughtful debates and eventually created our own short films which is less daunting than it sounds. Our lecturers encourage us to genuinely investigate the aspects of philosophy that interests us so that we are constantly interested in what we study and keen to contribute our own ideas."

Oray | BA Philosophy