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Mathematics and Philosophy (BA/BSc) (Full-Time, 2021 Entry)


Bachelor of Arts (BA) or Bachelor of Science (BSc)

3 or 4 years full-time

Start Date
27 September 2021

Department of Study
Department of Philosophy

Location of Study
University of Warwick

Mathematics and Philosophy (BA or BSc) enables you to pursue your interest in foundational questions about mathematics and logic.

Course overview

This course provides the freedom to choose your own path within the subjects. Our teaching will foster your intellectual development, supporting you to study mathematics and logic sequences at an advanced level. Your time will be evenly split between the Department of Philosophy and Warwick Mathematics Institute – both widely recognised for their excellent research.

There are two routes through the degree: the three year BA/BSc in Mathematics and Philosophy and the four-year BSc with Specialism in Logic and Foundations. You will be eligible for transfer to the Specialism in Logic and Foundations degree based on your first year exam results. If you remain on the Mathematics and Philosophy route, you may choose to apply for an intercalated year, spent either studying abroad or on a work placement. This extends the duration of your degree to four years, with your third year spent abroad or on placement, and will be reflected in your degree qualification (i.e. BSc Mathematics and Philosophy with Intercalated Year).

Course structure

There are two routes through the Mathematics and Philosophy degree: the three year BA/BSc in Mathematics and Philosophy and the four year BSc with Specialism in Logic and Foundations. You will be eligible for transfer to the four-year degree based on your first year exam results.

How will I learn?

Our main teaching methods are lectures, lecture-discussions, and seminars alongside private study and study skills sessions. Our students benefit from expert guidance from staff in developing strong analytical and critical skills, and our students highly rate the feedback they receive. In addition to compulsory teaching, we also offer many extra academic activities, including optional lectures, colloquia, discussion groups and workshops.

Contact hours

Typically three hours of contact time per week per module, in most cases this would be two hours lecture and one hour seminar but is variable depending on teaching methods.

Class size

Seminar sizes are typically 12-15 students. Lectures vary by module from 20-220.

How will I be assessed?

We track your progress and provide you with feedback through regular non assessed work, assessed essays and written examinations. Your final degree classification is based on assessed exercises and essays, other assessed work (which may include for example, group work or video presentations), examinations, and an optional dissertation or individual project. For the three year degree, the years are weighted 10%, 40%, 50% while the four year degree is weighted 10%, 20%, 30%, 40%.

Study abroad

We run successful undergraduate exchanges with Queen’s University, Ontario, and the University of Wisconsin-Madison, enabling second-year Philosophy students (single or joint honours) to compete for the chance to spend a full year studying in North America. Modules and examinations taken at Queen’s and Madison count towards your degree.

All students have the opportunity to apply for an intercalated year abroad at one of our partner universities, which currently include: Bourgogne, Dijon; Erasmus, Rotterdam; Copenhagen; Friedrich Schiller, Jena or Cologne; Vienna; Autonoma or Complutense, Madrid or Seville; Rome or Turin; and Koc, Istanbul. The Study Abroad Team in the Office for Global Engagement offers support for these activities, and the Department’s dedicated Study Abroad Co-ordinator can provide more specific information and assistance.

Work experience

Study skills will be built into your core modules in the first year. In those modules, you will develop skills in close reading, essay writing, exam technique, critical thinking and presentation. As well as the opportunity of individual careers appointments, there are a wide range of events and workshops – including small workshops for people with no career ideas, speaker events for people interested in a certain sector, and large career fairs for organisations wanting to recruit a large number of graduates each year.

We also offer specific sessions for second and third years, directed as honours level assessed work. Warwick also offers the Undergraduate Skills Programme and Academic Writing Programme to help you further develop academic and career-related skills.

General entry requirements

A level:

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


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


  • 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.


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 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. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity'?


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 most 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.

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.


If you’ve covered mathematical modules MA131 and MA132, this 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 co-efficients), and examine theoretical topics including independence of events and conditional probabilities. Using Bayes’ theorem and Simpson’s paradox, 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-Schwartz inequalities.

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 this module, you will learn methods to prove that every continuous function can be integrated, and prove the fundamental theorem of calculus. You will discuss how integration can be applied to define some of the basic functions of analysis and to establish their fundamental properties. You will develop a working knowledge of the Riemann integral; understand uniform and pointwise convergence of functions; study complex differentiability (Cauchy-Riemann equations) and complex power series; study contour integrals, Cauchy's integral formulas and applications.

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 will pay reduced tuition fees for their third year.

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

This information is applicable for 2021 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.