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Mathematics and Philosophy (BA) (Full-Time, 2019 Entry)



Full-time 2019 entry

This degree enables you to pursue your interest in foundational questions about mathematics and logic.

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You will be taught by world-leading experts from both the Mathematics and the Philosopy Department, who will challenge you on a range of philosophical and mathematical questions.

You will study mathematics in depth, while also learning about how the developments of mathematics and philosophy have informed one another. The fully integrated course includes specialised modules in Philosophy of Mathematics and Logic in every year.

Our graduates possess strong analytical and critical skills alongside the ability to integrate large bodies of information involving multiple perspectives. Their capacity to explain and argue through persuasive writing, presentation and negotiation are highly valued by employers in many spheres.

There are two routes through the Mathematics and Philosophy degree: the three year BSc/BA 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.

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 3 hrs of contact time per week per module, in most cases this would be 2hrs lecture and 1 hr seminar but is variable depending on teaching methods.

Class size

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

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%.

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.

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.

Student blogs

leyla"The tutors within the department are always available during their office hours and will encourage you to actually ‘do’ Philosophy rather than just memorize the ideas of Philosophers for your exams."

Check out Leyla's blog

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

You will also need to meet our English Language 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).

  • Access Courses: Access to HE Diploma (QAA- recognised) including appropriate subjects with distinction grades in level 3 units, and grade A* in A level Mathematics or equivalent. Typically, offers will also include a requirement in both a STEP paper and A level Further Mathematics.
  • 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). For full details of standard offers and conditions visit the IFP website.
  • We welcome applications from students with other internationally recognised qualifications. For more information please visit the international entry requirements page.
  • 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.

    Open Days All students who have been offered a place are invited to visit. Find out more about our main University Open Days and other opportunities to visit us.

Year 1
Central Themes in Philosophy

Your experience seems to present you with a wide variety of things, including people, paintings, conversations and rainbows. How much of that variety is genuine? Is the blue of the rainbow there independently of your experience? How should we understand these qualities and the things that seem to bear them? This module exposes you to major philosophical arguments on such topics, with the aim of deepening your understanding of the seemingly multi-faceted world that you inhabit.

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 2
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 construction of the integral of regulated functions, study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions, and use the concept of norm in a vector space to discuss convergence and continuity there. This will equip you with a working knowledge of the construction of the integral of regulated function.

Year 3
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 (BSc with Specialism in Logic and Foundations only)
Dissertation or Third year Maths essay
Selection of optional modules that current students are studying:

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

We work closely with the University Careers and Skills department and Alumni.

Our graduates enter a wide variety of careers, including: Analyst, EY; Marketing Co-ordinator, City and Guilds; Business Development, Bureau Recruitment; News Editor, European College of Liberal Arts; Assistant in Civil Service, Ministry of Justice. We invite alumni onto campus to speak with current students about career options.


"My goal is to pursue a challenging, rewarding, high impact career."

"I joined Warwick because it was progressive, with a very inclusive community. Mathematics offered a wider range of modules than other universities, with opportunities to study across many disciplines.

My advice for any potential applicants would be to exploit the fact that Maths is the cornerstone for half of the disciplines across the University. You should also engage with people outside the Maths department and gain important skills in the various societies on offer.

I knew I ultimately wanted to work in the public or charity sector, and the careers department gave me support in determining the necessary skills. As soon as I graduated, I felt prepared to take my place on the Civil Service Fast Stream."

Alexander Brush - Civil Service Fast Streamer (Finance)

Studied 'Mathematics' - Graduated 2016

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


Degree of Bachelor of Arts (BA) or BSc

3 or 4 years full time (depending on route of study)

Start Date

24 September 2019

Location of study
University of Warwick, Coventry

Tuition fees
Find out more about fees and funding

Additional costs

There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course.

This information is applicable for 2019 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.