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Mathematics and Philosophy (BA) (Full-Time, 2020 Entry)

Mathematics and Philosophy (BSc or BA)

Mathematics and Philosophy (BSc or BA)



  • UCAS Code
  • GV15
  • Qualification
  • BSc/BA
  • Duration
  • 3 or 4 years full-time
  • Entry Requirements
  • A level: A*A*A
  • IB: 39
  • (See full entry
  • requirements below)


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


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 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 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. BA Mathematics and Philosophy With Intercalated Year).

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 2 hrs 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.

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

Additional requirements: 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).

  • 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 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'?

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 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.

Probability A

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 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 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 (BSc with Specialism in Logic and Foundations only)
Dissertation or Third Year Maths Essay
Examples of optional modules/options for current students

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

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, and teaching and educational professionals.

Helping you find the right career

Our department has a dedicated professionally qualified Senior Careers Consultant who works within Student Careers and Skills to help you as an individual. Additionally your Senior Careers Consultant offers impartial advice and guidance together with workshops and events, tailored to our department, 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 our Careers & Skills Services here.

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

Additional requirements: You will also need to meet our English Language requirements.

UCAS code
GV15

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

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

Start date
28 September 2020

Location of study
University of Warwick, Coventry

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.

This information is applicable for 2020 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.

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