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Mathematics and Philosophy BA or BSc (GV15)

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Find out more about our Mathematics and Philosophy degree at Warwick

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We have revised the information on this page since publication. See the edits we have made and content history.

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Important Information

Please note the Mathematics and Philosophy degree is likely to change for 2022 entry. Changes to the core modules go through the University's rigorous academic processes. As module changes are confirmed, we will update the course information on this webpage. It is therefore very important that you check this webpage for the latest information before you apply and prior to accepting an offer.

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GV15

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

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3 or 4 years full-time

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26 September 2022

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Department of Philosophy

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University of Warwick

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

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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, philosophy and logic at an advanced level.

Your time will be evenly split between the Department of Philosophy and Warwick Mathematics Institute – both internationally recognised for their excellent research.

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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).

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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.

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Seminar sizes are typically 12-18 students. Lectures vary by module from 20-220.

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Typically, students do four modules per term, and have three hours of contact time for each module. For philosophy modules, this three hours is usually divided into two hours of lectures and a one hour seminar. For maths modules, students typically have three hours of lectures. Additional support for maths modules is provided by supervisors (a graduate student or final year undergraduate) or weekly support classes.

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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%.

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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 offers support for these activities, and the Department’s dedicated Study Abroad Co-ordinator can provide more specific information and assistance.

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Placements and 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.

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A level typical offer

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

A level contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria and whose predicted grades are close to, or slightly below, the contextual offer level. The typical contextual offer is A* in Mathematics, A* in Further Mathematics and B a third subject. You must be taking A levels in Mathematics and Further Mathematics. See if you're eligible.

General GCSE requirements

Unless specified differently above, you will also need a minimum of GCSE grade 4 or C (or an equivalent qualification) in English Language and either Mathematics or a Science subject. Find out more about our entry requirements and the qualifications we accept. We advise that you also check the English Language requirements for your course which may specify a higher GCSE English requirement. Please find the information about this below.

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IB typical offer

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

IB contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria and whose predicted grades are close to, or slightly below, the contextual offer level. The typical contextual offer is 38 including 6,6,6 in three Higher Level subjects including Mathematics. See if you're eligible.

General GCSE requirements

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

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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 teaches you formal logic, covering both propositional and first-order logic. You will learn about a system of natural deduction and understand how to demonstrate that it is both sound and complete. You will learn how to express and understand claims using formal techniques, including multiple quantifiers. Key concepts you will consider are logical validity, truth functionality and formal proof quantification.

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

Third Year Maths Essay

(BSc with Specialism in Logic and Foundations only)

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

For a list of current philosophy optional modules, click here.

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Find out more about fees and funding

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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.

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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

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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. https://warwick.ac.uk/services/careers/careers_skills]

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