The University of Warwick is a public research university located in Coventry, England. Founded in 1965, it has quickly established itself as one of the UK's leading universities, consistently ranking in the top ten in national league tables. Warwick has a reputation for academic excellence, particularly in the fields of business, economics, engineering, and the humanities. The university is known for its international outlook and has a diverse student body, with students from over 150 countries. With a strong commitment to research and innovation, the University of Warwick is a dynamic and exciting institution that offers a world-class education to its students.

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

If you remain on the Mathematics and Philosophy route you may choose to apply for an intercalated spent either studying abroad or on a work placement This extends the duration of your degree to four with your third spent abroad or on placement and will be reflected in your degree qualification (ie Mathematics and Philosophy with Intercalated Year)

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

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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

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Sets and Numbers
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

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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 will learn methods of counting (inclusion-exclusion formula and multinomial coefficients) and examine theoretical topics including independence of events and conditional probabilities You will study random variables and their probability distribution functions Finally you will study variance and co-variance including Chebyshev’s and Cauchy-Schwarz inequalities The module ends with a discussion of the celebrated Central Limit Theorem

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Mathematical 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 also covers construction of the integral and the Fundamental Theorem of Calculus

Read more about these modules including the methods of teaching and assessment (content applies to 2022 23 of study)

Mathematical Analysis ILink opens in a new window
Mathematical Analysis IILink opens in a new window
Methods of Mathematical Modelling 1 and 2
Methods of Mathematical Modelling 1 introduces you to the fundamentals of mathematical modelling and scaling analysis before discussing and analysing difference and differential equation models in the context of physics chemistry engineering as well as the life and social sciences This will require the basic theory of ordinary differential equations (ODEs) the cornerstone of all applied mathematics ODE theory later proves invaluable in branches of pure mathematics such as geometry and topology You will be introduced to simple differential and difference equations methods for obtaining their solutions and numerical approximation

In the second term for Methods of Mathematical Modelling 2 you will study the differential geometry of curves calculus of functions of several variables multi-dimensional integrals calculus of vector functions of several variables (divergence and circulation) and their uses in line and surface integrals

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Methods of Mathematical Modelling 1Link opens in a new window
Methods of Mathematical Modelling 2Link opens in a new window
Linear Algebra
Linear algebra addresses simultaneous linear equations You will learn about the properties of vector spaces linear mappings and their representation by matrices 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

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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

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Metric Spaces
This module lays the basis for many subsequent mathematically-inclined modules and it is concerned with fundamental notions of distances measuring and continuity Making these foundations into a consistent theoretical framework has kept many great mathematicians busy for many centuries and in this module you walk in their footsteps

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Multilinear Algebra
In this module you will develop and continue your study of linear algebra the Jordan normal form for matrices; functions of matrices; symmetric and quadratic forms; tensors; bilinear forms; dual spaces

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Groups and Rings
This first abstract algebra module roughly based on the current version of Algebra-2 Groups and Rings focuses on developing your understanding and application of the theories of groups and rings improving your ability to manipulate them and extending your knowledge and understanding of algebra from the Sets and Numbers module in Year One

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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

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Year Four
Dissertation

Or

Third Year Maths Essay

(with Specialism in Logic and Foundations only)

Optional modules
Optional modules can vary from to Example optional modules may include

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

• The University of Warwick is a world-renowned public research university located in Coventry, England. Established in 1965, it has rapidly established itself as one of the leading universities in the UK and the world, consistently ranking in the top ten in national and international league tables.
• Academic excellence is at the heart of the University of Warwick, with a reputation for excellence in fields such as business, economics, engineering, and the humanities. The university has four faculties: Arts, Science, Social Sciences, and Medicine, with over 30 academic departments and more than 300 degree courses at undergraduate, postgraduate, and doctoral levels.
• The Warwick Business School is one of the most respected business schools in the UK, with an international reputation for excellence in research and teaching. It offers a range of undergraduate, postgraduate, and executive education programs, including the highly regarded Warwick MBA.
• The university's commitment to research is evident in its world-class research facilities and centres, which focus on areas such as energy, healthcare, and digital technologies. Warwick is also home to a number of research institutes and centres, including the Warwick Manufacturing Group, the Warwick Medical School, and the Warwick Centre for Applied Linguistics.
• The University of Warwick is also renowned for its international outlook, with a diverse student body representing over 150 nationalities. It has strong partnerships with universities around the world, with opportunities for students to study abroad and for international students to study at Warwick.
• The university has a strong commitment to innovation and entrepreneurship, with numerous initiatives and programs aimed at supporting student startups and promoting innovation. The Warwick Enterprise Hub provides students with access to resources and support to develop their business ideas, while the Warwick Innovation Centre offers incubation and office space for startups and small businesses.
• The University of Warwick has a beautiful campus that spans over 700 acres and features state-of-the-art facilities, including a modern sports centre, a world-class arts centre, and numerous research facilities. The campus is located in Coventry, a historic city in the heart of England with excellent transport links to London and other major cities.
• In conclusion, the University of Warwick is a world-class institution that is known for its academic excellence, commitment to research and innovation, international outlook, and beautiful campus. With a diverse and dynamic student body, the university offers a rich and rewarding academic experience that prepares students for success in their chosen fields.

You will need to book the accommodation after you have been accepted.

You can choose to live on campus or off campus in private accommodation.

• Make a booking online after you have been accepted (in this case please let us know your choice when you apply).
• Register when you arrive - its not possible to reserve a room before arriving. You can arrive a few days before and book it