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
Our degree programme consists of core and optional modules In core modules you will study essential topics in algebra analysis and applied mathematics Optional modules cover the entire range of mathematical sciences including algebra combinatorics number theory geometry topology pure and applied analysis differential equations and applications to physical biological and data sciences

There are core modules in the first and second of study The third comprises solely of optional modules

At Warwick our wide range of options enables you to explore in depth your love of mathematics while the flexible system allows you to explore other subjects you enjoy outside of mathematics (as much as 50% of the third can be in non-maths modules)

Year One
Foundations
It is in its proofs that the strength and richness of mathematics are 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

Read more about the Foundations moduleLink opens in a new window including the methods of teaching and assessment (content applies to 2022 23 of study)

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

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

Methods of Mathematical Modelling 1Link opens in a new window
Methods of Mathematical Modelling 2Link opens in a new window
Algebra I and II
This first half of this module 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

The second half concerns linear algebra and 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

Read more about these modules including the methods of teaching and assessment (content applies to 2021 22 of study)

Algebra ILink opens in a new window
Algebra IILink opens in a new window
Mathematics by Computer
This module contains a Python mini-course and an introduction to the Latex scientific document preparation package It will involve a group project involving computation and students will develop their research skills including planning and use of library and internet resources and their presentation skills including a video presentation

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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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Year Two
Methods of Mathematical Modelling III
You will study a number of key concepts in mathematical modelling (i) Optimisation (including critical points in multi-dimensions linear programming least squares regression convexity steepest descent algorithms optimisation with constraints neural network); (ii) The Fast Fourier Transform (including its application to signal processing and audio and video compression) (iii) Hilbert Spaces (including orthogonal functions and their use in approximation problems)

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Algebra III
This course focuses on developing your understanding and application of the theories of groups and rings improving your ability to manipulate them and extending the results from one algebra You will learn how to prove the isomorphism theorems for groups in general and analogously for rings You will also encounter the Orbit-Stabiliser Theorem the Chinese Remainder Theorem and Gauss’ theorem on unique factorisation in polynomial rings and see applications in Number Theory Geometry and Combinatorics

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Norms Metrics and Topologies
Roughly speaking a metric space is any set provided with a sensible notion of the “distance” between points The ways in which distance is measured and the sets involved may be very diverse For example the set could be the sphere and we could measure distance either along great circles or along straight lines through the globe; or the set could be New York and we could measure distance “as the crow flies” or by counting blocks This module examines how the important concepts introduced in first-year Mathematical Analysis such as convergence of sequences and continuity of functions can be extended to general metric spaces Applying these ideas we will be able to prove some powerful and important results used in many parts of mathematics

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Mathematical Analysis III
In the first half of this module you will investigate some applications of 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

Read more about the Mathematical Analysis III moduleLink opens in a new window including the methods of teaching and assessment (content applies to 2024 24 of study)

Scientific Communication
You will undertake independent research on a mathematical topic with guidance and feedback from your Personal Tutor You will investigate mathematics that may not be covered in the core curriculum You will then communicate your research in a scientific report and an oral presentation

Read more about the Scientific Communication moduleLink opens in a new window including the methods of teaching and assessment (content applies to 2022 23 of study)

Year Three
There are no core modules Instead you will select from an extensive range of optional modules in both mathematics and a range of other subjects from departments across the university You will be able to take up to 50% (BSc) or 25% (MMath) of your options in subjects other than mathematics should you wish to do so

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

Mathematics Knot Theory; Fractal Geometry; Population Dynamics - Ecology and Epidemiology; Number Theory
Statistics Mathematical Finance; Brownian Motion; Medical Statistics; Designed Experiments
Computer Science Complexity of Algorithms; Computer Graphics
Physics Introduction to Astronomy; Introduction to Particle Physics; Quantum Phenomena; Nuclear Physics; Stars and Galaxies
Economics Mathematical Economics
Other Introduction to Secondary School Teaching; Climate Change; Language Options (at all levels)

• 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