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.

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.

Methods of Mathematical Modelling I and II

In this module you will learn the modelling cycle and learn to analyse simple models, using scaling, non-dimensionalisation and linear stability analysis to understand the main dynamics. 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 their solution and numerical approximation.

In the second term 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.

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.

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.

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.

Methods of Mathematical Modelling 3

This module studies several topics commonly used in mathematical modelling: (i) optimisation problems require an understanding of critical points in multi-dimensions, and methods you will see the techniques of linear programming, least squares and regression, convexity, steepest descent algorithms, optimisation with constraints (applications include neural nets); (ii) The Fast Fourier Transform is used in signal processing and audio and video compression; (iii) Hilbert space theory is a framework for discussing orthogonal functions and their use in approximation problems.

Algebra 3

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 year 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.

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.

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.

Scientific communication

This module includes an essay and presentation. You will be given the opportunity of independent study with guidance and feedback from your Personal Tutor. It will provide you with an opportunity to investigate some mathematics not covered in other modules, using a range of sources, and then develop your written and oral exposition skills.

Multilinear Algebra

On this course, 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.

Multivariable Analysis

There are many situations in pure and applied mathematics where the continuity and differentiability of a function f: R n. → R m has to be considered. Yet, partial derivatives, while easy to calculate, are not robust enough to yield a satisfactory differentiation theory. In this module you will establish the basic properties of this derivative, which will generalise those of single-variable calculus, including the inverse and implicit function theorems. The module will review line and surface integrals, introduce div, grad and curl and establish the divergence theorem, with some applications to partial differential equations.

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.

Research Project

Or

Maths-in-Action (MiA-Projects)

The primary aim of the Research Project is to give you experience of mathematics as it is being pursued close to the frontiers of research, not just as a spectator sport but as an engaging, evolving activity in which you can play a part. This project is primarily aimed at those who seek to further develop their skills in public speaking and writing. The project involves understanding deeply how mathematics underpins a particular topic in the modern world and then communicating this understanding in the form of a presentation to the general public, a written popular science article, and a written scholarly report at the MMath level.

Scholarships and bursaries

Learn about scholarships and bursaries available to undergraduate students.

Further information

Find out more about Warwick undergraduate bursaries and scholarships.

Eligibility for student loans

Your eligibility for student finance will depend on certain criteria, such as your nationality and residency status, your course, and previous study at higher education level.

Check if you're eligible for student finance.

Repaying your loans

You will repay your loan or loans gradually once you are working and earning above a certain amount. For students starting their course after 1 August 2023, the repayment threshold is £25,000. Repayments will be taken directly from your salary if you are an employee. If your income falls below the earnings threshold, your repayments will stop until your income goes back up above this figure.

Find out more about repaying your student loanLink opens in a new window.

Life at Warwick

Within a close-knit community of staff and students from all over the world, discover a campus alive with possibilities. A place where all the elements of your student experience come together in one place. Our supportive, energising, welcoming space creates the ideal environment for forging new connections, having fun and finding inspiration.

• Accommodation
• Arts, Culture and Events
• Campus
• Campus map
• Clubs and societies
• Food and drink
• Library
• Sports and Fitness
• Wellbeing support

Keep exploring life at Warwick

Find out how to apply to us, ask your questions, and find out more.

Warwick Accommodation

Finding the right accommodation is key to helping you settle in quickly.

We have 12 self-catering undergraduate halls of residence on campus.

Our student property management and lettings agency manages more than 8,000 rooms both on and off campus, and provides advice to all full-time undergraduates.

Explore Warwick Accommodation

Our campus

You won't be short of ways to spend your time on campus - whether it's visiting Warwick Arts Centre, using our incredible new sports facilities, socialising in our bars, nightclub and cafés, or enjoying an open-air event. Or if you need some peace and quiet, you can explore lakes, woodland and green spaces just a few minutes’ walk from central campus.

Explore our campus

Food and drink

We have lots of cafés, restaurants and shops on campus. You can enjoy great quality food and drink, with plenty of choice for all tastes and budgets. There is a convenience store on central campus, as well as two supermarkets and a small shopping centre in the nearby Cannon Park Retail Park. Several of them offer delivery services to help you stay stocked up.

And don't miss our regular food market day on the Piazza with tempting, fresh and delicious street food. Soak up the atmosphere and try something new, with mouth-watering food for all tastes.

Explore food and shops

Explore Students' Union venues

Clubs and societies

We currently have more than 300 student-run societies.

So whether you’re into films, martial arts, astronomy, gaming or musical theatre, you can instantly connect with people with similar interests.

Or you could try something new, or even form your own society.

Explore our societies

Sports and fitness

Staying active at Warwick is no sweat, thanks to our amazing new Sports and Wellness Hub, indoor and outdoor tennis centre, 60 acres of sports pitches, and more than 60 sports clubs.

Whether you want to compete, relax or just have fun, you can achieve your fitness goals.

Explore sports at Warwick

Studying on campus

Our campus is designed to cater for all of your learning needs.

You will benefit from a variety of flexible, well-equipped study spaces and teaching facilities across the University.

• The Oculus, our outstanding learning hub, houses state-of-the-art lecture theatres and innovative social learning and network areas.
• The University Library provides access to over one million printed works and tens of thousands of electronic journals
• Three Learning Grids offering you flexible individual and group study spaces.

Studying at Warwick

Travel and local area

Our campus is in Coventry, a modern city with high street shops, restaurants, nightclubs and bars sitting alongside medieval monuments. The Warwickshire towns of Leamington Spa and Kenilworth are also nearby.

The University is close to major road, rail and air links. London is just an hour by direct train from Coventry, with Birmingham a 20-minute trip. Birmingham International Airport is nearby (a 20-minute drive).

Travelling from campus

Wellbeing support and faith provision

Our continuous support network is here to help you adjust to student life and to ensure you can easily access advice on many different issues. These may include managing your finances and workload, and settling into shared accommodation. We also have specialist disability and mental health support teams.

Our Chaplaincy is home to Chaplains from the Christian, Jewish and Muslim faiths. We provide regular services for all Christian denominations and a Shabbat meal every Friday for our Jewish students. There is also an Islamic prayer hall, halal kitchen and ablution facilities.

Student support

Chaplaincy

Talk to us

Join us at a live event. You can ask about courses, applying to Warwick, life at Warwick, visas and immigration, and more.

See event calendar

Warwick Experience

Take a virtual, student-led campus tour. Then join an interactive panel session, where you can hear from and chat to our current students and staff.

Book a tour

Student blogs

Explore our student blogs in OurWarwick. You can read about campus life from students themselves, and register to post questions directly to students.

Ask a student

Explore campus with our virtual tour

Our 360 tour lets you:

• Watch student videos
• View 360 photography and drone footage
• Learn about facilities and landmarks

Explore our campus virtually through our 360 campus tour now

Come to an Open Day

Don’t just take it from us, come and see for yourself what Warwick is all about. Whether it's a virtual visit or in-person, our University Open Days give you the chance to meet staff and students, visit academic departments, tour the campus and get a real feel for life at Warwick.

Open Days at Warwick