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Mathematics BSc (UCAS G100)

Mathematics student using outdoor chalkboard at the University of Warwick

Undergraduate

Explore our Mathematics (BSc) degree at Warwick

Mathematics enhances your ability to think clearly, learn new ideas quickly, manipulate precise and intricate concepts, follow complex reasoning, construct logical arguments and expose dubious ones. Our challenging Mathematics (BSc) degree will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.


General entry requirements

  • Applicants are required to take an additional Maths test, typically TMUA, except for applicants who are eligible for a Contextual Offer – see our Contextual Offers webpage to check your eligibility.
  • Scores in TMUA will be assessed alongside other factors (including GCSEs, Contextual indicators and predicted grades) to determine which applicants receive an offer.
  • The exact requirements in TMUA will be set once all results have been received. We cannot advise on the TMUA requirements at this stage, but in previous years the level required by the Mathematics Institute has been 6.5 in TMUA.
  • Grade 2 in STEP will be a requirement of offer for applicants who have not taken or who have not achieved the required threshold in TMUA.

For further details including test dates and how to register for TMUA, please see the TMUA at Warwick webpageLink opens in a new window.

A level typical offer

A*A* in Maths and Further Maths, plus A in a third subject at A level

  • Grade 2 in STEP will be a requirement of offer for applicants who have not taken or who have not achieved the required threshold in TMUA.

A level contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is A*A*B with an A* 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.

IB typical offer

39 with 6 in three Higher Level subjects to include Mathematics ('Analysis and Approaches' only)

  • Grade 2 in STEP will be a requirement of offer for applicants who have not taken or who have not achieved the required threshold in TMUA.

IB contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is 38 with Higher Level 6,6,6 including Mathematics ('Analysis and Approaches' only). 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.

BTEC

We welcome applications from students taking a BTEC alongside A level Mathematics and Further Mathematics.

Scotland Advanced Highers

A1 in Advanced Higher Mathematics (C847), plus grades A2 in an additional Advanced Higher and A2 in Higher Mathematics (C847)

  • Grade 2 in STEP will be a requirement of offer for applicants who have not taken or who have not achieved the required threshold in TMUA.
Welsh Baccalaureate

A*A* in A level Mathematics and Further Mathematics and EITHER grade A in a third subject at A level, OR grade B in a third subject at A level and grade C in the Advanced Skills Baccalaureate Wales

  • Grade 2 in STEP will be a requirement of offer for applicants who have not taken or who have not achieved the required threshold in TMUA.
Access to Higher Education Diplomas

We will consider applicants returning to study who are presenting a QAA-recognised Access to Higher Education Diploma on a case-by-case basis.

Typically, we require 45 Credits at Level 3, including Distinction in 33 Level 3 credits and Merit in 12 Level 3 Credits. We may also require subject specific credits or an A level to be studied alongside the Access to Higher Education Diploma to fulfil essential subject requirements.

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.


International qualifications


English Language requirements

All applicants have to meet our English Language requirementsLink opens in a new window. If you cannot demonstrate that you meet these, you may be invited to take part in our Pre-sessional English course at WarwickLink opens in a new window.

This course requires: Band A

Learn more about our English Language requirementsLink opens in a new window.


Frequently asked questions

Warwick may make differential offers to students in a number of circumstances. These include students participating in a Widening Participation programme or who meet the contextual data criteria.

Differential offers will usually be one or two grades below Warwick’s standard offer.

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).

Find out more about standard offers and conditions for the IFP.

We welcome applications for deferred entry.

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.

Course overview

Our challenging degrees will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

You will be taught by world-leading researchers in a supportive environment, where learning spaces – including breakout areas and common spaces – are all geared towards you sharing, collaborating and exploring your academic curiosity with like-minded peers.

Pure mathematics modules combine the work of some of the world’s greatest thinkers, while applied mathematics addresses real-world problems in physics, biology, data science, climate science and finance. Many third and fourth year (fourth year for MMath only) modules offer glimpses of the latest research.


Study abroad

We encourage students to consider spending Year Three at one of 23 European partner universities in Belgium, France, Germany, Italy, The Netherlands, Spain and Switzerland.

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 years of study. The third year 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 year can be in non-maths modules).


Year One

Foundations

This module will bridge the gap between school and university mathematics, taking you from a calculation and method-based approach to a deeper understanding of mathematics based on proofs. In this module, you will learn the art of mathematical proofs through understanding key methods of proof and creating your own.

In addition to proofs, the module will also introduce you to essential university mathematics, including set theory, logic, number theory, algorithms and cryptography.

Read more about the Foundations moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year of study).

Analysis 1/2

Analysis is the rigorous study of calculus. In this module, there will be a considerable emphasis throughout on the need lay out mathematical arguments 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, say, differentiate and integrate a function, to the point where you can develop your own rigorous proofs of calculus results that you may have taken for granted. 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 2024/25 year of study).

Mathematical Methods and Modelling 1 and 2

Introduces the fundamentals of mathematical modelling, before discussing and analysing difference and differential equations in 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 Mathematical Methods and 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 2024/25 year of study):

Algebra 1 and 2

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 methods of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or a matrix. You will gain a solid 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 2024/25 year of study):

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.

Read more about the Mathematics by Computer moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year of study).

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 and famous probability theorems.

Year Two

Methods of Mathematical Modelling 3

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).

Read more about the Methods of Mathematical Modelling 3 moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year of study).

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’s theorem on unique factorisation in polynomial rings. You will study applications in number theory, geometry and combinatorics.

Read more about the Algebra 3 moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year of study).

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.

Read more about the Norms, Metrics and Topologies moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year of study).

Analysis 3

This module lays the basis for many subsequent mathematically-inclined modules, and it is concerned with further study of the notions of convergence and calculus seen in Analysis 1 and 2. Creating a consistent theoretical framework for these concepts has kept many great mathematicians busy for many centuries, and in this module you walk in their footsteps.

Read more about the Analysis 3 moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2024/25 year 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 2024/25 year 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 25% of your options in subjects other than mathematics should you wish to do so.


Optional modules

Optional modules can vary from year to year. Example optional modules may include:

  • Mathematics: Number Theory, Galois Theory, Fractal Geometry, Topology, Partial Differential Equations, Curves and Surfaces, Fluid Mechanics, Machine Learning
  • 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)

    Assessment

    Most modules are assessed by 85% exam and 15% homework, or by 100% exam. Mathematics by Computer is assessed via Python programming assignments.

    The Second Year Essay is assessed on the basis of a report and oral presentation.

    Years One, Two and Three are weighted 10:30:60.

    Teaching

    Most of our teaching is through lectures delivered by a member of academic staff.

    Undergraduates usually take four or five modules in each of Term One and Term Two. Term Three is mostly for revision and examinations. Each module is usually taught in three one-hour lectures per week.

    In your first year, you meet your supervisor (a graduate student or final-year undergraduate) twice a week to discuss the course material and go over submitted work. In your second and third years, most modules are accompanied by weekly support classes. Your personal tutor provides a further layer of learning and pastoral support via weekly tutorials in your first and second years.


    Class sizes

    Lectures vary from 10 to 400. Supervisions and tutorials are typically in groups of five.


    Typical contact hours

    Typical contact hours across lectures, seminars, supervisions etc: 18 hours/week during Term One and Term Two (15 hours of lectures and 3 hours of supervisions, problem classes and tutorials).

    Tuition fees

    Tuition fees cover the majority of the costs of your study, including teaching and assessment. Fees are charged at the start of each academic year. If you pay your fees directly to the University, you can choose to pay in instalments.

    Undergraduate fees

    If you are a home student enrolling in 2024, your annual tuition fees will be £9,250. In the future, these fees might change for new and continuing students.


    How are fees set?

    The British Government sets tuition fee rates.

    Learn more about fees from UCASLink opens in a new window.

    Undergraduate fees

    If you are an overseas or EU student enrolling in 2024, your annual tuition fees will be as follows:

    • Band 1 – £24,800 per year (classroom-based courses, including Humanities and most Social Science courses)
    • Band 2 – £31,620 per year (laboratory-based courses, plus Maths, Statistics, Theatre and Performance Studies, Economics, and courses provided by Warwick Business School, with exceptions)

    Fees for 2025 entry have not been set. We will publish updated information here as soon as it becomes available, so please check back for updates about 2025 fee rates before you apply.


    Fee status guidance

    We carry out an initial fee status assessment based on the information you provide in your application. Students will be classified as Home or Overseas fee status. Your fee status determines tuition fees, and what financial support and scholarships may be available. If you receive an offer, your fee status will be clearly stated alongside the tuition fee information.

    Do you need your fee classification to be reviewed?

    If you believe that your fee status has been classified incorrectly, you can complete a fee status assessment questionnaire. Please follow the instructions in your offer information and provide the documents needed to reassess your status.

    Find out more about how universities assess fee status.Link opens in a new window


    Additional course costs

    As well as tuition fees and living expenses, some courses may require you to cover the cost of field trips or costs associated with travel abroad.

    For departmental specific costs, please see the Modules tab on this web page for the list of core and optional core modules with hyperlinks to our Module CatalogueLink opens in a new window (please visit the Department’s website if the Module Catalogue hyperlinks are not provided).

    Associated costs can be found on the Study tab for each module listed in the Module Catalogue (please note most of the module content applies to 2024/25 year of study). Information about module specific costs should be considered in conjunction with the more general costs below:

    • Core text books
    • Printer credits
    • Dissertation binding
    • Robe hire for your degree ceremony

    Further information

    Find out more about tuition fees from our Student Finance team.


    Scholarships and bursaries

    Learn about scholarships and bursaries available to undergraduate students.

    We offer a number of undergraduate scholarships and bursaries to full-time undergraduate students. These include sporting and musical bursaries, and scholarships offered by commercial organisations.

    Find out more about funding opportunities for full-time students.Link opens in a new window

    If you are an international student, a limited number of scholarships may be available.

    Find out more information on our international scholarship pages.Link opens in a new window


    You may be eligible for financial help from your own government, from the British Council or from other funding agencies. You can usually request information on scholarships from the Ministry of Education in your home country, or from the local British Council office.


    Warwick Undergraduate Global Excellence Scholarship

    We believe there should be no barrier to talent. That's why we are committed to offering a scholarship that makes it easier for gifted, ambitious international learners to pursue their academic interests at one of the UK's most prestigious universities.

    Find out more about the Warwick Undergraduate Global Excellence Scholarship.Link opens in a new window

    We provide extra financial support for qualifying students from lower income families. The Warwick Undergraduate Bursary is an annual award of up to £3,000 per annum. It is intended to help with course-related costs and you do not have to pay it back.

    Find out more about your eligibility for the Warwick Undergraduate Bursary.Link opens in a new window

    As part of the 'City of Sanctuary' movement, we are committed to building a culture of hospitality and welcome, especially for those seeking sanctuary from war and persecution. We provide a range of scholarships to enable people seeking sanctuary or asylum to progress to access university education.

    Find out more about the Warwick Undergraduate Sanctuary Scholarships for asylum seekers.Link opens in a new window

    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.

    Tuition Fee Loan

    You can apply for a Tuition Fee Loan to cover your tuition fees. It is non-means tested, which means the amount you can receive is not based on your household income. The Loan is paid directly to the University so, if you choose to take the full Tuition Fee Loan, you won’t have to set up any payments.

    Maintenance Loan for living costs

    You can apply for a Maintenance Loan towards your living costs such as accommodation, food and bills. This loan is means-tested, so the amount you receive is partially based on your household income and whether you choose to live at home or in student accommodation.

    Find out more about government student loans for home students residing in England.Link opens in a new window

    If you’re starting a course on or after 1 August 2021, you usually must have settled or pre-settled status under the EU Settlement SchemeLink opens in a new window to get student finance.

    Tuition Fee Loan

    If you are an EU student and eligible for student finance you may be able to get a Tuition Fee Loan to cover your fees. It is non-means tested, which means the amount you may receive is not based on your household income. The Loan is paid directly to the University so, if you choose to take the full Tuition Fee Loan, you won't have to set up any payments.

    Help with living costs

    For the 2024 academic year, you may be eligible for help with your living costs if both of the following apply:

    • You have lived in the UK for more than 3 years before the first day of the first academic year of your course

    And

    If you are coming to the UK from 1st January 2021, you may need to apply for a visaLink opens in a new window to study here.

    Please note: Irish citizens do not need to apply for a visa or to the EU Settlement Scheme.

    Find out more about government student loans for EU studentsLink opens in a new window

    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 loan.Link opens in a new window

    Placements and work experience

    After Year Two, students can take a year’s placement to experience mathematics in action. The job must be deemed to provide learning experiences related to the degree course. A satisfactory placement leads to the award of a ‘BSc with Intercalated Year’ (and often to a potential job offer after graduation). We encourage you to speak to our Student OpportunityLink opens in a new window team for advice relating to finding a placement.

    Your career

    Recent graduates have pursued job roles such as:

    • Actuaries, economists and statisticians
    • Software developers
    • Chartered and certified accountants
    • Finance and investment analysts
    • Teachers
    • Telecommunication designers
    • Data scientists and engineers
    • Academics

    UK firms that have employed recent Warwick graduates from the Mathematics and Statistics Departments include:

    • Adder Technology
    • Amazon
    • BlackRock International
    • Merrill Lynch
    • Brainlabs
    • Civil Service
    • Conduent
    • Darktrace
    • Deloitte
    • Department of Health
    • eBay
    • Ford Motor Company
    • Fore Consulting
    • Goldman Sachs
    • Government Actuaries
    • Investec
    • Jane Street Capital
    • KPMG
    • Lloyds
    • MBDA
    • Metaswitch
    • Met Office
    • Ministry of Justice
    • RenaissanceRe (Syndicate 1458)
    • Oxford Clinical Trials Unit
    • Softwire
    • Solid Solutions
    • Sword Apak
    • Ten10
    • Towers Watson
    • Xafinity

    Helping you find the right career

    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:

    • Finding experience to boost your CV in Year One and Two
    • Careers in Data Science and Artificial Intelligence
    • Warwick careers fairs throughout the year
    • Interview skills for mathematics students
    • Maths and Stats Careers Fair

    Find out more about careers support at Warwick.

    Mathematics at Warwick

    Looking for that perfect combination?

    We offer a huge number of exciting modules allowing you to develop and pursue your interests within mathematics. Many 3rd and 4th year modules offer a glimpse of the latest developments in our research.

    You are free to study maths throughout your course if you prefer. However, we also offer the opportunity to choose options from several other world-class departments at Warwick. This provides flexibility to tailor your degree to suit your interests, and also your potential career.

    Find out more about us on our websiteLink opens in a new window


    Our courses

    Our challenging Maths BSc degree will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

    Mathematics (BSc)

    Our four-year Maths MMath shares the same core as our BSc but enables you to explore in greater depth areas of interest, both through specialized fourth-year modules and via a substantial Research or Maths-in- Action project.

    Mathematics (MMath)


    Related degrees

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    Travelling from campus

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    Student support

    Chaplaincy

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