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Mathematics BSc (Course full)


Please note: this course is full for 2019 entry.


Full-time 2019 entry

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 research 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.

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This course offers unparalleled flexibility, catering for the needs of future financial analysts, actuaries, software developers and school teachers, as well as academic and industrial mathematicians. Our approach to teaching is forward-looking and innovative. The first Analysis module, for example, is taught through structured group problem-solving. The Mathematics by Computer module is computer-based, introducing you to mathematical software that illustrates new concepts. The Experimental Mathematics module uses practical investigations into coupled pendula, soap films and nonlinear oscillators.

Pure Mathematics modules combine the work of some of the world’s greatest thinkers, while Applied Mathematics addresses real-world problems in biology, computing, climate science and finance. Flexible options enable you to explore in depth your love of mathematics, while studying other subjects you enjoy. Optional modules cover the entire range of mathematical sciences, including algebra, number theory, geometry, topology, pure and applied analysis, differential equations, and applications to physical and life sciences.

In the first year there are eight core modules (75% of normal load), in the second year: five core modules plus essay (55% of normal load) and third year: no core modules, but do at least 50% maths. The remaining modules can be chosen from mathematics or one of many subjects.

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 1 and Term 2. Term 3 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, lecture modules are accompanied by weekly support classes. Your personal tutor provides a further layer of learning and pastoral support.

Contact hours

Typical contact hours across lectures, seminars, supervisions etc: 18 hours/week during Term 1 and Term 2 (15 hours of lectures and 3 hours of supervisions, problem classes and tutorials).

Class size

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

Most modules are assessed by 85% exam and 15% homework, or by 100% exam. The Second Year Essay, Third Year Essay are assessed on the basis of an essay/dissertation and oral presentation.

Years 1, 2 and 3 are weighted 10:30:60.

We encourage students to consider spending Year 3 at one of 23 European partner universities in Belgium, France, Germany, Italy, Malta, The Netherlands, Portugal, Spain and Switzerland.

After Year 2, 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). The maths department is unfortunately unable to help with finding such placements.

A level: A*A*A + STEP (grade 1) or A*A*A* or A*A*AA including an A* in both Mathematics and Further Mathematics

  • IB: 39 + STEP (grade 1) ) with three 6s at Higher Level OR 39 with 7,6,6 at Higher Level to include 6 in Higher Level Mathematics

You will also need to meet our English Language requirements.

  • Applicants are encouraged to sit either the Mathematics Admissions Test (MAT), or the Test of Mathematics for University Admissions (TMUA). Students doing particularly well in either test may receive a reduced offer.
  • Contextual data and differential offers: Warwick may make differential offers to students in a number of circumstances. These include students participating in the Realising Opportunities programme, or who meet two of the contextual data criteria. Differential offers will be one or two grades below Warwick’s standard offer.
  • Access Courses: Access to HE Diploma (QAA-recognised) including appropriate subjects with distinction grades in level 3 units and grade A* in A level Mathematics or equivalent. Offers will also typically include a requirement in both a STEP paper and A level Further Mathematics.
  • Warwick International Foundation Programme (IFP) 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). For full details of standard offers and conditions visit the IFP website.
  • We welcome applications from students with other internationally recognised qualifications. For more information please visit the international entry requirements page.
  • Taking a gap year Applications for deferred entry welcomed.

    Interviews 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.

    Open Days All students who have been offered a place are invited to visit. Find out more about our main University Open Days and other opportunities to visit us.

Year 1
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.

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.

Maths by Computer

By the end of this module you will find the computer to be a tool that can aid you throughout your life as a mathematician and, in particular, in many modules you will take at Warwick. You will be shown how the computer may be used, throughout all of mathematics, to enhance understanding, make predictions and test hypotheses. Using the software tool ‘Matlab’, you will learn how to graph functions and study vectors and matrices graphically and numerically.

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.


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.

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.

Analysis I/II

Analysis is the rigorous study of calculus. In this module there will be 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. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity'?


If you’ve covered mathematical modules MA131 and MA132, this 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 co-efficients), and examine theoretical topics including independence of events and conditional probabilities. Using Bayes’ theorem and Simpson’s paradox, 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-Schwartz inequalities.

Year 2
Multivariable Calculus

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. The module will review line and surface integrals, introduce div, grad and curl and establish the divergence theorem.

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 this module, you will learn methods to prove that every continuous function can be integrated, and prove the fundamental theorem of calculus. You will discuss how integration can be applied to define some of the basic functions of analysis and to establish their fundamental properties. You will develop a working knowledge of the construction of the integral of regulated functions, study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions, and use the concept of norm in a vector space to discuss convergence and continuity there. This will equip you with a working knowledge of the construction of the integral of regulated function.

Algebra II: Groups and Rings

This course focuses on developing your understanding and application of the theories of groups and rings, improving your ability to manipulate them. Some of the results proved in MA242 Algebra I: Advanced Linear Algebra for abelian groups are true for groups in general. These include Lagrange's theorem, which says that the order of a subgroup of a finite group divides the order of the group. 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.

Second Year Essay

This module is made up of an essay and presentation. You will be given the opportunity of independent study with guidance from a Personal Tutor. It will provide you with an opportunity to learn some mathematics directly from books and other sources. It will allow you to develop your written and oral exposition skills. You will be able to develop your research skills, including planning, use of library and of the internet.

Selection of optional modules that current students are studying
  • Combinatorics
  • Experimental Maths
  • Games Decisions and Behaviour
  • Introduction to Number Theory
  • Metric Spaces
  • Programming for Scientists
  • Theory of ODEs
  • Plus options from other departments such as: Design of Information Structures (Computer Science), Foundations of Finance (WBS), and Introduction to Astronomy (Physics)

Our graduates have gone on to work for organisations including: AIG, BAE systems, Centrica, Derivation Software, PwC.

Examples of our graduates’ job roles include: Actuarial Associate, Computer Games Developer, Cryptographer, Investment Analyst, Operational Researcher.


"My goal is to pursue a challenging, rewarding, high impact career."

"I joined Warwick because it was progressive, with a very inclusive community. Mathematics offered a wider range of modules than other universities, with opportunities to study across many disciplines.

My advice for any potential applicants would be to exploit the fact that Maths is the cornerstone for half of the disciplines across the University. You should also engage with people outside the Maths department and gain important skills in the various societies on offer.

I knew I ultimately wanted to work in the public or charity sector, and the careers department gave me support in determining the necessary skills. As soon as I graduated, I felt prepared to take my place on the Civil Service Fast Stream."

Alexander Brush - Civil Service Fast Streamer (Finance)

Studied 'Mathematics' - Graduated 2016

A level: A*A*A + STEP (grade 1) or A*A*A* or A*A*AA including an A* in both Mathematics and Further Mathematics

IB: 39 + STEP (grade 1) ) with three 6s at Higher Level OR 39 with 7,6,6 at Higher Level to include 6 in Higher Level Mathematics


Degree of Bachelor of Science (BSc)

3 years full time

Start Date

24 September 2019

Location of study
University of Warwick, Coventry

Tuition fees
Find out more about fees and funding

Additional costs

There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course.

This information is applicable for 2019 entry.

Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.

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