Mathematics (MMath) (FullTime, 2019 Entry)
MATHEMATICS (MMath)
Fulltime 2019 entry
The fouryear MMath shares the same core as our BSc but enables you to explore in greater depth areas of interest, both through specialized fourthyear modules and via a substantial Research or Mathsin Action project.
This challenging degree offers unparalleled flexibility. You will be taught by worldleading researchers in a supportive environment. Our graduates are rigorous thinkers with advanced analytical, problem solving and computing skills that can be applied across many career settings.
Pure Mathematics modules combine the work of some of the world’s greatest thinkers, while Applied Mathematics addresses realworld 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.
1st year: 8 core modules (75% of normal load), 2nd year: 5 core modules plus essay (55% of normal load) and 3rd year: no core, but do at least 50% maths. The remaining modules can be chosen from mathematics or one of many subjects.
Students must do at least 75% maths each year.
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 onehour 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.
Class size
Lectures vary from 10 to 400. Supervisions and tutorials are typically in groups of five.
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).
Most modules are assessed by 85% exam and 15% homework, or by 100% exam. The Second Year Essay, Third Year Essay, and the MMath Project are assessed on the basis of an essay/dissertation and oral presentation.
Weighted 10:20:30:40
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

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 (QAArecognised) 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 page.
 We welcome applications from students with other internationally recognised qualifications. For more information please visit the international entry requirements page.

Further Information

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. We want to make our admissions process as straightforward as possible, so find out more about how to make an application, alongside the latest entry requirements.
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 firstorder equations, linear secondorder equations and coupled firstorder linear systems with constant coefficients, and solutions to differential equations with oneand twodimensional 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 vectorvalued 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.
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 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 and 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'?
Probability A & B
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 coefficients), 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 covariance, including Chebyshev’s and CauchySchwartz inequalities.
Year 2
Vector Analysis
The first part of the module provides an introduction to vector calculus. After a brief review of line and surface integrals, div, grad and curl are introduced and followed by the two main results, namely, Gauss' Divergence Theorem and Stokes' Theorem. The second part of the module introduces you to the rudiments of complex analysis leading up to the calculus of residues. You will be taught to work with functions of two or three variables and vector fields. You will see the theorems of Gauss and Stokes as generalisations of the fundamental theorem of calculus to higher dimensions.
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 OrbitStabiliser Theorem, the Chinese Remainder Theorem, and Gauss’ theorem on unique factorisation in polynomial rings.
Differentiation
There are many situations in pure and applied mathematics where the continuity and differentiability of a function f: Rn → Rm 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 singlevariable calculus. You will also study norms on infinitedimensional vector spaces and some applications. By the end of this module you will have a basic working knowledge of higherdimensional calculus.
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
Entry Requirements
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
UCAS Code
G103
Award
Degree of Bachelor of Science (BSc)
Duration
4 years fulltime
Course start date
September 2019
Location of study
University of Warwick, Coventry
Tuition fees
Find out more about fees and funding
Other course 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.