Mathematics (MMath) (FullTime, 2020 Entry)  course full
Mathematics (MMath)  Course full
 UCAS Code
 G103
 Qualification
 MMath
 Duration
 4 years fulltime
 Entry Requirements
 A level: A*A*A
 IB: 39
 (See full entry
 requirements below)
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 fouryear Mathematics (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.
Our challenging degree will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics. You will be taught by worldleading 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. 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. Many third and fourth year modules offer glimpses of the latest research.
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 75% 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 to include A* in both Mathematics and Further Mathematics
IB: 39 + STEP (grade 1) with 6 in three Higher Level subjects to include Mathematics or 39 with 7, 6, 6 in three Higher Level subjects to include Mathematics
BTEC: Applicants studying a BTEC Level 3 National Extended Certificate alongside ALevel Mathematics and Further Mathematics will be considered on a case by case basis by the department
If you choose to take the Mathematics Admissions Test (MAT) or the Test of Mathematics for University Admissions (TMUA) then, depending on your performance in your test/s, you may be eligible for a reduced offer. For further information, please click here.
Additional requirements: You will also need to meet our English Language requirements.
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 (to a minimum of BBB).
 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 One
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.
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.
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.
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.
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.
Probability
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.
Mathematics by Computer
This course aims to show how the computer may be used, throughout all of mathematics, to enhance understanding, make predictions and test hypotheses. The module will be taught using the Matlab software package. Through using this software tool you will be introduced to the rudiments of computer programming. You will learn how to graph functions, study vectors and matrices graphically and numerically, how to iterate and use iteration to study sequences and series, how to solve algebraic and differential equations numerically and how to study statistical properties of sets of numbers.
Mathematical Analysis
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'?
Year Two
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 singlevariable 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 Riemann integral; understand uniform and pointwise convergence of functions; study complex differentiability (CauchyRiemann equations) and complex power series; study contour integrals, Cauchy's integral formulas and applications.
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.
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.
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.
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.
Year Four
Research Project or MathsinAction Project
As with the third year you will also choose from an extensive range of optional modules, 25% of which can be in subjects other than mathematics from departments across the University.
Examples of optional modules/options for current students
Knot Theory; Fractal Geometry; Population Dynamics  Ecology and Epidemiology; Number Theory; Combinatorics; Experimental Maths; Games Decisions and Behaviour; 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)
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; academics.
UK firms that have employed recent Warwick graduates from Mathematics and Statistics include: Adder Technology; 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; Softwire; Solid Solutions; Sword Apak; Ten10; Xafinity.
Helping you find the right career
Our department has a dedicated professionally qualified Senior Careers Consultant who works within Student Careers and Skills to help you as an individual. Additionally your Senior Careers Consultant offers impartial advice and guidance together with workshops and events, tailored to our department, throughout the year. Previous examples of workshops and events include:
 Careers with Mathematics
 Careers in Data Science and Artificial Intelligence
 Warwick careers fairs throughout the year
 Mathematics at work
 Placement and graduate opportunities at the Government Actuary’s Department
Find out more about our Careers & Skills Services here.
"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 to include A* in both Mathematics and Further Mathematics
IB: 39 + STEP (grade 1) with 6 in three Higher Level subjects to include Mathematics or 39 with 7, 6, 6 in three Higher Level subjects to include Mathematics
BTEC: Applicants studying a BTEC Level 3 National Extended Certificate alongside ALevel Mathematics and Further Mathematics will be considered on a case by case basis by the department
If you choose to take the Mathematics Admissions Test (MAT) or the Test of Mathematics for University Admissions (TMUA) then, depending on your performance in your test/s, you may be eligible for a reduced offer.
Additional requirements: You will also need to meet our English Language requirements.
UCAS code
G103
Award
Master of Mathematics (MMath)
Duration
4 years full time
Start date
28 September 2020
Location of study
University of Warwick, Coventry
Tuition fees
Find out more about fees and funding
Additional course costs
There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course. Students who choose to complete a work placement will pay reduced tuition fees for their third year.
This information is applicable for 2020 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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