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Discrete Mathematics MEng (UCAS G4G3)

General entry requirements

A levels

A*A*A to include A* in Mathematics or Further Mathematics. Offers normally exclude General Studies and Critical Thinking at A level.

IB

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


BTEC

We welcome applications from students taking BTECs alongside A level Mathematics.

Applications are considered on an individual basis and subjects with overlapping curricula will only be counted once.


International qualifications


Language requirements

All applicants have to meet our English Language requirements. If you cannot demonstrate that you meet these, you may be invited to take part in our Pre-sessional English course at Warwick.


Frequently asked questions

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 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

This course draws on areas of both computer science and mathematics. You will acquire skills in software engineering, combinatorial analysis, formal proof and algorithmic analysis. Regular individual and group projects will consolidate what you have learned by allowing you to apply it to practical problems.

Your learning experiences throughout the course will enable you to both analyse and solve problems in an abstract sense, and realise solutions through computer software. These abilities, alongside transferable skills in communication, planning, and self-organisation are highly valued by employers.

By studying the four-year MEng, you have the flexibility in your final year to choose optional modules, tailoring the degree to your interests.


Study abroad

You can spend a year at one of our partner institutions overseas.

We have an established exchange programme with the Hong Kong University of Science and Technology, which provides opportunities for our students to experience teaching and learning at another world-leading institution.

In addition to benefitting from a rich cultural experience, students returning from studying overseas exhibit an international profile that is attractive to potential employers.

Core modules

Your first year will establish the foundations of Discrete Mathematics and its applications, covering proof, formal arguments, rigour and calculations, as well as mathematical reasoning, combinatorial analysis and discrete structures.

In your second year, you will develop a rigorous understanding of the subject's theoretical basis, which will prepare you for later specialisation.

In your third year, you will work alongside academics on an individual project as well as focusing on applications of Discrete Mathematics to Computer Science, and completing advanced modules on algorithms and computation.

In your fourth year, you will have the flexibility to choose optional modules, tailoring the degree to your interests.

In each year of their course, students are expected to study a core group of modules and to make up the required normal load for the year by choosing a set of optional modules. There is a choice of optional modules available and there may be requirements to be satisfied by the choices: that a minimum number be chosen from a specific list.


Year One

Programming for Computer Scientists

On this module, whatever your starting point, you will begin your professional understanding of computer programming through problem-solving, and fundamental structured and object-oriented programming. You will learn the Java programming language, through practical work centred on the Warwick Robot Maze environment, which will take you from specification to implementation and testing. Through practical work in object-oriented concepts such as classes, encapsulation, arrays and inheritance, you will end the course knowing how to write programs in Java, and, through your ability to analyse errors and testing procedures, be able to produce well-designed and well-encapsulated and abstracted code.

Design of Information Structures

Following on from Programming for Computer Scientists, on the fundamentals of programming, this module will teach you all about data structures and how to program them. We will look at how we can represent data structures efficiently and how we can apply formal reasoning to them. You will also study algorithms that use data structures. Successful completion will see you able to understand the structures and concepts underpinning object-oriented programming, and able to write programs that operate on large data sets.

Discrete Mathematics and its Applications 1

On this foundation module, you’ll learn the basic language, concepts and methods of discrete mathematics, while develop your appreciation of how these are used in algorithms and data structures. By the end, you should be able to appreciate the role of formal definitions, mathematical proofs and underlying algorithmic thinking in practical problem-solving. You’ll acquire knowledge of logic, sets, relations and functions, and learn summation techniques (manipulations and finite calculus) and concepts including asymptotics and the big-O notation to prepare you for more advanced techniques in computer science.

Discrete Mathematics and its Applications 2

During this module, you will build on your foundations in discrete mathematics through the study of concepts such as discrete probability and number theory; learning how to apply these methods in problem-solving. By the end of your course, you’ll be able to use algebraic techniques (including linear and matrix algebra) to analyse basic discrete structures and algorithms, and understand the importance of asymptotic notation, and be able to use it to analyse asymptotic performance for some basic algorithmic examples. Also, you will study the properties of graphs and related discrete structures, and be able to relate these to practical examples.

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.

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'?

Sets and Numbers

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.

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 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 One

Combinatorics

Algorithmic Graph Theory

This project-based module will provide you with experience of designing, developing and implementing a significant project, under supervision. From submission of the outline and detailed specification, you will produce regular progress reports, until presenting your final results. This is an excellent opportunity to develop important professional business skills, including independent learning, self-discipline, organisation and time management. Providing you with experience of undertaking a significant individual design and development exercise from conception through to design, implementation and delivery.

Formal Languages

You will gain a fundamental understanding of formal languages and how the Chomsky hierarchy classifies them. You’ll study techniques for exploring the regularity of languages using closure properties and pumping lemmas, whilst also considering automata models, alongside the notion of computability. These concepts are central to computer science, and completion will see you able to specify between, and translate, various forms of formal language descriptions. You’ll learn methods of lexical analysis and parsing, and be able to argue whether a formal language is regular or context free. The teachings will discuss Turing machines and philosophical concepts such as decidability, reducibility and the halting problem.

Algorithms

Data structures and algorithms are fundamental to programming and to understanding computation. On this module, you will be using sophisticated tools to apply algorithmic techniques to computational problems. By the close of the course, you’ll have studied a variety of data structures and will be using them for the design and implementation of algorithms, including testing and proofing, and analysing their efficiency. This is a practical course, so expect to be working on real-life problems using elementary graph, greedy, and divide-and-conquer algorithms, as well as gaining knowledge on dynamic programming and network flows.

Mathematical Analysis 3

Norms, Metrics and Topologies

Year Three

Discrete Mathematics Project

Through this practical module, you’ll gain experience in undertaking a significant individual design and development exercise in discrete mathematics, from conception through to design, implementation and delivery. Starting with the selection of a topic and location of a suitable supervisor, you’ll be responsible for regular progress reports, and a presentation of your final results alongside a detailed written report. In addition to enhancing your technical knowledge, this process will help you develop important skills such as self-discipline, time management, organisation and professional communications.

Complexity of Algorithms

Are you ready for a challenge? In this module, you’ll learn to analyse the intrinsic difficulty of various computational challenges, and to specify variations that may be more tractable. This will require you to learn notions of the complexity of algorithms, and what makes some computational problems harder than others. You’ll undertake a close study of what makes an algorithm efficient, and study various models of computation, in particular, models of classical deterministic and non-deterministic computations.

Approximation and Randomised Algorithms

On this module, you will gain an introductory understanding of approximation and randomised algorithms, which often provide a simple, viable alternative to standard algorithms. You’ll learn the mathematical foundations underpinning the design and analysis of such algorithms. Whilst gaining experience of using suitable mathematical tools to design approximation algorithms and analyse their performance. You’ll also learn techniques for designing faster but weaker algorithms for particular situations, such as large running times. You can expect to cover important concepts, including linearity of expectation, Chernoff bounds, and deterministic and randomised rounding of linear programs.

Measure Theory

Probability Theory

Year Four

In the fourth year you will select from an extensive range of both Computer Science and Mathematics optional modules, as well as some options from other departments.


Optional modules

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

  • Experimental Mathematics
  • Introduction to Geometry
  • Geometry and Motion
  • Introduction to Abstract Algebra
  • Probability
  • Professional Skills
  • Functional Programming
  • Visualisation
  • Computer Security
  • Advanced Linear Algebra
  • Stochastic Processes

The precise modules available to students may depend on module prerequisites (i.e. for some module choices it is necessary for you to have taken a particular module in a previous year).

Assessment

Your performance on most modules will be assessed by a combination of coursework and written examination.

The coursework may be individual or group work involving programming, research, writing and presentation.

The final-year project work is fully assessed by a presentation and project reports. Each year contributes to the final degree classification, typically in the ratio of 10:20:35:35 for a MEng degree.

Teaching

Our courses offer a balance of core material delivered through lectures, small-group seminars and hands-on laboratory sessions. Approximately a quarter of your time is spent in timetabled classes, with the remainder being used for private study, completing assignments and projects, and practical work in the dedicated computing laboratories, which are open 24/7.


Typical contact hours

On average, a student will have 20 hours of contact time a week, which should be supplemented by 20 hours of independent study.

These contact hours will include between 2-3 hours of lectures for each module, each week, and 1-2 hours of labs and seminars for each module, each week.

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 2021, your annual tuition fees will be £9,250. In the future, these fees might change for new and continuing students.


2+2 course fees

If you are a home student enrolling in 2021 for a 2+2 course through the Centre for Lifelong Learning, your annual tuition fees will be £6,750. 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 UCAS.

Undergraduate fees

If you are an EU student enrolling in 2021, the tuition fee will be charged in line with government policy and therefore the same as Overseas Tuition Fee rates.

For details please see Overseas students section below.

Undergraduate fees

If you are an overseas or EU student enrolling in 2021, your annual tuition fees will be as follows:

  • Band 1 – £21,220 per year (classroom-based courses, including Humanities and most Social Science courses)
  • Band 2 – £27,060 per year (laboratory-based courses, plus Theatre and Performance Studies, Economics, and courses provided by Warwick Business School, with exceptions)

Fees for 2022 entry have not been set. We will publish updated information here as soon as it becomes available, so please check back for updates about 2022 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 from 2021 entry will be classified as Home or EU/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.


Additional course costs

There may be extra costs related to your course for things such as stationery, books, materials and field trips.


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.

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

Find out more information on our international scholarship pages.


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 2021

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. This new scheme will offer international fee-paying students 250 tuition fee discounts ranging from full fees to awards of £13,000 to £2,000 for the full duration of your Undergraduate degree course.

Find out more about the Warwick Undergraduate Global Excellence Scholarship 2021.

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.

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.

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.

Tuition Fee Loan

For the 2020 academic year, you can apply for a Tuition Fee Loan to cover your tuition fees if you’re from an EU country. 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.

Help with living costs

For the 2020 academic year, you may be eligible for help with your living costs if you’ve lived in the UK for more than 5 years before the first day of the first academic year of your course.

If you are starting a course on or after 1 August 2021, you must have settled or pre-settled status under the EU Settlement Scheme to get student finance.

Find out more about government student loans for EU students.

Repaying your loans

You will repay your loan or loans gradually once you are working and earning above a certain amount (from April 2021 the repayment threshold is £27,295 and is expected to rise each year). 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.

Placements and work experience

We provide support for students wanting to spend a year in industry by promoting opportunities, hosting departmental careers fairs and offering one-to-one sessions with our departmental careers advisor.

Intercalated year students are supported by their personal tutor and our Industrial Liaison Team during their year in industry. Students working in the UK are visited by academic representatives to review their development during the year.


Your career

Graduates from the Department of Computer Science in the past have entered careers in these industries and companies:

Automobiles and Aviation

  • British Airways
  • Ford Motor Company
  • Jaguar Land Rover

Computer Security

  • BAE
  • GCHQ

Computer Systems

  • ARM
  • Citrix
  • IBM

Consulting:

  • Accenture
  • Deloitte
  • EY
  • KPMG

Consumer goods

  • M&S
  • Tesco
  • Unilever

Finance

  • Barclays
  • Bloomberg
  • Goldman Sachs
  • JPMorgan
  • Morgan Stanley

Research

  • CERN
  • Mintel
  • The University of Warwick

Software Development

  • Apple
  • Amazon
  • D.E.Shaw
  • Microsoft
  • Google
  • Sega

They have pursued roles such as:

  • Software engineer
  • Systems analyst
  • Investment analyst
  • Web designer/developer
  • Business analyst
  • Actuary
  • Economist and statistician
  • Computer science researcher
  • University academic
  • Teacher
  • Entrepreneur
  • Start-up owner

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:

  • Computing Your Career
  • Technology in Professional Services
  • Warwick careers fairs throughout the year
  • Working in the Computer Games industry
  • Computer Science Alumni Event

Find out more about careers support at Warwick.

Computer Science at Warwick

What are computers capable of? How do we use them to solve major world problems? What are their limitations?

Computer Science at Warwick offers you a community of excellence across the breadth of computer science. Join like-minded thinkers and friends who relish the challenges of shaping future technology.

You will study the theoretical foundation in established areas of the discipline. You will then apply your learning to industrially relevant problems, developing technical and transferable skills which will position you excellently for your future career.

Find out more about us on our website


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