Discrete Mathematics BSc (UCAS G190) (2022 Entry)
Learn more about our Discrete Mathematics BSc at Warwick
Discrete Mathematics (BSc) 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 to consolidate what you have learned by applying it to practical problems.
General entry requirements
A levels
A level typical offer
A*A*A to include A* in Mathematics or Further Mathematics.
A level additional information
Offers normally exclude General Studies and Critical Thinking at A level.
A level contextual offer
We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is A*AB including A* in Mathematics or 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
IB typical offer
39 with 6, 6, 6 in three Higher Level subjects to include 6 in Higher Level Mathematics ('Analysis and Approaches' only)
IB contextual offer
We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is 38 including 6 in Higher Level 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 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 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
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.
Study abroad
You can spend a year at one of our partner institutions overseas.Link opens in a new window
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 each year of your course, you are expected to study a core group of modules and 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.
Calculus
Calculus is the mathematical study of continuous change. 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.
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’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 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-Schwarz inequalities. The module ends with a discussion of the celebrated Central Limit Theorem.
Year Two
Combinatorics
In this module you learn the basics about discrete structures that lie at the heart of many real-world problems. A key notion is that of a graph, which is an abstract mathematical model for a network, such as a street network, a computer network, or a network of friendships. You learn to argue about these structures formally, and to prove interesting theorems about them. This will train your ability to think outside of the box."
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.
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.
Optional modules
- Professional Skills
- Functional Programming
- Visualisation
- Computer Security
- Logic and Verification
- Groups and Rings
- Combinatorial Optimisation
- Introduction to Number Theory
- Metric Spaces
- Stochastic Processes
- Introduction to Mathematical Statistics
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 10:30:60 for a BSc 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 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.
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.
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.
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.
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.
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
- You have Settled Status (see further details on Settled Status)Link opens in a new window
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 loanLink opens in a new window.
Placements and work experience
We provide support for students wanting to spend a year in the 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 the 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
- 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 WarwickLink opens in a new window.
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.
We play a leading role in five interdisciplinary research centres and are one of the founding partners of the prestigious Alan Turing Institute for Data Science. This institute – a £42 million collaboration between UK leaders in Computer Science and Mathematics – will shape policy in the UK and stimulate research activity in data science for decades to come, creating unique opportunities for all of our students.
Find out more about us on our websiteLink opens in a new window
Our courses
- Computer Science (BSc)
- Computer Science (MEng)
- Computer Science with Business Studies (BSc)
- Computer Systems Engineering (BEng)
- Computer Systems Engineering (MEng)
- Discrete Mathematics (BSc)
- Discrete Mathematics (MEng)
Related degrees
Life at Warwick
Within a close-knit community of staff and students from all over the world, discover a campus alive with possibilities. A place where all the elements of your student experience come together in one place. Our supportive, energising, welcoming space creates the ideal environment for forging new connections, having fun and finding inspiration.
Find out how to apply to us, ask your questions, and find out more.
Warwick Accommodation
Finding the right accommodation is key to helping you settle in quickly.
We have 12 self-catering undergraduate halls of residence on campus.
Our student property management and lettings agency manages more than 8,000 rooms both on and off campus, and provides advice to all full-time undergraduates.
Our campus
You won't be short of ways to spend your time on campus - whether it's visiting Warwick Arts Centre, using our incredible new sports facilities, socialising in our bars, nightclub and cafés, or enjoying an open-air event. Or if you need some peace and quiet, you can explore lakes, woodland and green spaces just a few minutes’ walk from central campus.
Food and drink
We have lots of cafés, restaurants and shops on campus. You can enjoy great quality food and drink, with plenty of choice for all tastes and budgets. There is a convenience store on central campus, as well as two supermarkets and a small shopping centre in the nearby Cannon Park Retail Park. Several of them offer delivery services to help you stay stocked up.
And don't miss our regular food market day on the Piazza with tempting, fresh and delicious street food. Soak up the atmosphere and try something new, with mouth-watering food for all tastes.
Clubs and societies
We currently have more than 300 student-run societies.
So whether you’re into films, martial arts, astronomy, gaming or musical theatre, you can instantly connect with people with similar interests.
Or you could try something new, or even form your own society.
Sports and fitness
Staying active at Warwick is no sweat, thanks to our amazing new Sports and Wellness Hub, indoor and outdoor tennis centre, 60 acres of sports pitches, and more than 60 sports clubs.
Whether you want to compete, relax or just have fun, you can achieve your fitness goals.
Studying on campus
Our campus is designed to cater for all of your learning needs.
You will benefit from a variety of flexible, well-equipped study spaces and teaching facilities across the University.
- The Oculus, our outstanding learning hub, houses state-of-the-art lecture theatres and innovative social learning and network areas.
- The University Library provides access to over one million printed works and tens of thousands of electronic journals
- Three Learning Grids offering you flexible individual and group study spaces.
Travel and local area
Our campus is in Coventry, a modern city with high street shops, restaurants, nightclubs and bars sitting alongside medieval monuments. The Warwickshire towns of Leamington Spa and Kenilworth are also nearby.
The University is close to major road, rail and air links. London is just an hour by direct train from Coventry, with Birmingham a 20-minute trip. Birmingham International Airport is nearby (a 20-minute drive).
Wellbeing support and faith provision
Our continuous support network is here to help you adjust to student life and to ensure you can easily access advice on many different issues. These may include managing your finances and workload, and settling into shared accommodation. We also have specialist disability and mental health support teams.
Our Chaplaincy is home to Chaplains from the Christian, Jewish and Muslim faiths. We provide regular services for all Christian denominations and a Shabbat meal every Friday for our Jewish students. There is also an Islamic prayer hall, halal kitchen and ablution facilities.
How to apply
Learn more about our application process.
Key dates
Key dates for your application to Warwick.
Writing your personal statement
Make an impression and demonstrate your passion for your course.
After you've applied
Find out how we process your application.
Our Admission Statement
Read Warwick's Admission Statement
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Talk to us
Join us at a live event. You can ask about courses, applying to Warwick, life at Warwick, visas and immigration, and more.
Warwick Experience
Take a virtual, student-led campus tour. Then join an interactive panel session, where you can hear from and chat to our current students and staff.
Student blogs
Explore our student blogs in OurWarwick. You can read about campus life from students themselves, and register to post questions directly to students.
Explore campus with our virtual tour
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- Watch student videos
- View 360 photography and drone footage
- Learn about facilities and landmarks
Explore our campus virtually through our 360 campus tour now
Come to an Open Day
Don’t just take it from us, come and see for yourself what Warwick is all about. Whether it's a virtual visit or in-person, our University Open Days give you the chance to meet staff and students, visit academic departments, tour the campus and get a real feel for life at Warwick.
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