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Discrete Mathematics MEng (G4G3)

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Find out more about our Discrete Mathematics MEng at Warwick

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G4G3

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Master of Engineering (MEng)

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4 years full-time

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26 September 2022

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Department of Computer Science

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University of Warwick

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Discrete Mathematics (MEng) 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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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.

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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.

Metric Spaces

This module lays the basis for many subsequent mathematically-inclined modules, and it is concerned with fundamental notions of distances, measuring and continuity. Making these foundations into a consistent theoretical framework has kept many great mathematicians busy for many centuries, and in this module you walk in their footsteps.

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.

Combinatorics II

This module expands your knowledge about reasoning and working with discrete structures, and moves you to more advanced topics beyond graphs. In particular, you will learn about partially ordered sets, matroids and set systems. This will enable you to see and appreciate the role of combinatorial reasoning in a broader context of mathematics and computer science.

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.

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Professional Skills
Functional Programming
Visualisation
Computer Security
Logic and Verification
Groups and Rings
Combinatorial Optimisation
Introduction to Number Theory
Stochastic Processes
Introduction to Mathematical Statistics

In the fourth year, the following optional modules may be of interest:

Advanced Topics in Algorithms and Complexity
Quantum Computing
Agent Based Systems
Algorithmic Game Theory
Graph Theory
Advanced Topics in Data Science

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).

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Find out more about fees and funding.

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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 or study abroad will pay reduced tuition fees for their third year.

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