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MSc Discrete Mathematics and its Applications

Why we're great

  • Be part of our small but influential department
  • Take the opportunity to work alongside well-published world leaders in their individual specialisms
  • Our specialists facilities give you the chance to gain real-world application in your area of expertise

Course options2016-17

Duration: 1 year
Start month: October
Location: Colchester Campus
Based in: Mathematical Sciences
Fee (Home/EU): £5,950
Fee (International): £14,500

Course enquiries

Telephone 01206 872719
Email pgadmit@essex.ac.uk

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About the course

Discrete mathematics underlies some vital situations in practical life.

Game theory, with roots in mathematics, statistics and economics, is routinely applied to understanding and predicting human behaviour. Problems of protection of digital information against piracy are closely related to aspects of set systems. And the RSA cryptosystem, used on computers all over the world, depends on classical results of number theory.

Our MSc Discrete Mathematics and its Applications covers many aspects of discrete mathematics and their potential use in practice, and provides you with options in:

  • Optimisation
  • Machine learning
  • Data mining
  • Statistics

Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

Our Department of Mathematical Sciences has an international reputation in many areas including semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.

Specialist facilities

  • Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
  • We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple
  • We host regular events and seminars throughout the year
  • Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

Your future

Key employability skills you gain from this course include analytic reasoning, problem solving, techniques of discrete mathematics and an understanding of application areas of these techniques, algorithm design and implementation, and data analysis.

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

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Example structure

Postgraduate study is the chance to take your education to the next level. The combination of compulsory and optional modules means our courses help you develop extensive knowledge in your chosen discipline, whilst providing plenty of freedom to pursue your own interests. Our research-led teaching is continually evolving to address the latest challenges and breakthroughs in the field, therefore to ensure your course is as relevant and up-to-date as possible your core module structure may be subject to change.

For many of our courses you’ll have a wide range of optional modules to choose from – those listed in this example structure are, in many instances, just a selection of those available. Our Programme Specification gives more detail about the structure available to our current postgraduate students, including details of all optional modules.

Year 1

How do standard coding techniques in computer security work? And how does RSA cryptography work? Examine the principles of cryptography and the mathematical principles of discrete coding. Analsye the concepts of error detection and correction. Understand the algebra and number theory used in modern cryptography and coding schemes.

Can you prove basic results in the theory of graphs? Or deal with basic theory about matchings, like Hall’s theorem? Examine key definitions, proofs and proof techniques in graph theory. Gain experience of problems connected with chromatic number. Understand external graph theory, Ramsey theory and the theory of random graphs.

Mathematics is a tool used in many fields of research, and this module introduces students to techniques and ways of thinking designed to enable them to carry out their own mathematical investigations, or to apply mathematical ideas to an investigation of their own (typically for most students on this module, this will be their Dissertation project). We use the industry standard mathematical software Matlab, although the techniques introduced can also be applied using other software, and we study a range of techniques for numerical computation and processing of data.

How do you apply multivariate methods? Or demographical and epidemiological methods? And how do you apply sampling methods? Study three application areas of statistics – multivariate methods, demography and epidemiology, and sampling. Understand how to apply and assess these methods in a variety of situations.

What do you understand about Bayes’ theorem and Bayesian statistical modelling? Or about Markov chain Monte Carlo simulation? Focus on Bayesian and computational statistics. Understand the statistical modelling and methods available. Learn to develop a Monte Carlo simulation algorithm for simple probability distributions.

Constraint satisfaction is about decision-making. It is about making a large number of decisions, satisfying complex constraints. Constraint techniques have been employed by many companies, including IBM, British Telecom, British Airway. This module will introduce the basic techniques in constraint satisfaction, with emphasis on its applications to real world problems such as logistics and finance. Constraint satisfaction is the core of computer science. Students in artificial intelligence, operations research, computational finance, etc. should all benefit from taking this module.

Evolutionary computation is an exciting area of artificial intelligence that focuses on systematic methods (known as evolutionary algorithms) inspired by Darwinian evolution for getting computers to automatically solve problems starting from a high-level statement of what needs to be done. Evolutionary algorithms are today routinely used to solve difficult problems in industry, medicine, biology, finance, and much more. Evolutionary algorithms can even consistently solve difficult problems which require solutions in the form of computer programs. This is a form of automatic programming that is known as genetic programming. In this module you will learn how to use evolutionary algorithms and genetic programming to solve real-world problems from an international authority in these areas.

What are the main game theory concepts in modern economics? And how do you apply such models in the world today? Understand game theory methodology and learn how to formulate models for various socio-economic phenomena, such as industrial organisation, public goods, bargaining, and labour markets.

Humans can often perform a task extremely well (e.g., telling cats from dogs) but are unable to understand and describe the decision process followed. Without this explicit knowledge, we cannot write computer programs that can be used by machines to perform the same task. “Machine learning” is the study and application of methods to learn such algorithms automatically from sets of examples, just like babies can learn to tell cats from dogs simply by being shown examples of dogs and cats by their parents. Machine learning has proven particularly suited to cases such as optical character recognition, dictation software, language translators, fraud detection in financial transactions, and many others.

How do you formulate financial decision problems mathematically? And how do you identify an appropriate method of solution? Understand the basic models and mathematical methods underlying modern portfolio management. Assess the limitations of these models and learn to correctly interpret your results from calculations.

Can you calculate confidence intervals for parameters and prediction intervals for future observations? Represent a linear model in matrix form? Or adapt a model to fit growth curves? Learn to apply linear models to analyse data. Discuss underlying assumptions and standard approaches. Understand methods to design and analyse experiments.

How do you apply an algorithm or numerical method to a problem? What are the advantages? And the limitations? Understand the theory and application of nonlinear programming. Learn the principles of good modelling and know how to design algorithms and numerical methods. Critically assess issues regarding computational algorithms.

Teaching

  • Core components can be combined with optional modules, to enable you to gain either in-depth specialisation or a breadth of understanding
  • Learn to use LATEX to produce a document as close as possible to what professional mathematicians produce in terms of organisation, layout and type-setting
  • Our postgraduates are encouraged to attend conferences and seminars on a Thursday afternoon

Assessment

  • Courses are assessed on the results of your written examinations, together with continual assessments of your practical work and coursework

Dissertation

  • You will be provided with a list of dissertation titles or topics proposed by staff and it may be possible to propose a project of your own
  • Most dissertations are between 10,000 and 30,000 words in length. However, these are guidelines, not mandatory word counts
  • Close supervision by academic staff

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Qualifications

UK entry requirements

A degree with an overall high 2:2.

International and EU entry requirements

We accept a wide range of qualifications from applicants studying in the EU and other countries. Email pgadmit@essex.ac.uk for further details about the qualifications we accept. Include information in your email about the undergraduate qualification you have already completed or are currently taking.

IELTS entry requirements

IELTS 6.0 overall with a minimum component score of 5.5

If you do not meet our IELTS requirements then you may be able to complete a pre-sessional English pathway that enables you to start your course without retaking IELTS.

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Visit us

Open days

We hold postgraduate events in February/March and November, and open days for all our applicants throughout the year. Our Colchester Campus events are a great way to find out more about studying at Essex, and give you the chance to:

  • tour our campus and accommodation
  • find out answers to your questions about our courses, student finance, graduate employability, student support and more
  • meet our students and staff

If the dates of our organised events aren’t suitable for you, feel free to get in touch by emailing tours@essex.ac.uk and we’ll arrange an individual campus tour for you.

Virtual tours

If you live too far away to come to Essex (or have a busy lifestyle), no problem. Our 360 degree virtual tour allows you to explore the Colchester Campus from the comfort of your home. Check out our accommodation options, facilities and social spaces.

Exhibitions

Our staff travel the world to speak to people about the courses on offer at Essex. Take a look at our list of exhibition dates to see if we’ll be near you in the future.

Applying

You can apply for our postgraduate courses online. You’ll need to provide us with your academic qualifications, as well as supporting documents such as transcripts, English language qualifications and certificates. You can find a list of necessary documents online, but please note we won’t be able to process your application until we have everything we need.

There is no application deadline but we recommend that you apply before 1 July for our taught courses starting in October. We aim to respond to applications within two weeks. If we are able to offer you a place, you will be contacted via email.

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Although great care is taken in compiling our course details, they are intended for the general guidance of prospective students only. The University reserves the right to make variations to the content and method of delivery of programmes, courses and other services, to discontinue programmes, courses and other services and to merge or combine programmes or courses, if such action is reasonably considered to be necessary by the University.

The full procedures, rules and regulations of the University are set out in the Charter, Statues and Ordinances and in the University Regulations, Policy and Procedures.