Mathematical Sciences Undergraduate Programmes

Mathematical Sciences Undergraduate Programmes

Mathematics at Durham

Research

Mathematical Sciences is a thriving, friendly department of around 60 permanent staff with an annual intake of about 150 Single Honours undergraduates plus many Joint Honours students. The department is situated on the Science Site to the south of the City centre, within easy reach of all Durham City Colleges and is close to the University Library.

At Durham you will be taught by some of the top international leaders in mathematical research and have the opportunity to see many important areas of cutting edge mathematical thought and application during your degree. The Department of Mathematical Sciences is one of the strongest research units in the UK -- in the most recent UK assessment of research outputs the Department was rated extremely highly on both the Impact and the Intensity of its research(see www.durham. ac.uk/mathematical.sciences/research/ref2014/ for more details). Durham mathematicians are actively engaged with a wide variety of research areas, including Pure Mathematics, Mathematical Physics, Numerical Analysis, Probability and Statistics, and this leads to a vibrant set of choices in the later years of your studies. A list of staff, together with their research interests, may be found at www.durham.ac.uk/mathematical. sciences

We offer a balanced honours degree programme which allows choice from a wide spectrum of pure mathematics, applied mathematics (including mathematical physics) and statistics. Our courses can also be taken in combination with other subjects through the Natural Sciences programme, a route followed by around 180 students per year.

As a Durham graduate you will leave the University having acquired much more than a simple technical proficiency in your subject. You will have been exposed to the elegance of mathematics as an intellectual discipline and to its enormous power as a tool for solving scientific problems, and encouraged from a very early stage to take pride in the presentation of your work.

Your course will help you to produce logical arguments and express yourself precisely, and to actively enjoy solving problems. These are qualities which will make you attractive to potential employers.

Left: Science Site, Durham University

Durham Cathedral, Durham City

Durham Castle, Durham City

The Durham University Difference

Why Durham University?

Durham University offers you a unique opportunity to experience the history, tradition and quality of one of the oldest and highest ranking universities in England.

Since its foundation in 1832 Durham University has flourished and cemented a place of distinction both nationally and internationally.

Durham City has captured the admiration of writers and artists for centuries, and as the only university in England to occupy a World Heritage Site (Durham Cathedral and Castle), it continues to capture the attention of travellers from all over the world.

Located in the small and ancient City of Durham in the heart of North East England you will have the opportunity to experience life in a traditional British University.

Maths Graduation, Palace Green

The Collegiate experience College life is a big part of what makes Durham so different from almost anywhere else. Many of our students say that the College system is one of the best aspects of University life. Ask Durham students about living and studying in Durham and they’re sure to mention their College, even years after they’ve left!

With their variety of character, location, age and size, it is an essential aspect of the student experience to carefully research which College would provide the best match for your personality and non-academic interests. Every College has its own Community, each with its own bar and dining facilities, TV room, laundry services, sports teams and facilities, clubs and Societies.

Getting involved in College life is a wonderful way to meet new people. We try to take your College personal preference into account at the time of your application; however, placement in a particular College is ultimately based on availability. www.durham.ac.uk/colleges www.durham.ac.uk/undergraduate/ accommodation/choosing Take a virtual College tour: www.durham.ac.uk/tour

Our Degrees BSc Honours Mathematics 3 years, G100

The three year BSc Mathematics programme gives you the opportunity to study a wide range of mathematics topics, with a particularly large choice of modules in your final year. It will prepare you for many graduate jobs as well as for further study including the PGCE and many MSc programmes in mathematics or related subjects.

Our programme covers pure, applied, statistics & probability. You will cover the background to all areas in year one, while in year two you can begin to specialise, allowing you to choose to fully specialise in one area choosing from a broad range of modules in year three. In your final year, you will develop your research and communication skills in a double project module.

Master of Mathematics 4 years, G103

The four year MMath programme should be your choice if you wish to go on to do research or to enter other careers where you will use mathematics professionally. In comparison to the BSc Mathematics (G100), this programme allows you to study both more advanced and a broader range of topics.

In the third year you choose up to six mathematics modules from a wide selection. In the fourth year you choose four optional modules together with a final year double module project.

This project is more in depth and at a very high level. It gives you the opportunity to apply the mathematical knowledge you have gained during your degree, and allows you to study in depth your chosen topic.

Master of Mathematics (European Studies) 4 years, G101

This four year programme is based on the four year MMath (G103) programme, with two years in Durham followed by a year spent studying mathematics in an EU country (see Study Abroad) before returning to Durham for the final year.

Unlike the BSc Honours Mathematics (with year abroad) programme, the year abroad is a replacement of year three in Durham but your marks do contribute towards your degree classification. Other than the year abroad, the only difference from the MMath programme is the requirement to take an appropriate language module in year one.

This programme is available to students admitted initially to the G100 or G103 programme with the transfer to G101 typically taking place after successful completion of year 1 and after having demonstrated competency in the relevant language (normally the equivalent of at least grade B at the A-level and successful completion of the first year language module).

BSc Honours Mathematics (with year abroad) 4 years, G104

This four year programme is based on the three year BSc Mathematics (G100) programme, with two years in Durham followed by an extra year spent studying mathematics in a foreign country before returning to Durham for the final year.

You must successfully complete the year abroad and submit a written report, but your marks do not contribute towards your degree classification.

Other than the additional year abroad, the only difference from the three year programme is the requirement to take an appropriate language module in year one.

This programme is available to students admitted initially to the G100 or G103 programme with the transfer to G104 typically taking place after successful completion of year 1 and after having demonstrated competency in the relevant language (normally the equivalent of at least grade B at the A-level and successful completion of the first year language module).

BSc Honours Mathematics (with placement) 4 years, G108

Like BSc Honours Mathematics (with year abroad), this four year programme is based on the three year BSc G100 programme, with the third year spent in an industrial or business position.

This programme is available to students admitted initially to the G100 or G103 programme with the transfer to G108 typically taking place after successful completion of year 1.

"The teaching at Durham, for me, is a highlight. I find lectures to be informative and entertaining.They also come with lots of supplementary material to allow you to learn in the best way possible for you."

Jordan Moore, MMath student

Our Degrees BSc or MSci Honours in Natural Sciences 3 or 4 years FGCO

The popular Natural Sciences programme offers you the opportunity to study mathematics modules in conjunction with other subjects.

There are various three and four year combinations. It is possible to take Mathematics as part of a Joint Honours degree (that is with one other subject) as well as taking Mathematics as part of a more general Natural Sciences degree (which might involve more than one other subject). To take Joint Honours degrees involving Mathematics we recommend that you take the three mathematics modules (Calculus and Probability, Linear Algebra, and Analysis) in your first year. This will maximise your Mathematical options in subsequent years.

The Joint Honours degrees involving Mathematics are with Biology, Chemistry, Computer Science, Earth Sciences, Economics, Geography, Philosophy, Physics and Psychology. Other subject combinations are also possible within Natural Sciences or alternatively Combined Honours in Arts or Social Sciences.

For further details of the Natural Sciences degree programmes, you should consult the Natural Sciences website www.durham.ac.uk/natural.sciences For information about Combined Honours see www.durham.ac.uk/combined.honours

Throughout your degree, you can take up to 4 maths modules each year, with the same choice of modules as on one of our Mathematics programmes. In year 4 of the MSci, you can even choose to study only mathematics.

The main undergraduate prospectus contains details of the choices available along with numbers of applications and standard offers for each course.

Right: Durham City

Our Approach

We set the highest standards in research-led education, linking research and education in distinctive and creative ways.

Lectures and Tutorials

Most of the teaching in mathematics consists of fifty-minute lectures (12 per week on average), supplemented by tutorials. The tutorials, held in small groups in the first year, are informal and provide an opportunity to raise any questions you may have. As a single honours student you will have at least three tutorials per week during each of the first two years. We will monitor your progress carefully. Problems are set in lectures on a weekly basis, and your marked solutions may form the topic for discussion in a tutorial or problems class. You will be encouraged to work with other students, and to make use of the University's library and computing resources.

For most mathematics modules, the assessment is based mostly or entirely on an end of year written examination. Exceptions include Project III, Mathematics Teaching III and Project IV which are assessed via written reports, student presentations & posters.

Staff-Student Relations

We work very hard to ensure good communication between all members of our department. Our staff-student committees meet in each of Michaelmas and Epiphany terms, and we issue a detailed questionnaire for every course. Four undergraduates are observers on our Board of Studies.

Caption Top: Professor Thomas Willmore Sculpture

Assessment

Left: Hyperbolic plane

Successful completion of the first year examinations qualifies you for admission to year two. Your degree classification is based on your results from year 2 onwards. For the BSc programmes, year 2 and the final year are weighted in the ratio 2:3. For the MMath programmes, years 2, 3 and 4 are weighted in the ratios 2:3:4. (For the MMath European Studies programme, your performance in year 3 abroad is assessed by the overseas university using their standard examination procedure. The results are converted to their equivalent Durham grades and count fully towards the award of your final degree.)

Right: Physics of ribbon curling

Course Structure BSc and MMath Each year you follow a total of six modules (each worth 20 credits). Core modules in the first two years (four in year one, two in year two) provide a sound base from which to specialise. As you proceed through the programme your choices increase, enabling you to follow your own interests whether they are in Pure Mathematics, Applied Mathematics or Probability and Statistics. The course structure is shown on the following pages.

All our programmes include a double project module in the final year. This will give you the opportunity to treat a mathematical topic of your choice in depth and, in many cases, come close to the frontiers of current research.

Current Module Lists

Level I Modules

Level III & IV Modules

Core (or compulsory) modules for maths students:

Please note, some of these modules are only available alternate years. Analysis; Bayesian Statistics; Continuum Mechanics; Cryptography & Codes; Decision Theory; Differential Geometry; Dynamical Systems; Galois Theory; Geometry; Maths Biology; Maths Finance; Maths Teaching; Number Theory; Numerical Differential Equations; Operations Research; Partial Differential Equations; Probability; Project ; Quantum Info; Quantum Mechanics; Representation Theory; Solitons; Statistical Mechanics; Statistical Methods; Stochastical Processes; Topics in Statistics.

Calculus and Probability; Linear Algebra; Analysis; Programming and Dynamics. Two further modules chosen from a wide range, offered in all three faculties, which includes two mathematics modules: Discrete Mathematics and Statistics.

Level II Modules Core (or compulsory) modules for maths students: Analysis in Many Variables; Complex Analysis.

Four mathematics modules chosen from a list currently including: Algebra; Analysis in Many Variables; Complex Analysis; Electromagnetism; Geometric Topology; Mathematic Modelling; Mathematical Physics; Monte Carlo; Numerical Analysis; Probability; Special Relativity and Elementary Number Theory; Statistical Concepts.

Level III Modules Cryptography & Codes; Decision Theory; Differential Geometry; Dynamical Systems; Galois Theory; Mathematical Biology; Mathematics Teaching; Operations Research; Quantum Information; Quantum Mechanics; Statistical Methods; Topology; Project III (double module). It is also possible to take a module from outside the department at this level.

Level IV Modules Advanced Quantum Theory; Algebraic Topology; Elliptic Functions; General Relativity; Riemannian Geometry; Project IV (double module).

The First Year

The Core Modules Calculus and Probability

The calculus section will allow you to reinforce ideas met at Alevel by considering them with a fresh perspective. It covers techniques for differentiation and integration, differential equations and Taylor's theorem.

The key idea, that of a limiting process, is treated informally to be taken up again in Analysis.

The Probability section starts with a brief introduction to the standard methods for evaluating and re-expressing sums and double and triple integrals. The theory of probability is then developed with the calculus and analysis available and with applications in mind. Among the topics covered are: probability axioms, conditional probability, special distributions, random variables, expectations, generating functions, applications of probability, laws of large numbers, central limit theorems.

Linear Algebra

The course gives an introduction to some major ideas and covers techniques that are used in all of mathematics. It includes solutions of linear equations, the theory of vector spaces and linear transformations, solving the eigenvalue problem, generalisation of the notions of length, distance and angle to any vector space, and applications to geometry and calculus.

Analysis

Provides a firm foundation for the operations of differentiation and integration. You will learn to analyse the properties of infinite sequences and series in a mathematically precise way.

By constructing logical arguments (proofs) using the correct language and style you will develop an understanding of mathematical rigour.

Programming & Dynamics

Programming skills are studied in term 1. These skills are useful in mathematical/ scientific computing, and may boost your employment chances after graduation. However, the process of writing a computer program also develops general

mathematical skills: logical reasoning, attention to details and the habit of checking one’s work. The computer is an ideal tool for this, as it rejects nonsensical constructs and syntax errors, and it provides instantaneous feedback on your work.

Dynamics is studied in term 2 and concerns evolution with time. In this course we study a module of time-development called ‘classical mechanics’.

This applies to the world around us and describes the motion of everyday objects via ‘forces’. This introductory course treats firstly the motion of point particles, and then the motion of a certain extended body-a flexible stretched string.

Highlights include conservation laws and use of Fourier series.

The Dynamics course leads on naturally to the second-year courses ‘Mathematical Physics II’ and ‘Analysis in Many Variables II’.

Subsequent Years Two core modules in year 2 are taken by all single honours students and, together with the first year courses, provide a solid foundation from which to specialise. The remainder of the second year, together with years 3 and 4, offer the opportunity to choose those areas of Mathematics and Statistics which appeal most to you.

For example, at Level III you may wish to study the properties of curves and surfaces in Euclidean space (Differential Geometry); the deep and elegant algebra behind attempts to find a formula expressing the roots of a polynomial in terms of its coefficients (Galois Theory); the type of nonlinear differential equation which models the motion of a unicyclist (Dynamical Systems); the mathematical and philosophical subtleties of the behaviour of matter on an atomic scale (Quantum Mechanics); problems where you have a choice of decision and the outcome is uncertain (Decision Theory); the interpretation of the results of clinical trials of medical treatments, and the incidence of leukaemia near power stations (Statistical Methods); or current issues relating to pupils’ learning in secondary schools (Mathematics Teaching).

The Mathematics Teaching module combines sessions in schools with a study of school mathematics from an advanced standpoint.

The complete list of options, all of which last a whole year, is shown earlier in this booklet. You may choose mainly options in Applied Mathematics, or Pure, or Probability and Statistics, or have a more general programme involving all three. The choice is entirely yours, subject of course to the prerequisites needed for each individual module.

There is a compulsory double module project in the final year of all mathematics programmes.

Mathematical Sciences

Entry Requirements

Standard entry requirements

We strongly encourage applicants to sit the general Test of Mathematics for University Admission (TMUA), and will also request them to provide any available UMS marks for all Mathematics and Further Mathematics modules, irrespective of certification or intention to re-sit, as we give a high weighting in our selection process to evidence of ability in Mathematics. We will email all applicants to ask for this information, but any information concerning performance in the 2016 pilot TMUA will be provided optionally to us by applicants on an entirely voluntarily basis: suitable performance will entitle the applicant to the reduced A*AA offer. Taking part in the 2016 pilot TMUA can therefore only increase the chances of receiving an offer. More information will be made available on the Mathematics Department website, and will be made available on the ATS website and in most schools nationwide.

•TMUA + A*A in Mathematics and Further Mathematics either way + A in one other subject excluding Critical Thinking and General Studies

Students registering to take the Oxford MAT and not wishing to also take the TMUA will be able to substitute (MAT results will be treated equivalently to TMUA results).

•A*A* in Mathematics and Further Mathematics either way + A in one other subject excluding Critical Thinking and General Studies •A*A in Mathematics and Further Mathematics either way + A in one other subject excluding Critical Thinking and General Studies + 1 in STEP •TMUA + A* in Mathematics A-level and A in Further Mathematics AS-level + AA in two other subjects excluding Critical Thinking and General Studies

Application

Costs

All applications to Durham University should be made through the Universities and Colleges Admissions Service (UCAS) www.ucas.co.uk

Studying in England is much more affordable than you might think. Most undergraduate degrees in England can be completed within three years, and US students can pay for their studies with the US Federal Student Loan.

You can apply any time between mid-September and the end of June, and you may apply for a maximum of 5 programmes in the UK. Guidance on making an application to Durham University can be found on our website www.

durham.ac.uk/study/undergraduate/apply or if you have any questions please do not hesitate to contact us.

For more information about the costs of study at Durham University please visit our website www.durham.ac.uk/undergraduate/finance/ international

Further information For more information about studying Mathematical Sciences at Durham University or would like information about alternative entry requirements to A-levels please contact the admissions team T +44 191 33 43050 E maths.ugadmissions@durham.ac.uk

University Library, Science Site

Contact us Department of Mathematical Sciences Durham University Lower Mountjoy Stockton Road DURHAM DH1 3LE UNITED KINGDOM T 44 (0)191 334 3050 E maths.ugadmissions@durham.ac.uk www.durham.ac.uk/mathematical.sciences

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