Cardiff School of Mathematics

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1 Cardiff School of Mathematics Undergraduate Degree Programmes Entry

2 Cardiff School of Mathematics Bright prospects World-class research Outstanding facilities Award-winning student society Choice One of the best institutions in Britain... this powerhouse of academic and research excellence boasts one of the best graduate employment rates in Britain. Students don t just get any old job either - most secure degree level posts with decent starting salaries. Sunday Times University Guide 2013

3 1 Professional recognition Teaching excellence Great placements Friendly atmosphere Capital city location Insider Information - Find out more... Want to know what life at Cardiff is really like? Our Insiders are real students studying a range of subjects. You can read their blogs, post comments, ask questions and message them on Facebook and Twitter. To find out more:

4 2 Discover the Cardiff Experience A leading university... You ll be part of a Russell Group university - one of the UK s world-class universities with global recognition. You can choose from more than 300 degree programmes. The Cardiff University degree is known and respected worldwide, with a substantial number accredited by the professions and other external bodies. in an outstanding city... You ll benefit from outstanding teaching in a research-led environment. Staff include a Nobel Laureate and numerous Fellows of the Royal Society. You ll live in a friendly, compact and safe city, with all of your study, living and leisure needs within walking distance. with able and motivated students... Your money will go further at Cardiff with capital city attractions at affordable prices - including one of the lowest rates of all university cities for student accommodation. 1 You ll be at a first choice university where demand for places is strong. You ll be at an international university with students from more than 100 countries. You'll be studying in an environment with other able and motivated students who have high grades at A-level or equivalent. who have excellent career prospects. You can be confident of your future - in 2011/12, 93.7% of our students were employed or had entered further study within six months of completing their studies. 2 You ll be in demand - Cardiff is among the top 25 universities targeted by employers seeking high calibre graduates. 3 Notes 1. Moneysupermarket.com The true cost of going to university HESA Destination of Leavers Survey High Fliers Research The Graduate Market 2013

5 Welcome 3 Welcome Contents Mathematics is an exciting, enjoyable, interesting and highly rewarding subject to study at University. Not only does it offer you intellectual challenges, introducing you to new theories, new applications, and new horizons, but it also equips you with skills that are highly valued by employers. In addition to subject-specific knowledge, a maths degree will also equip you with analytical, writing, problem-solving, presentation, communication, team-working and computing skills that are sought after by key employers in market sectors such as science, industry, commerce, engineering and finance. At Cardiff you will find that we have a carefully planned range of Honours Degrees which are designed to challenge and to stimulate academic curiosity and to enable you to fulfil your potential. Our courses cover traditional subject areas which provide you with the core mathematical knowledge and techniques you need to undertake advanced study, and we also offer the opportunity to study new application areas which will prepare and empower you for satisfying careers. In particular, we are one of only a few UK mathematics schools teaching Operational Research at undergraduate level. There is a high demand for places studying maths at Cardiff. Students are attracted by our reputation for excellent teaching quality standards, the friendly atmosphere that pervades the School, and the care and support students receive from the staff. We strive to ensure that our students react enthusiastically to their courses and thoroughly enjoy their learning experience. We are proud of our students and their achievements. The School offers one of the strongest professional development programmes schemes for mathematics undergraduates in the UK in which undergraduate students at the end of their second academic year can opt to take a 12-month period of training in a mathematics environment in industry, commerce or government. These programmes play a significant role in bringing high quality undergraduates to Cardiff and preparing our graduates for fulfilling careers. There are also opportunities to spend a year studying abroad. Most students develop a strong attachment to Cardiff and some stay on in the School of Mathematics to study for a postgraduate degree. We are an internationally recognised centre of excellence for research in the mathematical sciences, and host visits from distinguished mathematicians from all over the world. New research and the needs of modern technology inform and dictate novel directions for undergraduate teaching. That is the way that mathematics has developed in the past, and will continue to develop in the future. I hope you decide to study at the Cardiff School of Mathematics and become part of a thriving mathematical community where you can enjoy excellent facilities, tuition of the highest quality, and a friendly supportive environment. Professor Tim Phillips Head of School Cardiff: The City 4 Cardiff: The University 6 Living in Cardiff 8 Student Life 8 Degree Programmes 11 Mathematics BSc 14 Mathematics MMath 16 Mathematics and its Applications 18 Mathematics, Operational Research and Statistics BSc 20 Joint Honours 22 Professional Training 24 Careers & Employability 26 Research 27 What the Students Say A Week in the Life of a Mathematics Student at Cardiff 31 Admissions Information 32 This brochure will provide you with more details of our programmes. We hope that they will give you more than just a flavour of what we have to offer you. However, we are always ready to answer any questions you may have, by telephone or , or when you come to Cardiff to visit. You will find appropriate contacts at the end of this brochure. Important information. Please read carefully. The University offers the information contained in this brochure as a guide only. It does not constitute a contract and is not binding on prospective students, current students or the University. While the University makes every effort to check the accuracy of the factual content at the time of publication, some changes will inevitably occur in the interval between publication and the academic year to which the brochure relates (Entry 2015). For example, degree programmes may have changed in line with market and student demand, and research development. Applicants should not, therefore, rely solely on this brochure and should visit the website for up-to-date information concerning course content, accreditation, and entry requirements for the relevant academic year when considering applying to the University. 5000MATHS09/14

6 4 Cardiff: A capital city Cardiff: A capital city Cardiff is a popular student city, relatively inexpensive and with a good range of nightlife and cultural venues. Times Good University Guide 2014 The University is alongside attractive parkland and is adjacent to Cardiff Castle and the city centre

7 Cardiff: A capital city 5 More online at: Cardiff is a thriving and attractive city which is widely recognised as an outstanding place in which to live and study. It combines all the advantages of a compact, friendly and inexpensive location with the cultural and recreational facilities of a modern capital city. Cardiff offers everything from the excitement of the city to the peace and tranquillity of the nearby coast and countryside. With its distinctive character, good quality of life, and growing national and international reputation, it hosts many high-profile cultural and sporting events, including international rugby, soccer, cricket and motor sport. When it comes to entertainment, Cardiff is well-equipped to satisfy student needs. There is a multitude of cafes, pubs and nightclubs. The City is home to the world-renowned Welsh National Opera, it boasts prestigious concert venues such as the Wales Millennium Centre, St David s Hall and the Motorpoint Arena, as well as the iconic Millennium Stadium, the National Museum and Gallery of Wales, several theatres and the historic Cardiff Castle. Cardiff is the location for award-winning television productions, including Dr Who, Sherlock, Torchwood and Casualty, and the Dr Who Experience in Cardiff Bay is a popular new attraction. The city is one of the UK s best shopping destinations, a status enhanced by the opening of the 750 million St David s Dewi Sant retail centre standing alongside pedestrianised shopping streets, indoor and outdoor markets, and a fascinating network of glass-canopied Victorian and Edwardian arcades. Cardiff also has more urban green space than any other UK city, and offers easy access to the countryside, coast and mountains. Lively, elegant, confident, cosmopolitan and ambitious are all words readily used to describe modern-day Cardiff. Together, the city and the University provide students with the Cardiff Experience, a lifestyle our students remember long after graduation. The Millennium Stadium nestles in the heart of the city, and is home to numerous sporting events and concerts throughout the year Don t just take our word for it Modern Cardiff combines the best of the old and the new...it has a relatively small population and is fairly inexpensive to live in. Close to the campus, the city centre has an array of shops and entertainment options to cater to all tastes and budgets. The Telegraph Guide to UK Universities 2012 Come and see for yourself Cardiff benefits from excellent road and rail links with Britain s other major towns and cities. London, for example, is two hours by train, and the M4 links both the west and south of England, as well as west Wales. Travel to the Midlands and to the North is equally convenient. The journey by road from Birmingham, for example, takes only two hours. The main coach and railway stations are both centrally placed, and Cardiff also benefits from an international airport. Cardiff is one of the UK s most successful retail centres Cardiff Bay, the city s waterfront

8 6 Cardiff: A leading university Cardiff: A leading university Cardiff University is one of Britain s leading teaching and research universities. Telegraph Guide to UK Universities 2014

9 Cardiff: A leading university 7 More online at: Cardiff University has an international reputation for excellence in teaching and research, built on a history of service and achievement since 1883, and recognised by our membership of the Russell Group of leading research-led universities. With attractive and compact campuses, excellent student accommodation, and a hugely popular Students Union, all within easy walking distance of each other in a thriving city, it is not surprising that Cardiff is a university of first choice among wellprepared applicants. We admit approximately 5,000 undergraduate entrants each year, the majority of whom are school and college leavers, and have high grades at A-level or equivalent. While competition for entry is strong, Cardiff is an inclusive university with a good record on widening participation and fair access, and we welcome applications, irrespective of background, from everyone with the potential to succeed at Cardiff University. The University s Cathays Park campus is located in and around the impressive Portland stone buildings, parks and wide treelined avenues that form Cardiff s attractive civic centre. The majority of academic schools are located here - just a few minutes walk from the city centre. The three academic schools offering healthcare courses (excluding Optometry and Pharmacy) are based at the Heath Park campus, approximately one mile away, which is also home to the University Hospital of Wales. Although dating from 1883, Cardiff University is focused on the 21st century, and has modern state-of-the-art buildings and facilities. The University has invested substantially in its estate in recent years and most academic schools have benefited from major refurbishment, including new and wellequipped laboratories, lecture theatres, libraries and computing facilities. International opportunities are available via our Global Opportunity Centre. These include study, work and volunteering placements in 27 EU countries as well as international exchange opportunities. All students also have the opportunity to study a language in addition to their degree through the University s Languages For All programme. The University takes its environmental, safety and security responsibilities very seriously. It has comprehensive policies in place which are making great savings in energy consumption and, to support the safety and security of all members of the University community and their property, there is 24-hour security cover throughout the campus. What the Guides say [Cardiff] University is the acknowledged leader of higher education in Wales. It is the Principality s only member of the Russell Group of research-led universities and has two Nobel Laureates on its staff. It is our 2014 Best Welsh University. Times Good University Guide 2014 The University is as confident and forwardlooking as the city it s located in, and has an excellent reputation for the quality of its teaching and research. Almost 60% of its research is ranked as world leading and it is a member of the Russell Group of leading universities. Guardian University Guide 2013

10 8 Living in Cardiff Living in Cardiff As a fast developing capital city, Cardiff is a great place to be a student. It s large enough to offer you an exciting variety of activities and entertainment, but small enough for you to feel comfortable in. Accommodation Cardiff offers guaranteed University accommodation, good quality and value, and a range of residences to suit individual preferences and budgets. All first year undergraduates who apply during the normal UCAS admissions cycle (ie come to Cardiff as a firm or insurance applicant) are guaranteed a single occupancy place in University residences during the first year of study. Please see our website for full details: The University is continually investing in its student residences, and the views of students are taken into account at the design stage. Unusually for a civic university, most of our residences are within easy walking distance of lecture theatres, libraries, laboratories, the Students Union and city centre. There are 14 different residences, providing more than 5,300 study bedrooms and students can apply for the residences which best suit their preferences, interests and budgets. Some 70% have en-suite shower and toilet facilities and all halls of residence have computer network connection points and access to WiFi. Fees depend on the facilities included and whether catered, part-catered or self-catered, but prices compare very favourably with those of other UK universities. Besides managing University property, the Residences Office maintains close links with the private sector and provides assistance to students seeking to rent or share houses or flats. Student Life The Students Union Cardiff Students Union is one of the biggest, best and most active in Britain. Solus, the Great Hall and the Taf Bar are among the Union s major attractions. Solus is the students own high quality nightclub, and is one of the largest in Wales. The Great Hall is a 1,500 capacity venue for major concerts and the Taf Bar is the Union s very own local. Other facilities include The Kitchen, CF10 café, a bank, a print shop, a hair salon and a bookshop. The Lounge offers IT and Skyping facilities, meeting rooms and a chillout area, as well as snooker tables and multi-faith prayer room. The Union also has its own letting agency and an Advice and Representation centre. In addition, it is home to CU TV and Xpress Radio (the students own TV and radio stations) and more than 200 cultural, political, religious, social and sporting societies. Jobshop Jobshop is the Union s own student employment service and provides casual, clerical and catering jobs around the University to hundreds of students. All study bedrooms in the halls of residence have computer network connection points and access to WiFi The Fitness and Squash Centre is located at the heart of the main campus Solus is the Students Union high quality nightclub

11 Living in Cardiff 9 More online at: CURRYS P P 125 Students have access to a wide range of modern facilities, including Skype booths P P 132 What the Guides say A place in one of the University s 5,300 single study bedrooms is guaranteed to all first year undergraduates applying through the normal UCAS admissions cycle. Guardian University Guide 2014 The cost of living for a student in Cardiff is generally lower than elsewhere in the UK. The Independent A-Z University Guide 2014 The Union offers an exciting entertainment programme, a comprehensive range of student support services and 150 clubs and societies. The Complete University Guide Key Cardiff School of Mathematics 134 University Buildings Student Residences How to find the School The Cardiff School of Mathematics is situated in a modern building, known as the Mathematics Institute, located in a central position within the University campus, yet within five minutes walking time of the main city shopping complex and Cardiff's magnificent Civic Centre. P P P 121 P P 135 P P 123 P 137 P P P

12 The University offers ample space for quiet study

13 Degree Programmes Offered by the School of Mathematics The School More online at: 11 The Cardiff School of Mathematics offers 14 undergraduate degree programmes, which are listed in the following pages. In addition with our Single Honours Degrees there is an opportunity to spend a year abroad at an overseas university. You will take 12 modules each year, usually six in each semester. Modules currently on offer in each programme are listed on later pages. There is a choice of modules in each year, especially in the final year. The modules studied in the first year of the single honours courses are mostly common, so transfer between programmes is possible up to the start of the second year. It is also normally possible to transfer from joint honours to single honours programmes, although because some second and final year modules are dependent on first year ones there may be limitations on the module choices available. The School is situated on the Cathays Park Campus (see the map on page 9) in the civic centre of the City of Cardiff. The building houses lecture theatres, computer suites, a library and a cyber café. Access to the library and computer facilities is available throughout the day and early evening during term times. Mathematics courses in Cardiff cover a wide range of topics. The programmes are designed to be stimulating and flexible, allowing you to make choices that suit your mathematical interests as you develop your mathematical skills. A mathematics degree in Cardiff provides a good foundation for further study after graduation or for a career in many industries. The problem solving and logical reasoning skills that are learned in these degrees are sought after by many employers. It is also possible to spend a year overseas at one of our partner universities on each of our single honours degree programmes. The fee for this option is only 15% of the normal tuition fee and there are opportunities to study in the US, Canada, Australia, China as well as European universities. Please contact us for further information. Access to library and computing facilities is available throughout the day and until 9pm during term time

14 12 Degree Programmes Overview A project may replace one or two modules in the final year, providing a valuable opportunity to apply the knowledge and skills you have acquired and to develop communication and presentation skills BSc Mathematics (UCAS Code: G100) This three-year single honours course allows you to choose from a wide range of mathematical topics, with a core of pure mathematics. Additional optional modules in pure mathematics, applied mathematics, operational research, statistics and computing allow you to acquire a good general knowledge of mathematics. MMath Mathematics (UCAS Code: G101) This four-year single honours course allows you to delve more deeply into the areas of pure and applied mathematics. There is also the opportunity to undertake your own substantial research in the fourth year in a subject area of your choice supervised by a member of staff. BSc Mathematics and its Applications (UCAS Code: G120) This is a three-year single honours course for students who wish to study those topics in mathematics that are applied to solve problems in science, business and commerce. There is a core of essential mathematics in Years One and Two. BSc Mathematics and its Applications (UCAS Code: G111) This is a four-year sandwich course in which the third year is spent in a salaried post away from the University undertaking professional training. The academic part is identical to G120. BSc Mathematics, Operational Research and Statistics (UCAS Code: G991) This is a three-year single honours course for students who have a strong interest in operational research and statistics, subjects that are applied to the solution of problems in, for example, medical and pharmaceutical research, planning and management. BSc Mathematics, Operational Research and Statistics (UCAS Code: G990) This is a four-year sandwich course in which the third year is spent in a salaried post away from the university undertaking professional training. The academic part is identical to G991. BSc Mathematics and Physics (UCAS Code: FG31) This is a three-year joint honours course that enables you to combine a study of pure and applied mathematics with theoretical and experimental physics. Equal time is spent on each subject. BSc Computing and Mathematics (UCAS Code: GG14) This is a three-year joint honours course that enables you to combine a study of pure mathematics and numerical analysis or statistics with computer science and information systems. BSc Computing and Mathematics (UCAS Code: IG11) This is a four-year joint honours sandwich course in which the third year is spent in a salaried post away from the university undertaking professional training. The academic part is identical to GG14.

15 Degree Programmes Overview 13 More online at: Cardiff offers a range of joint honours degree programme which can be studied with mathematics BA French and Mathematics (UCAS Code: GR11) This is a four-year joint honours course in which you spend the third year abroad. A study of French language and culture is combined with mathematics, where there is a choice of modules available, especially in the final year. There is an opportunity to study a third subject or more mathematics in Year One. BA German and Mathematics (UCAS Code: GR12) This is a four-year joint honours course in which you spend the third year abroad. A study of German language and culture is combined with mathematics, where there is a choice of modules available, especially in the final year. There is an opportunity to study a third subject or more mathematics in Year One. BA Mathematics and Philosophy (UCAS Code: GV15) This is a three-year joint honours course. Equal time is spent on the two subjects in the second and final years, but in the first year, there is an opportunity to study more mathematics or a third subject. Both in mathematics and philosophy there is a choice of modules, especially in the final year. BA Mathematics and Music (UCAS Code: GW13) This is a three-year joint honours course in which equal time is spent on the two subjects throughout the course. A study of musical theory and performance is combined with pure mathematics and either further pure mathematics, applied mathematics or statistics. Students on the Mathematics and Music degree programme also have the opportunity to spend a year in Europe studying at one of our partner universities. BA Mathematics and Welsh (UCAS Code: QG51) This is a three-year joint honours course in which equal time is spent on the two subjects throughout the course. A study of Welsh language and literature is combined with pure mathematics and either additional pure mathematics or statistics. Please note that this course is only available to people whose first language is Welsh. Further information on all the courses listed above is given on the following pages.

16 14 Mathematics BSc Mathematics BSc UCAS Code G100 Three-year course UCAS Code G103 Four-year course including a year abroad Mathematics BSc is our most general degree programme and provides you with a firm foundation in all the main areas of mathematics, providing skills much in demand for a wide range of careers. It is a very flexible degree programme so you can specialise in the areas of mathematics that are of particular interest pure mathematics, applied mathematics, operational research, statistics and computing. There is an essential core of pure mathematics in the first two years of study but you can start to tailor your degree to your interests even in Year One. You will study 12 modules each year. In the first year, you can choose to study only mathematics modules or you may choose up to four modules from other disciplines, for example computing, physics, music or a language. In Year Two, six core modules are studied, together with six modules chosen from a list of options. One module may be taken from other disciplines. In the final year, there are no core modules. Instead you choose the 12 modules that are of most interest to you from a wide and diverse choice of options. Lectures and tutorials are informed by the latest research

17 Mathematics BSc 15 More online at: Modules Currently on Offer Year One You will study: Calculus Elementary Differential Equations Algebra I and II Analysis I and II Geometry Introduction to Probability Computing for Mathematics And two modules chosen from the following: Mechanics I Statistical Inference I Number Theory I Introduction to Java Note: In Year One, students can replace up to 40 credits in Maths with credits from other subjects. Ben Craft Ben graduated from Cardiff with a first class honours degree in Mathematics and its Applications. During his degree he spent an industrial training year at the Higher Education Funding Council for Wales. He is now working for Smartodds, a company providing statistical research and football modelling services in the betting sector. Year Two Specialisation continues in the second year. You will study: Calculus of Several Variables Matrix Algebra Complex Analysis Series and Transforms Analysis III Linear Algebra And six modules (or equivalent) selected from the following list: Number Theory II Modelling with Differential Equations Numerical Analysis II Mechanics II Elementary Fluid Dynamics Vector Calculus Ordinary Differential Equations Operational Research Visual Basic Programming for Operational Research Foundations of Probability and Statistics Computational Statistics Accountancy Algorithms and Data Structures Informatics One module from a different subject Year Three Specialisation is developed further and a project can be taken, which may involve practical application of theoretical knowledge. You will study twelve modules (or equivalent), chosen from the following: Knots Coding Theory and Data Compression Combinatorics Complex Function Theory Introduction to Functional and Fourier Analysis Groups, Rings and Fields Theoretical and Computational Partial Differential Equations Fluid Dynamics Applied Nonlinear Systems Methods of Applied Mathematics Discrete Optimisation Stochastic Models and Applications to Finance Regression Analysis and Experimental Design Elements of Mathematical Statistics Mathematical Programming Medical Statistics Operational Research II Time Series Analysis and Forecasting Survey Sampling Mathematical Methods for Data Mining Mathematical Education (in Welsh) Graphics, Visualisation and Computer Vision Computational Intelligence Project (Single Module) Project

18 16 Mathematics MMath Mathematics MMath UCAS Code G101 Four-year course UCAS Code G104 Five-year course including a year abroad The four year MMath degree programme is offered to satisfy the need for a more advanced level of mathematical training than is available in a 3-year programme. It gives the opportunity to delve more deeply into the areas of Pure and Applied Mathematics. The modules offered in the first three years of the programme are common to the 3-year degree programmes in mathematics, allowing the flexibility of transfer between courses. In the first year you study a variety of mathematics modules. In the second and third years you take a selection of advanced modules that allow you to build on the interests developed in the first year. In the fourth year the course develops research training and enhanced mathematical skills, especially in Mathematical Analysis, Mathematical Physics and Fluid Dynamics. There is also a major piece of project work in which you would be undertaking novel research. The course is an ideal preparation for students wishing to go on to research work in mathematics, work for a technological company or who simply want to gain a deeper understanding of mathematics and is highly regarded by prospective employers. A typical lecture at the School of Mathematics

19 Mathematics MMath 17 More online at: Modules Currently on Offer Year One You will study: Calculus Elementary Differential Equations Algebra I and II Analysis I and II Geometry Introduction to Probability Computing for Mathematics Number Theory I And one module chosen from the following: Mechanics I Statistical Inference I Year Two Specialisation continues in the second year. You will study: Calculus of Several Variables Matrix Algebra Complex Analysis Series and Transforms Analysis III Linear Algebra Numerical Analysis II Vector Calculus And four modules (or equivalent) selected from the following list: Number Theory II Modelling with Differential Equations Mechanics II Elementary Fluid Dynamics Ordinary Differential Equations Operational Research Foundations of Statistics Year Three You will study: Introduction to Functional and Fourier Analysis Theoretical and Computational Partial Differential Equations Groups, Rings and Fields Complex Function Theory And six modules chosen from: Coding Theory and Data Compression Combinatorics Knots Methods of Applied Mathematics Fluid Dynamics Applied Nonlinear Systems Discrete Optimisation Time Series Analysis and Forecasting Mathematical Statistics Mathematical Programming Year Four You will study: MMath Project And four modules chosen from: Operator Algebras and Non-Commutative Geometry Measure Theory Computational Fluid Dynamics Mathematical Principles of Image Processing Functional Analysis Elasticity Number Theory Reading Module All are Double Modules (40 credits) Cardiff University Maths Support Service

20 18 Mathematics and its Applications BSc Mathematics and its Applications BSc UCAS Code G120 Three-year course UCAS Code G111 Four-year sandwich course UCAS Code G900 Four-year course including a year abroad Mathematics is the language of science, technology and engineering, and its various branches are used throughout commerce and the business world. The Mathematics and its Applications degree programme aims to provide you with the skills and tools that are used extensively in these fields. This course is available as either a three-year course or as a four-year sandwich course, in which the third year is spent undertaking professional training away from the University. Full details and some case studies can be found on pages 24 and 25. This gives you the opportunity of seeing and being involved in work in which mathematics or one of its applications plays a major role. The academic parts of the three and four-year programmes are identical. You study calculus, algebra and analysis in the first year, together with the applications branches of modelling, mechanics, statistics and computation. In the second year there are six core modules, four in essential core mathematics and two in applied mathematics. The remainder of the curriculum is optional and can either be in the applied mathematical side of the subject or the statistical field, including operational research, an important topic much used in business and commerce. In the final year you can choose from a wide range of applicable topics in applied mathematics, operational research, statistics, computational mathematics or mathematical physics. A project may replace one or two modules in the final year, providing the opportunity to develop communication and presentational skills and to learn how to apply your mathematical skills to an investigation of your choice. A typical small group tutorial

21 Mathematics and its Applications BSc 19 More online at: Modules Currently on Offer Year One You will study: Calculus Elementary Differential Equations Algebra I and II Analysis I and II Geometry Introduction to Probability Computing for Mathematics And two modules chosen from the following: Mechanics I Statistical Inference I Number Theory I Ketan Ketan graduated from Cardiff University with a first class honours degree in Mathematics and its Applications. He started work for the Ministry of Defence as an Operational Research Analyst primarily working for front line support. Having spent a year with the MOD he decided that he wanted to experience a more business-oriented role and accepted a job as an analyst with Royal Bank of Scotland Insurance. Year Two Specialisation starts in the second year. You will study: Calculus of Several Variables Complex Analysis Matrix Algebra Series and Transforms Modelling with Differential Equations Vector Calculus And the equivalent of six more modules selected from the following: Elementary Fluid Dynamics Mechanics II Ordinary Differential Equations Numerical Analysis II Number Theory II Operational Research Visual Basic Programming for Operational Research Foundations of Probability and Statistics Computational Statistics Analysis III Accountancy Linear Algebra Year Three Specialisation is developed further. You will study twelve modules (or equivalent), chosen from the following: Knots Coding Theory and Data Compression Combinatorics Complex Function Theory Functional and Fourier Analysis Groups, Rings and Fields Fluid Dynamics Theoretical and Computational Partial Differential Equations Applied Nonlinear Systems Discrete Optimisation Stochastic Models and Applications to Finance Methods of Applied Mathematics Mathematical Statistics Mathematical Programming Medical Statistics Operational Research II Regression Analysis and Experimental Design Time Series Analysis and Forecasting Survey Sampling Data Mining Mathematical Education (in Welsh) Project (Single Module) Project

22 20 Mathematics, Operational Research and Statistics BSc Mathematics, Operational Research and Statistics BSc UCAS Code G991 Three-year course UCAS Code G990 Four-year sandwich course UCAS Code GG23 Four-year course including a year abroad The Mathematics, Operational Research and Statistics BSc degree course is a programme that enables you to combine the study of mathematical topics with the more practical ones of operational research and statistics. In the final year of the course it is possible to specialise in operational research and statistics, but in the first two years there is also a core of pure mathematics in the curriculum. The four-year sandwich course is identical to the three-year course but a year is spent between the second and final years in a period of professional training. More information on the establishments who collaborate with us in this programme can be found on page 24. Operational Research and Statistics are both topics that are widely used outside of universities and there are many career opportunities in these areas. There are 12 modules in each year of study. In the first year these modules are in pure mathematics, statistics and computation, with the option of taking a module in applied mathematics. Alternatively a module can be chosen from another School, for example a language, music or education. In Year Two there are eight core modules in pure mathematics, operational research and statistics, with the other four being chosen from topics in pure or applied mathematics, accountancy or computation. Alternatively, one module can be selected from those available in another School. There are no core modules in the final year, but at least six have to be in operational research and statistics. This flexibility enables you to combine a study of statistics and operational research with pure or applied mathematics modules up to a final year level. A project may replace one or two modules in the final year, providing the opportunity to develop communication and presentational skills and to learn how you can apply operational research or statistical techniques to an investigation of your choice. Cardiff School of Mathematics is modern and well equipped

23 Mathematics, Operational Research and Statistics BSc 21 More online at: Modules Currently on Offer Year One You will study: Calculus Elementary Differential Equations Algebra I and II Analysis I and II Geometry Introduction to Probability Statistical Inference I Computing for Mathematics And either: Mechanics I Or: Number Theory I Year Two Specialisation starts in the second year. You will study: Calculus of Several Variables Complex Analysis Matrix Algebra Series and Transforms Foundations of Statistics Operational Research And four more modules selected from the following: Accountancy Linear Algebra Modelling with Differential Equations Numerical Analysis II Number Theory II Ordinary Differential Equations Analysis III Visual Basic Programming for Operational Research Computational Statistics Year Three Specialisation is developed further. The equivalent of at least six modules have to be taken in statistics and operational research (from the first nine listed). Discrete Optimisation Stochastic Models and Applications to Finance Regression Analysis and Experimental Design Mathematical Statistics Mathematical Programming Medical Statistics Operational Research II Survey Sampling Time Series Analysis and Forecasting Applied Nonlinear Systems Knots Coding Theory and Data Compression Complex Function Theory Combinatorics Groups, Rings and Fields Methods of Applied Mathematics Data Mining Project (Single Module) Project There is a good staff-student relationship within the School Krupa Krupa studied for the BSc Mathematics, Operational Research and Statistics degree course and spent her placement year working with GlaxoSmithKline, a large pharmaceutical company, based at their site in Greenford, Middlesex. After graduation Krupa decided that she would embark on a career in the financial industry. She is now working as a trainee accountant for a large firm of chartered accountants who are sponsoring her while she studies for her professional qualifications.

24 22 Joint Honours Joint Honours Many employers look favourably on students who can demonstrate their abilities in more than one subject area. We offer a wide range of Joint Honours degree programmes, each of which opens up interesting possibilities for choice of career. BA Joint Honours Mathematics and a Humanities Subject Mathematics is combined with one of a range of other disciplines from the Humanities for the award of a BA degree. These are: French, German, Music, Philosophy, Religous Studies and Welsh. If French or German is your second subject, the course is of four years duration, with the third year spent abroad in an appropriate country. Twelve modules or their equivalent (120 credits) are taken each year. In the second and final years 60 credits are taken in each subject. In the first year of the joint honours degrees with Music and Welsh, 60 credits are studied from each subject. For the remainder of the programmes 60 credits must be studied in mathematics and at least 40 credits in the other subject. The additional 20 credits can be gained from either modules from a third subject or extra mathematical modules, increasing the choice of modules in later years. UCAS Codes for BA Joint Honours Mathematics and a Humanities Subject Mathematics and French Mathematics and German GR11 GR12 Year Two You will study: Calculus of Several Variables Complex Analysis Matrix Algebra Series and Transforms The mathematics component of the courses has been designed to give you maximum flexibility, while ensuring that you have a good background knowledge of essential mathematical ideas. In the first two years there is a core of 40 credits of compulsory pure mathematics. The remaining 20 credits in mathematics are chosen to reflect your interests, either in additional pure mathematics, applied mathematics or statistics. A range of final year modules that follow on from your choices in Years One and Two is open to you, although timetabling constraints may mean that you will not necessarily have a completely free choice of modules. Further details can be found in the prospectus and by contacting the Admissions Tutor for the relevant subject. Alternatively see our website at: Mathematics and Music Mathematics and Music with a year in Europe Mathematics and Philosophy Mathematics and Religous Studies Mathematics and Welsh Year One You will study: Calculus Elementary Differential Equations Algebra I and II And at least two modules from: Analysis I & II Geometry Mechanics I Introduction to Probability Statistical Inference I Plus other modules depending on your second subject, to make up twelve (or equivalent) in all. GW13 GW31 GV15 VG61 QG51 And at least two modules from: Analysis III Linear Algebra Modelling with Differential Equations Vector Calculus Foundations of Probability and Statistics Plus other modules in your second subject. Year Three Six modules are chosen from: Knots Groups, Rings and Fields Complex Function Theory Coding Theory and Data Compression Combinatorics Methods of Applied Mathematics Applied Nonlinear Systems Regression Analysis and Experimental Design Survey Sampling Plus other modules in your second subject.

25 Joint Honours 23 More online at: BSc Joint Honours Mathematics and Computing (UCAS Code: GG14 / IG11) The BSc in Mathematics and Computing is a joint degree with equal contributions from the two subjects. In the first two years there is a core of four compulsory modules in pure mathematics, with choice for the other two. You can choose these modules to reflect your interests, either additional pure mathematics, numerical mathematics or statistics. There is a wide choice of modules in the final year, though timetable restrictions may limit your choice. The IG11 course includes a year of professional training. More information can be found on pages 24 and 25. Year One In mathematics the four core modules are: Calculus Elementary Differential Equations Algebra I and II And you choose two modules from: Analysis I and II Introduction to Probability Statistical Inference I Plus six modules in computing. Year Two In mathematics the four core modules are: Calculus of Several Variables Complex Analysis Matrix Algebra Series and Transforms Plus the equivalent of two modules chosen from: Numerical Analysis II Analysis III Linear Algebra Foundations of Probability and Statistics Plus six modules in computing. Year Three In mathematics six modules are chosen from: Complex Function Theory Coding Theory and Data Compression Combinatorics Knots Data Mining Groups, Rings and Fields Survey Sampling Regression Analysis and Experimental Design You will also study six modules in computer science. Computing Admissions Tutor: Dr Jianhua Shao Telephone: +44 (0) J.Shao@cs.cardiff.ac.uk BSc Joint Honours Mathematics and Physics (UCAS Code: FG31) The BSc in Mathematics and Physics is a joint degree with equal contributions from the two subjects. In the first year you are introduced to essential applied and pure mathematical concepts. There is some choice in Year Two, allowing a selection to be made from a range of options in applied mathematics and mathematical physics in the final year. Year One The core modules in mathematics are: Calculus Elementary Differential Equations Algebra I and II Analysis I and II Year Two You will study the following core modules: Calculus of Several Variables Matrix Algebra Modelling with Differential Equations Series and Transforms Vector Calculus And one of: Elementary Fluid Dynamics Complex Analysis You will also study six modules in physics. Year Three Six modules in mathematics are chosen from the following: Coding, Theory and Data Compression Groups, Rings and Fields Combinatorics Methods of Applied Mathematics Theoretical and Computational Partial Differential Equations Applied Nonlinear Systems Fluid Dynamics You will also study the equivalent of six modules in physics. Physics Admissions Tutor: Dr Phil Buckle Telephone: +44(0) BucklePD@astro.cardiff.ac.uk Plus six modules in Physics.

26 24 Professional Training Professional Training On the BSc Mathematics and its Applications and BSc Mathematics Operational Research and Statistics courses there is the opportunity for some students to spend a year working as a salaried employee between the second and final years. If you chose this option, you would work in a post related to mathematics or statistics in an establishment approved by the School. Our training officer will help you find a suitable placement from amongst those available at the time, and your preferences in type of work and location will be taken into account. Although you will be an employee during this year, you will also still be classified as a student and eligible for any student benefits. You will be visited by your University personal tutor and your progress at work will be monitored and discussed with your training supervisor. At the end of the year you complete a report on your training and you will be eligible to apply for a City and Guilds Senior Award at the licentiateship (LCGI) level. The professional training programme has proved to be popular, and has been running successfully for many years. It gives some of our undergraduate students the opportunity of experiencing mathematical, statistical and computing work that is done outside of the University environment. We have links with a wide range of establishments who take part in the programme. Because of the experience of these employers in taking on undergraduate trainees, they are aware of the standard of expertise that they can expect. The links have been developed so that both the student and the employer benefit from the experience. For many of our students, a professional training year has been the first step on the career ladder, and after graduation the first permanent job is sometimes with the establishment where the training year was spent. Even for those students who seek a career elsewhere after graduating, the training year is attractive to future employers, who hold the period of work experience in high regard. If you are interested in the professional training year, but are uncertain at the moment whether you want to commit yourself, this would not stand in the way if you change your mind later. It is possible to transfer between the three and four-year courses at any time up to enrolment at the beginning of the second year. We have a wide range of contacts, and in recent years have helped around 30 students each year to find a professional training post. Among the branches of government who have employed our students are HM Revenue and Customs (London), Ministry of Defence (Warminster and Shrivenham), Office for National Statistics (Newport) and Welsh Assembly Government (Cardiff). The business and finance sector has also participated, including Barclaycard (Northampton), Lloyds Banking Group (Cardiff, Bristol and London) and PriceWaterhouseCoopers (various locations). In the industrial sector we have placed students with many companies including BAe Systems (Bristol), Corus (Newport), GSK (Greenford and Harlow), National Air Traffic Services Ltd (near Southampton), Roche Pharmaceuticals (Welwyn Garden City), Rolls Royce (Derby) and Rutherford Appleton Research Laboratories (near Didcot). It is also possible for students on the joint honours Computer Science and Mathematics to undertake a year of Professional Training. These placements are normally organised by the Cardiff School of Mathematics.

27 Professional Training 25 More online at: Nathan My industrial undergraduate placement was in the Investment Management and Private Equity department within the audit sector at Deloitte. This was the culmination of a lengthy application process, consisting of an online application, telephone interview, online numerical and verbal reasoning tests, competency based interview, e-tray exercise, report drafting and a final partner interview. I was the first of only four undergraduates accepted by Deloitte. My role involved being part of numerous audit teams, obtaining evidence and testing the amounts and disclosures in the financial statements of clients, sufficient to give reasonable assurance that the financial statements are free from material misstatement, whether caused by fraud or error. Deloitte offer great opportunities to develop, providing excellent support and encouragement. One unique opportunity during my placement was the level of client interaction and the opportunities to work with a variety of different management levels within different organisations. This was not a 9-5 office based job, but one where I was able to travel and work within and outside of central London, at the offices of some of the company s biggest clients. At Deloitte, there was a clear ethic of working hard and reaping the rewards. Some of the feedback I received included working well for long hours under exceptional pressure, going over and above what was expected, and being an asset to both the audit team and firm. Fantastic opportunities arose such as attending an event at Deloitte s Olympic House. Overall, I thoroughly enjoyed and benefited from my industrial placement with Deloitte, and have accepted a graduate position with the company upon completing my degree. Emily I opted to undertake a placement year as part of my BSc Mathematics, Operational Research and Statistics course. I had the opportunity to spend this year working at Roche as a Biostatistician; this placement has been an amazing experience allowing me to link my university studies to their application within the Pharmaceutical industry. Roche have been involved in a number of major medical breakthroughs improving the quality of life for their patients and it has been a pleasure to be a part of this group, working on statistical analyses for clinical trials. As a Biostatistician, my position was in the Product Development department. I was a member of a smaller subgroup of statisticians working on the statistical analysis of data from clinical trials. This placement has provided both knowledge and a strong interest in the Pharmaceutical industry, which I hope to pursue further at University, and enabled me to develop invaluable professional skills crucial for employment. Most importantly it has converted previous studies and skills into invaluable practical experience. This year has made me even more motivated to work hard, it is so refreshing to be around people who are incredibly enthusiastic and love what they do. I better understand how I work to be most productive and I have gained a lot of confidence in my abilities. This confidence is from being challenged with difficult work during this year. I have also developed much more confidence in my ideas, I am happier to put across my thoughts in meetings, present to my team and make conversation with all colleagues, either internal or external to Roche. This has come with familiarity with people at work and experience in situations where it is important to make conversation with colleagues, such as conferences, and has been a huge benefit to me. Other skills I have developed are the ability to work both in a team and independently. With independent work, I feel very trusted when given the responsibility of a piece of work but always very supported if I have any issues or questions. I have been given the opportunity to work with colleagues in other functions, mainly programmers or scientists; this has been a great experience to communicate and determine the requirements of all functions and collaborating with them to achieve a common objective. I have also improved my time management skills, by ensuring I prioritise work to meet deadlines, I have achieved this by being more organised with work, planning ahead and assessing the time a piece of work will take. I have loved my placement year and cannot wait to come back!