Mathematics at University and beyond

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Maths Is ImportantMathematics is a universal part of human culture. It is the tool and language of commerce, engineering and other sciences – physics, computing, biology etc. It helps us recognise patterns and to understand the world around us. Mathematics plays a vital, often unseen, role in many aspects of modern life, for example:•Space travel•Safeguarding credit card details on the internet•Modelling the spread of epidemics•Predicting stock market prices•Business decision makingAs society becomes more technically dependent, there will be an increasing requirement for people with a high level of mathematical training. Analytical and quantitative skills are sought by a wide range of employers. A degree in mathematics provides you with a broad range of skills in problem solving, logical reasoning and flexible thinking. This leads to careers that are exciting, challenging and diverse in nature. Whatever your career plans, or if you have no plans at present, a degree in mathematics provides you with particularly good job prospects

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Why study mathematics?

historysociology

english literatureart history

music

biologyfrench

sport science

geography

Because...

• you love it• it's interesting• it's easy• it's a conversation stopper• it's beautiful• it's difficult

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Other good reasons... • 5 years after graduating those with mathematics

degrees earn more on average than any other graduates.

• 96% of 2012/2013 mathematics graduates are now employed, higher than any other subject apart from medicine and dentistry.

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Maths Has Good Career ProspectsAnalytical and quantitative skills are sought by a wide range of employers. A degree in mathematics provides you with a broad range of skills in problem solving, logical reasoning and flexible thinking. This leads to careers that are exciting, challenging and diverse in nature

Whatever your career plans, or if you have no plans at present, a degree in mathematics provides you with particularly good job prospects

The generic nature of mathematics means that almost all industries require mathematicians. Mathematicians work in business, finance, industry, government offices, management, education and science.

A proportion of students will use their degree in mathematics as preparation for further studies at Masters or Doctorate levels.

The experience gained through a sandwich course increases your employability even further. The opportunity of a year's salaried work experience during your degree enables you to try a job of your choosing and provides employers with evidence of your achievements and skills.For more information on the types of placements available please click here.

Cardiff's Mathematics graduates for the year 2012 their destinations were as follows:

37% Professions/Commerce (e.g. Finance, Computing etc.)

9% Industry

17% Public Service

12% Teaching

25% Research and further study

Studying mathematics allows you to keep your career options open.

HSBC KPMG Lloyds TSB MGM Assurance Motorola National Air Traffic ServicesNational Assembly for WalesNatWest Bank Norwich Union Office for National Statistics PA ConsultingPatents Office Pearl Assurance Price Waterhouse Coopers QinetiQ RM Computers Somerfield Standard Life Bank Sun Life Assurance Vodafone Waterstons

Recent mathematics graduates at Cardiff have joined: American ExpressAsdaAutomobile Association AXA Insurance Barclays Bank Bacon & Woodrow British Aerospace British Airways British Telecom Charles Schwab Cheltenham & Gloucester Clerical Medical Investment Group Coopers & LybrandDEFRArnst & Young GEC Avionics General Accident Glaxo Smith Klein Glencore UK Ltd. HBOS

Mathematics at University

Maths at universitySchool mathematics is mostly about how to solve particular problems. For example, examinations usually consist of questions which are solved by selecting a method from a list of methods you have been taught.

This approach changes when you study mathematics at University: When you go into the world with a degree which says you are a mathematician, you may be asked questions with no obvious method of solution.

For example there are mathematicians developing ways of answering the following questions: •How can you tell whether a new treatment for a disease offers value for money when the very ideas of value and cost are uncertain? •How can you investigate the internal structure of the sun when you see only its surface - and from a very long way off? •How can you relate particle trajectories in space-time to the various ways you can knot pieces of string?

To work on such problems you need to know how mathematicians have tried to answer similar questions in the past - sometimes successfully, sometimes not!

You need to know methods which might give an approximate answer good enough for practical purposes because many real-life problems cannot be given definitive answers!

And perhaps, above all, you need to be able to give a logical argument which guarantees that your conclusions follow from the information you began with.

These conclusions may only be approximate, so your argument should tell you how good your approximation might be.

The main point here is that mathematics not only produces results, but produces results which can be relied upon!

What do you study? Calculus: differentiation/integration in higher dimensions Algebra/Geometry: vectors/matrices/lines/planes/conic sections Analysis: sequences/series/limits/convergence Computer programming: Matlab/Maple Many other interesting things

How do you learn?

Number of contact hours A typical term contains: 4 courses A typical week for each course consists of: 3 hours of lectures 1 hour exercise class Additional contact hours per week: 1 hour tutorial Office hours (2x1 hour)

Which University to choose?

Entry requirements

Quality of teaching and support

National Student Survey

Location

The campus

The city

Maths Courses on the UCAS web site

Actuarial Mathematics Applied Mathematics Business Mathematics Computing Computing Mathematics Discrete Mathematics Engineering Mathematics Environmental Mathematics Finance Mathematics General Mathematics Industrial Applied Mathematics Industrial Mathematics Mathematical Science Mathematics Education Philosophy Of Mathematics Pure Mathematics Secondary Mathematics Statistics

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience. In the United Kingdom, and several other countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.

Actuarial science includes a number of interrelating subjects, including probability, mathematics, statistics, finance, economics, financial economics and computer programming. Historically, actuarial science used deterministic models in the construction of tables and premiums.

The science has gone through revolutionary changes during the last 30 years due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory

Many universities have undergraduate and graduate degree programs in actuarial science.

In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States.

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry.

Thus, "applied mathematics" is a mathematical science with specialized knowledge.

The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation and study of mathematical models.

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake.

Thus, the activity of applied mathematics is vitally connected with research in pure mathematics.

Business mathematics is mathematics used by commercial enterprises to record and manage business operations.

Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.

Mathematics typically used in commerce includes elementary arithmetic, elementary algebra, statistics and probability.

Business management can be made more effective in some cases by use of more advanced mathematics such as calculus, matrix algebra and linear programming.

Computational science (or scientific computing) is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems.

In practical use, it is typically the application of computer simulation and other forms of computation to problems in various scientific disciplines.

The field is distinct from computer science (the study of computation, computers and information processing). It is also different from theory and experiment which are the traditional forms of science and engineering.

The scientific computing approach is to gain understanding, mainly through the analysis of mathematical models implemented on computers.

Scientists and engineers develop computer programs, application software, that model systems being studied and run these programs with various sets of input parameters.

Typically, these models require massive amounts of calculations and are often executed on supercomputers or distributed computing platforms.

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits.

Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.

Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.

Maths Courses on the UCAS web site – with linksActuarial Mathematics Applied Mathematics Business Mathematics Computing Computing Mathematics Discrete Mathematics Engineering Mathematics Environmental Mathematics Finance Mathematics General Mathematics Industrial Applied Mathematics Industrial Mathematics Mathematical Science Mathematics Education Philosophy Of Mathematics Pure Mathematics Secondary Mathematics Statistics

What Grades are RequiredA variety of entry grades are listed below

Warwick A* Maths A*F Maths ASouthampton A A AExeter A*A BA*AA-AABReading 340pts A in mathsUEA A Maths B BNottingham A A ASheffield A A BLeicester A A BBath A* A APlymouth 280 pts B in mathsKent 300 pts A in mathsPortsmouth 260-300ptsKingston 280 ptsDerby 280 pts D in mathsSheffield Hallam 280pts C in mathsWolverhampton 160-220pts C in maths

Loughborough A A ANewcastle A A BSussex A A BLeeds A A BManchester A A BEssex A A BBirmingham Aberystwyth 300 pts B in mathsLancaster A B BBristol A* A ACardiff A A BHertfordshire 240 pts C in mathsNottingham Trent 280 pts B in mathsSurrey A A BKeele 300 pts A in maths

• Once you have researched your courses and narrowed down your choice of HE establishments you need to begin on your personal statement.

Focus on the subject you wish to study. Your statement should be at least 80% subject specific and only ~20% on other interests.

Try to include subject specific activities outside of your normal class work. This could include books you have read, courses or conferences attended, work experience or links with outside agencies/people.

Try to convey a sense of enthusiasm for your subject. You need to stand out against lots of other applicants.

Destinations of Recent Students2010

2007

University Departmental Gradings other Subjects

University Maths Department Gradings

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Interesting applications

of Mathematics• Special effects in films

• Pattern formation in nature

• Digital photography

• Medical imaging

Mathematics in the Movies Maths is used in creating many special effects

In order to create realistic animations of smoke, water and firecomplicated systems of equations (see next slide) need to be solved

Pirates of the Caribbean

Harry Potter and the Goblet of Fire

Finding Nemo

The Navier Stokes Equations

∂u + 1 ∆u + u · ∇u + p = 0 in Ω x (0,T),∇

∇ · u = 0 in Ω x (0,T),

t

− ∂ Re−

Here u(x,y,z,t)=(u ,u ,u ) is a vector field

denoting the fluid’s velocity

p=p(x,y,z,t) is a scalar field denoting pressure

1 2 3

(a system of nonlinear partial differential equations)

∇ is the vector differential operator del or nabla

∆ = · is the scalar differential operator ∇ ∇ Laplacian

When Toy Story was made in 1999 simple,

hard, plastic toys were used in the

animations

Maths is used in the making of animated movies

By 2001 when Monsters Inc was

made advances in maths helpedenable the animation of more

visually rich human-like characters

Maths is used in animations to morph one shape into another

Mathematical Biology:

pattern formation

By solving relatively simple equations on complicated domains you can obtain many naturally occurring pattern formations

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Spots or stripes?Changing the domain but keeping the coefficients fixed gives rise to different patterns

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Slightly changing the coefficients in the equation but keeping the domain fixed also gives different patterns

Image processing: maths is used in removing noise from digital camera

photos

Number Plate Recognition

Similarly MRI scans include random noise which needs to be smoothed

out

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