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What is Mathematical Engineering?

Do you enjoy mathematics and feel that you would like to use it to solve important real world problems of direct engineering, scientific or industrial relevance? In recent years there has been an extraordinary growth in the application of mathematics to these fields as well as to information technology, management and finance. Engineering mathematicians develop and apply advanced mathematical and computational techniques to understand these problems.

Engineering is the art of creating and improving our environment. It involves planning, design, construction, quality assessment and control. None of these would be possible without mathematics. Engineering mathematics is at the core of all branches of engineering, from aerospace engineering to electronics and from mechanical engineering to computer science. As engineering evolves and develops, mathematics forms the common foundation of all new disciplines.

We are learning that engineering systems, which seem straightforward to design, exhibit unpredicted and unstable behaviour when constructed. Take the example of a bridge that is made up of a simple suspension structure. Tests on scale models can show the bridge to be both strong and stable, but when the real structure is built it may sway unsteadily. Nonlinear dynamics, the mathematics of chaos, can help us to predict such behaviour and correct the design before construction begins. Similar techniques enable the engineering mathematician to understand phenomena as diverse as chaos in semiconductor lasers and patterns in traffic jams, to predict the weather, or to send spacecraft to the sun using only a tiny amount of fuel!

In our data-rich society we also see how engineering mathematics fulfils a pivotal role. From the deluge of data collected from sounds, images, videos and text we need to extract important and appropriate information. Knowledge engineering can help us to solve problems where traditional computer science techniques fail. Take the example of global warming. This environmental phenomenon is causing devastating problems around the world. Countries formerly arid are suffering from massive floods while fertile countries face unexpected droughts. Artificial intelligence techniques enable us to learn patterns from satellite images and rainfall data. We can then fuse this information with expert geological knowledge and mathematical models of river basins to predict when rivers are likely to flood.

Today, even if a product does not contain a computer, you can be sure one was used in its design. What you may not realise is that all of these computers need mathematics. From the error correction algorithm in your mobile phone to stress analysis programs that let engineers design giant bridges or aircraft, scientific computing is ubiquitous in the modern world. Engineering mathematics students are exposed to a wide range of computer programming. Not only do they graduate with knowledge of industry standard programming languages such as C, C++, Java and Matlab, but see first hand how mathematicians use these tools. They could find themselves writing software to diagnose lung disease automatically, or inventing new algorithms to explore and understand chaotic systems.

Computing, however must be combined with expertise in mathematical analysis and awareness of engineering systems. Even though complicated problems can be coded into software packages and the results made available very rapidly by people with little scientific skill, the usefulness of the computing is highly dependent on the problem formulation. Mathematical modelling becomes vitally important, as one model created for one set of conditions may be disastrous in another (compare the shapes of a 747 and an F-111). Even with a tried and tested model, few computer codes can deal with regions of rapid variation of (say) temperature or pressure. In these areas, mathematical ideas such as asymptotic analysis and boundary layer theory are indispensable as tools to aid understanding.

The range of courses studied as part of an Engineering Mathematics degree enable students to work on ‘case study’ activities: technological problems, often derived from actual industrial situations, and presented in a real-life format. By the time students reach their final year, they are perfectly placed to take part in cutting edge research by undertaking a major project. Project work is an excellent opportunity to put into practice skills taught during the rest of the degree course. Moreover it is a creative and highly enjoyable experience, providing students with a wide range of skills for their future careers.

Examples of case study activities:

  • Modelling water levels in a hydroelectric dam system
  • Development of a digital television system
  • Modelling blood sugar levels in patients with diabetes
  • Estimation of the power requirement for the drive motor in a radar system
  • Investigation of bearing erosion in diesel engines

Opportunities
Industry now requires an increasing number of numerate graduates who can apply mathematics in practical situations. Engineering Mathematics graduates are called on to use their logical skills to formulate a problem; their modelling skills to translate the problem into mathematical terms; their technical skills to write a computer program; their mathematical understanding to question and interpret the results; and their knowledge of engineering to implement the solution. Engineering Mathematics graduates are superbly employable - students graduate with technical and transferable skills that enable them to play a leading and creative role as mathematicians and engineering professionals in industry, academic research, and elsewhere.

Skilled in the analysis, design and development of a huge variety of real world engineering problems, the core skills developed by engineering mathematicians are transferable to all engineering disciplines. Engineering Mathematics is at the heart of engineering.

Author:
Dr. Martin Homer
Lecturer in Engineering Mathematics
University of Bristol

 
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