New areas of mathematics

New Areas of Mathematics

 

Many activities involve the construction of mathematical models in which the resulting equations are so complicated that the current body of mathematical knowledge is inadequate to provide an answer. Research is then needed to extend existing theories to cope with these new problems. We shall discuss briefly a few examples which, between them, illustrate the all-pervasive nature of Mathematics in the modern world.

 

1. Mathematical Finance

All the major banks and finance houses employ teams to develop models to predict the future behaviour of share prices on the Stock Exchange, interest rates and many other economic indicators. Major roles are played by the areas of probability and statistics which could be said to model the Mathematics of Uncertainty.

 

2. Nonlinear Dynamical Systems

A good example is provided by the weather which is constantly changing (dynamic) and modelled by very complicated (nonlinear) equations. Forecasts are based on measurements from satellites, weather stations, etc. However, whenever a measurement is made, small errors will arise. Often these have no effect but in some situations, as time goes by, they not only persist but get worse and calculations eventually become worthless. This is linked to a phenomenon called chaos. Mathematical advances could lead to long-range forecasts becoming more reliable.

 

3. Liquid Crystal Displays (LCDs)

Think of a plasma screen television. You will probably be aware that Physics, Chemistry and Engineering have been involved in its construction but Mathematics has also played a role. Attempts are constantly being made to improve picture quality, e.g. to cope with footballers moving quickly. Examples of LCDs are all around us. In my own Department at Strathclyde there is an internationally-renowned research group collaborating with colleagues in other disciplines to produce better LCDs.

 

4. Security

Security issues dominate our lives in various shapes and forms. Consider internet shopping, where the buyer is required to type in a credit card number and other personal details. To avoid a hacker emptying out the buyer’s bank account, the details of the transaction have to be encrypted (scrambled) at the buyer’s end and decrypted (unscrambled) at the seller’s end so that the hacker can make no sense of them as they go down the wire. Number Theory provides the key. Thus one of the oldest and most beautiful branches of Mathematics has really come into its own, even if it has had to wait 2000 years to find an everyday use!

 

Careers

 

Given the range of applications listed above, it is no surprise that career opportunities for graduates in the mathematical sciences are enormous. Everyone knows that teaching and lecturing are options but that is only the start.

 

  • The financial sector takes a large percentage who become accountants, actuaries, traders on the Stock Exchange, fund managers, investment analysts, bankers, etc.
     
  • Statisticians are employed by government departments, health boards and pharmaceutical companies.
     
  • The IT sector employs Maths graduates as programmers and systems analysts.
     
  • Although some industries have declined in recent years, opportunities still exist in Research and Development.
     
  • Less obvious destinations include jobs in business, such as Personnel Management.

 

Employers are looking for people who can think logically, analyse a situation rigorously and then make a sensible decision on the basis of their conclusions. These so-called transferable skills are an integral part of a mathematician’s training and make Maths graduates highly marketable. Indeed such graduates can do ALMOST ANYTHING !

 

Conclusion

 

Studying for a Maths-based degree keeps many doors open. At the same time you can enjoy a subject that combines elegance and beauty with relevance to the world in which we live.

 

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