The Learning Process For Mathematical Modelling

It is easy to describe real modelling problems undertaken by the professionals, but how are you to begin your own expertise? As you start, you are probably reasonably confident about elementary calculus, algebra, and trigonometry and perhaps also statistic and mechanics, but constructing mathematical models is a different matter. It is not necessary to attempt complicated modelling problems based on industrial aplications. The 'art and craft' of model building can be learned by startting with quite commonplace situations which contain a mathematical input based only on the mathematical work done at secondary-school level. As experience and knowledge are gained both in conventional mathematics and statistics as well as in modelling, then increasingly demanding problem can be considered. The first examples need not be contrived or false, for there are plenty of simple real-life situations available for study.

By the time that you have worked, you should have gained considerable experience ot mathematicals models and modelling. It is important to do modelling yourself, to try out your own ideas and not to be afraid to risk making mistake. Learning modelling is rather like learning to swim or to drive a car; it is no good merely reading a book on how to do it. Similarly, with modelling, it is not sufficient to read someone else's completed model. Also mathematics has perhaps acquired a reputation for being a very precise and exact subject where there is no room for debate: you are either right or wrong. Of course, it is etirely appropriate and necessary that mathematical principles are based on sound reasoning and development but, when we come to model some given problem, we must feel free to construct the model using whatever mathematical relationship and techniques seem appropriate, and we may well change our minds several times before we are satisfied with a particular model.

It is often important, for the best results, not to work on your own. In industry, it is normal for a team of people to work together on the same model, and the team may consist of engineers or economists as well as mathematicians. It should be the same for beginners at the student level, we hope that the most of the modelling exercises are tried amongst a group. Different people have different suggestions to make, and it is important to pool ideas.

To be a succesful mathematical modeller, it is not sufficient to have axpertise in the techniques of mathematics, statistics and computing. Additional skills to acquired, together with the following general qualities: clear thinking, alogical approach, a goodl feel of data, an ability to communicate and enthusiasm.

Source :
Edwards, Dilwyn & Hamson, Mike. 1990. Guide to Mathematical Modelling. Boca Raton, Florida, USA : CRC Press, Inc.