Mathematical Modelling

The mathematical Model of a phenomenon is a mathematical description that is as simple as possible but captures all important characteristics of the phenomenon. The construction of the model for a specific phenomenon is called modelling. Possible reason of modelling is to understand the phenomenon and to predict its behavior. The simpler and more accurate the model is, the better is the modelling.

Every problem that should be solved with the help of a computer must first be translated into a mathematical language. This mathematical expression is called a model and the process of translation is called modelling. To do justice to the solution of the problem, the model must be chosen with great care - every effort expended in a problem's solution is connected to the model. A good model is already half the solution.

Usually there are many possible models for any one phenomenon. Which is the "best" depends on the application for which the model is to be constructed. Is the computing speed of primary concern, as for example in weather prediction, one chooses a simpler model. If the accuracy is more important, as for example in safety testing, one chooses a more complex model.

Example: A computer is to automatically decide whether a document belongs to the category "novel" or "non-fiction". This task is only to be accomplished by first creating a precise but nevertheless flexible definition of both terms. As the computer is to perform its task automatically, this definition must be calculable, must therefore not require an understanding of the text at hand. This problem (for every library category) was solved by algorithmica technologies.


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