An introduction to mathematical modelling

 

Sans les mathématiques on ne pénètre point au fond de la philosophie.

Sans la philosophie on ne pénètre point au fond des mathématiques.  
Sans les deux on ne pénètre au fond de rien. 
 
Leibniz 

The use of mathematical modelling mainly consists in replacing the cognitive object with its mathematical image (its mathematical model) which implemented by logical and numeric algorithms through computers, allows studying the main patterns of the actual process. Such a cognitive method shows the advantages of theoretical and empirical approaches. Working with the mathematical model instead of focusing into the cognitive object, in a fast and cheap manner, permits to analyze and forecast state properties theoretically. At the same time numeric methods allow, using the computer calculation power, through numeric experiments, to verify behavior and patterns not easily reached by the analytical approach. A rising of mathematical modelling took place with the emergence of the computer in the 40-50th. and was encouraged by the unprecedented requirements of the United States and Soviet governments (Samarsky  y Mikhailov, 1997) for the building of anti-aircraft shields. In this case, mathematical modeling fulfills the expectations, nuclear explosions, ballistic trajectories and satellite release were previously done in the heart of computers using the respective mathematical models. Such successfulness has contributed to the development of mathematical modeling positioning this cognitive method as the kernel of the information society.   

 
 

This is recommended to use this method in such situations where the analysis of the cognitive object looks unfeasible, expensive or too risky. Working with the mathematical model, instead of handling the actual system gives the advantage of studying the cognitive object properties in a safely, fast and cheap way and for any conceivable situation.

 

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