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Between one and another can be described as follows: Nature presents a physical, chemical, biological, social reality .... it seems desirable to explore and control. From the observation of this reality a mathematical model is extracted which appears to be adjusted in its functioning. This model is developed with existing appropriate mathematical tools and techniques, or new mathematical structures are created that allow for their deeper knowledge. In this study the mathematician, driven by the desire to know in depth the mental structure underlying the model, goes on many occasions much farther than the mere dominion of the initial reality would require. Once you know the model and the laws that govern it, it is a question of rehearsing this conceptual domain in the reality of departure. The attained knowledge of the model, partly perhaps superfluous for the moment, is stored and maybe one day will be used.
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In describing the diverse environments of the fundamental mathematics and the mathematics of the applications it is necessary to bear in mind also that the mathematics nowadays constitutes an organic unit in which the interdependence between its diverse fields is perhaps one of the most striking notes of the contemporary mathematics. One cannot, for example, speak of mathematical logic without taking into account the modern computer science, nor of geometry ignoring the analysis.
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In the description that follows from the different fields of the current mathematics we will try to indicate specifically some of the points in which this interaction is presented.
At the end of our journey we will briefly examine the deep sense of mathematical activity and its role in human culture. |
The brief description that follows from the different branches of the fundamental mathematics aims to give an idea, without technicalities, of the spirit and intentions that animate the activity of those who work in them. To get a more accurate idea we refer to the bibliography at the end of this work, where you can find more detailed exhibitions written by specialists.
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