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Model is a miniature representation of something; a pattern of something to be made; an example for imitation or emulation; a description or analogy used to help visualize something (e.g., an atom) that cannot be directly observed; a system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs. This definition suggests that modeling is an activity, a cognitive activity in which we think about and make models to describe how devices or objects of interest behave. We can use words, drawings or sketches, physical models, computer programs, or mathematical formulas. In other words, the modeling activity can be done in several languages, often simultaneously. Since we are particularly interested in using the language of mathematics to make models. Mathematical model is a representation in mathematical terms of the behavior of real devices and objects. We want to know how to make or generate mathematical representations or models, how to validate them, how to use them, and how and when their use is limited. However, before delving into these important issues, it is worth talking about why we do mathematical modeling.

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Ghassan Ezzulddin Arif has been awarded Ph.D. in Applied Mathematics with more than 30 years experience.Yarub Al-Douri has been awarded Ph.D in Materials Science. He is specialist is Nanoscience and Nanotechnology. He is Editor-in-Chief of International Journal of Nanoelectronics and Materials, and World Journal of Nano Science and Engineering.

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