Advanced Mathematical Techniques for Data Analysis

Mathematical models as constituents of the theory have played an important role in shaping the course of research. They enable one to simplify, abstract and analyze the data so as to have a better understanding of the real life situations. Data analysis for the determination of the fundamental variables is an important aspect of mathematical modeling. It involves a high degree of creativity. One looks a real model and attempts to identify the operative process at work. The goal is the expression of the entire situation in symbolic terms. As a consequence, a model becomes a mathematical tool in which the real quantities and processes are replaced by mathematical symbols, relations and operations. One may find that several mathematical models may be appropriate for the same real life situation. In such circumstances, it may be the case that one model accounts especially well for certain observation while another model accounts for something different. There may not be a ¿best¿ model; the one to be used will depend on the precise questions to be studied. The motivation for the mathematical study is to produce new information about the situation being studied.