Basic Concepts of Data Modeling:

We live in a real world and face many situations where we require mathematics to help us; in last centuries much of our progress has made it compulsory to apply mathematical models in various problems across many fields. Somewhere this approach has become more efficient because of increase in computing methods. This translation of real-life problems into mathematical a form for a better solution and representation is known as Mathematical Modeling or Data Modeling. 

Mathematical Modeling or Data Modeling is a method of practice or an artistry taken from fine arts to convert physical situation into mathematics using some conditions.

The process of Data Modeling involves four steps:

Understanding the Problem: This basically includes studying and understanding the process or behavior of the problem. On the basis of this understanding we form a statement henceforth it is very necessary to have a clear understanding of the problem. For example, in displaying creature development to go about as a guide for horticultural consultants, an exact model containing terms for the most critical determinants of development might be very sufficient. The model can be viewed as a synopsis of current comprehension. Such a model is plainly of exceptionally constrained use as an exploration device for planning trials to examine the procedure of ruminant nourishment.

Formulation: The process of formulation consists of two steps:

Identifying the relevant factors: this is a step where we figure out the necessary parameters which are the part of the problem. After creating a list of necessary parameters, we discover the essential parameters by carrying out certain experiments. The process of searching essential parameters is very crucial for the next steps.

Mathematical Description: this is a step to find an equation, inequality or a geometric figure related to the identified parameters.

Finding the Solution: Mathematical formulation does not give the answer directly. There is a certain process of operations which are needed to be done. These operations include solving an equation, calculation or applying a formula or theorem etc.

Interpretation or Validation: As mentioned above mathematical modeling is a representational study of real life problems. Sometimes we get the result by assuming an ideal situation otherwise we reject it and test it again. Thus the effectiveness of the model is measured by comparing the results obtained from a mathematical model, with the known facts about the real problem. The process of measuring effectiveness is called validation of the model. After accepting the model, we interpret it. The solution is then described in reference to the real solution; this process is called the interpretation of the model. In this manner Newton expected that mass is a widespread steady, though Einstein considered mass as being variable. This is one of the key contrasts between established mechanics and generally hypothesis. Utilization of the consequences of established mechanics to items venturing out near the speed of light prompts irregularities amongst hypothesis and perception. In the event that the presumptions are adequately exact, they may lead straightforwardly to the mathematical models administering the framework.

These four steps are repeated until we get the relevant mathematical model according to our requirements. 

Importance of Mathematical Modeling or Data Modeling:

Mathematical Modeling is an essential tool for understanding the world. According to the history the Chinese, Egyptians, Babylonians and Greeks used mathematical modeling to predict the natural phenomenon. Many architects, artisans and craftsmen use geometric principles for their work. Surveyor uses it to measure the height of a tower as it is impossible to measure the height of a tower using an inch tape. Mathematical Modeling is very useful to study various real life problems. Proper blood flow is a necessity for transmission of oxygen and nutrients in various parts of human body; mathematical modeling finds its importance in developing the relationship between blood flow and blood vessels psychological characteristics. Hawkeye used in cricket to take the decision of LBW is based on mathematical modeling, by deriving mathematical equations on the basis of the path of balls. Mathematical models are implanted in a financial system to help basic leadership. Expenses are joined to different contributions to the model. Input levels are picked in a way that fulfils any requirements on the framework. Contingent on the level of these inputs, the model is utilized to gauge yields. These yields themselves will have a money-related esteem (e.g. deal value) joined to them. The contrast amongst yield and information qualities is then a gauge of gross benefit. Meteorology departments use mathematical modeling for the prediction of weather. Weather conditions are affected by parameters like temperature, air pressure, wind speed etc. Thermometers measure temperature, barometers measure air pressure, hygrometers measure humidity and wind speed is measured by anemometers. This data is collected at different stations and then fed into a computer for analysis and interpretation. It is also used by Agriculture Department to estimate the yield of rice in a country from the standing crops. This estimation is done on the basis of some statistical techniques. Mathematical Modeling also plays an important role in building algorithms and codes in the field of computer science. There is much to be picked up from acquiring an investigative answer for a model. This will enable us to play out the majority of the controls suggested by the model with the base of the object. Take note of that a full scientific answer for a stochastic model includes finding the dispersion of results, however, we may feel fulfilled in the event that we can settle the conditions for the mean and standard deviation. When all is said in done, getting a diagnostic arrangement is once in a while a basic matter. In certain unique cases, it is conceivable to acquire mathematical model for an arrangement of conditions.

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