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Mathematical model


A mathematical model theoretically describes an object that exists outside the field of Mathematics. Weather forecasts and economic forecasts, for example, are based on mathematical models. Its success or failure depends on the precision with which this numerical representation is constructed, the fidelity with which natural facts and situations are concretized in the form of variables related to each other.

Basically, in a mathematical model we notice 3 phases:

* construction, the process in which the object is converted to mathematical language;
* he analysis o study of the ready made model;
* the interpretation of said analysis, where the results of the study are applied to the object from which it was based.

The usefulness of these models is that they help study how behaviors behave. complex structures in the face of situations that cannot be easily seen in the real world. There are models that work in certain cases and are not very accurate in others, as is the case with Newtonian mechanics, whose reliability was questioned by Albert Einstein himself.

It can be said that mathematical models are sets with certain relationships already defined , which enable the satisfaction of propositions that derive from the theoretical axioms. To do this, they use various tools, such as linear algebra, which, for example, facilitates the analysis phase, thanks to the graphic representation of the different functions.

Classifications according to various criteria

According to the origin of the information on which the model is based, we can distinguish between heuristic model, which is based on the definitions of the causes or natural mechanisms that originate the phenomenon in question, and empirical model, focused on the study of the results of the experimentation.

Also, with respect to the type of intended result, there are two basic classifications:

* qualitative models, which can use graphics and do not seek an exact result, but try to detect, for example, the trend of a system to increase or decrease a certain value;

* quantitative models, which, on the contrary, need to find a precise number, for which they rely on mathematical formulas of varied complexity.

Another factor that divides the types of mathematical models is the randomness of the initial situation; Thus we distinguish between the models stochastic , which return the probability of obtaining a certain result and not the value itself, and deterministic , when the data and the results are known, so there is no uncertainty.

Depending on the objective of the model, we can describe the following types:

* simulation model, which tries to anticipate a result in a given situation, whether it can be measured accurately or randomly;

* optimization model, which includes different cases and terms, alternating values, to find the most satisfactory configuration;

* control model, through which the necessary adjustments can be determined to obtain a particular result.

Mathematical models as a support for consumerism

Different dice factors cultural and educational, Mathematics is the least attractive science for a large percentage of people, which relate it to ominous memories of his student age. Many of them dedicate their lives to humanistic or artistic tasks, and believe they live outside the numbers and the complex functions that will one day threaten school failure; but these formulas are the pillars of the system and, if they were presented in a friendly and close way, they would not generate that typical rejection, often justified in a lack of capacity.

Mobile phones with touch screens, television pays with hundreds of channels and virtual movie rental services, or the Internet itself, with its infinite possibilities, are the favorite entertainment forms of today globally. Now, if we visited the companies that manufacture the devices, or that design and develop the aforementioned services, we would find great quality control departments, that do nothing other than analyze, through mathematical models, possible interactions between users and systems, potential failures, and that seek to improve the final product, based only on tests and their resulting numbers.

Suppose we have a video on demand service, and that, when paying for a certain movie, we are asked if we have a discount coupon. At that time, we are also informed that, since we are in a week of promotion, a bonus of one hundred amount will be applied. All this, if we had to do it by hand, for a particular client, it would not be very complicated; With paper, pencil and a calculator, we would solve the final price. But in the case of a platform with which millions of people interact per day, it is necessary to prepare and rigorously test all possible combinations to prevent, for example, that a coupon is used more than once, or after its expiration, among other potential violations of the system.