*Recently I got a lot of requests from Russian followers who also want to read my article by couldn't do so due to language barriers. So I decided to conduct experiment and also start to provide a link to Russian translation at the end of each article with the hope that it will broad my standing and, equally important, to help Russian audience explore useful information about popular science, math, and modern technologies.*

***Before we start talking about mathematical modeling, let's learn what, in general, the process of modeling is. As you might have guessed - it is a kind of study about specific systems or single objects by creating and further studying of their models.***

![enter image description here](http://i84.fastpic.ru/big/2016/0915/af/c19817f427be8a4ece4e33e8ab81daaf.jpg)

*During the study of any cumbersome and difficult phenomenon will be replaced with a simpler scheme, which will then be used for the calculations.*

*A mathematical model is a major part of the study and creation of the developing of any system. In order to be easy in use, this model must be accurate, adequate, complete and logically justified.*


# Classification of mathematical models
There are many different classifications of mathematical models for entirely different fields, but the main are **determinate** and **stochastic**.


![enter image description here](http://i84.fastpic.ru/big/2016/0915/5a/70bc176fdab7a1fe450a7d9307da135a.jpg)

The **determinate** can be called those models that have mutually - unique correspondence of variables, which describe the desired phenomenon or object of study.


Often these phenomena are extremely complex, and mechanisms for their implementation or operation can’t be deciphered or it takes so much time that the process is deemed unprofitable. In such cases, the following occurs - the original object passes all necessary testing and research, after getting the results of this test a partial processing of the data and the results occurs after which, the researcher neglects the study of the principles of operation of the object, and through mathematical statistics and probability theory provides the description of variables relations of the simulated object.

![enter image description here](http://i85.fastpic.ru/big/2016/0915/99/e9d15c2fca613ec181e882d0315fb799.png)

Thus, a **stochastic** model where any communication of all the variables is random and therefore lead to the exact mathematical modeling of the object occurs.


# A mathematical model, of course, has different requirements listed below

- The most important of these is flexibility - a feature that displays the accuracy and completeness of conformity of all the features of the original object and this model.
- The second requirement – is an adequacy - characteristic that shows that the various required features of the object are calculated with minimum errors, or without them.
- An important criterion is a precision - it is a characteristic, which should show a full match of all the desired features of the object and the constructed model.

![enter image description here](http://i84.fastpic.ru/big/2016/0915/80/f02acb88fe87006de43d7df7572ae280.png)

- And last, but not least important is the economy - a characteristic that shows how much time and computer's memory you need for a complete description of the model, its implementation, and exploitation.


# The main stages of mathematical modeling

- Creating a model. This stage is characterized by giving "non-mathematical" object, for example, a natural phenomenon, in which the main characteristics and certain relations between them are determined. Then all this is made in a mathematical form, so we develop a mathematical model.
- The solving of mathematical problems derived from the model. This phase includes the development of algorithmic methods of solving this problem on a computer with getting the result with the specified accuracy and in the allotted time.

![enter image description here](http://i84.fastpic.ru/big/2016/0915/6c/935e77e5ce162378e3bc6cb4b0c8286c.jpg)

- Interpretation of the consequences of the previously composed mathematical model. At this stage consequences, which were derived from the model of the object in the language of mathematics, will be interpreted into another language used in this field.
- Check the adequacy of the model. This step includes determining whether numerical values  after the calculation of model converge to the real experiment.

![enter image description here](http://i85.fastpic.ru/big/2016/0915/25/53ff6c553c48d7239ef1f2ce7fb45525.png)

- Transformation and improvement of the model. At this stage, an improvement of existing model is made to reach the reliable compliance with the physical and mathematical laws and practical use in production.

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***I want to finish my article with few examples of the use of mathematical modeling:***

![enter image description here](http://i84.fastpic.ru/big/2016/0915/3e/a191cf629145e390bf5bfd055ca85b3e.jpg)

- *Mathematical modeling of venture capital investment allows making any forecasts about the development of venture investment project with a complete prediction of the ideal time of leaving the project by the investor.*
- *A mathematical model of the state management of the economy, which operates with the link between the GDP of the state, and other factors such as inflation, etc.*
- *Mathematical modeling of the scoring process, in which the information about timing and size of the credit in relation to the client's salary is collected, and on this basis, the decision whether to grant him such amount of money or not is made.*

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**With Love,
Kate**

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Image credit: [1](http://myabccoolimages.com/mathematical+modelling+activity), [2](http://birmaga.ru/dosta/Математическое+моделирование+температурных+полей+силовых+биполярных+транзисторовa/main.html), [3](https://www.regonline.com/builder/site/Default.aspx?EventID=1215517), [4](http://ucsmp.uchicago.edu/resources/conferences/2011-09-11/), [5](http://www.azquotes.com/quote/126792), [6](http://id-ea.org/mathematical-models-with-complicated-dynamics-for-disease-study/)

*As promised, [here is a link](https://hackmd.io/s/r1MXZ_O3) to the Russian version of this article. I know that some people don't like to click on external links as afraid that there could be some malware. In this case, you probably should incognito mode of your browser.*

*Как и обещала, [вот ссылка](https://hackmd.io/s/r1MXZ_O3) на русскую версию статьи. Если боитесь переходить по внешним ссылкам, то используйте приватную вкладку браузера*