Stages of information modeling. Practical work in a word processor MS Word

REMEMBER! Life-threatening voltages are supplied to every workplace.

During work, you should be extremely careful.

In order to avoid accident, electric shock, equipment breakdown, it is recommended to follow these rules:
Enter the computer class calmly, without hurrying, without pushing, without touching furniture and equipment, and only with the permission of the teacher.
Do not turn computers on or off without your instructor's permission.
Do not touch the power wires and connectors of the connecting cables.
Do not touch the screen or the back of the monitor.
Do not place foreign objects in the workplace.
Do not get up from your seats when visitors enter the office.
Do not try to troubleshoot the equipment yourself; in case of problems or malfunctions in the computer, stop working immediately and inform the teacher about it.
Operate the keyboard with clean, dry hands; Press the keys lightly, avoiding harsh impacts or holding the keys down.

REMEMBER! If you do not take precautions, working on your computer can be hazardous to your health.

In order not to harm your health, you must follow a number of simple recommendations:
Improper sitting at the computer can cause pain in the shoulders and lower back. Therefore, sit freely, without tension, without stooping, without bending over or leaning against the back of a chair. Put your feet straight on the floor, one next to the other, but stretch them out and do not bend them.
If the chair is height adjustable, then it should be adjusted so that the angle between the shoulder and forearm is slightly more than straight. The body should be at a distance of 15-16 cm from the table. The line of sight should be directed to the center of the screen. If you have glasses for permanent wear, work with glasses.
When working, the shoulders should be relaxed, the elbows should slightly touch the body. The forearms should be at the same height as the keyboard.
With strenuous long-term work, the eyes overwork, so every 5 minutes, take your eyes off the screen and look at something in the distance.

Correct fit

The most important thing

1. When working at a computer, it is necessary to remember: life-threatening voltage is supplied to each workplace. Therefore, during work, you must be extremely careful and comply with all safety requirements.

2. So that working at a computer does not turn out to be harmful to health, you must take precautions and monitor the correct organization of your workplace.

Safety poster

The main stages of modeling

After studying this topic, you will learn:

What is modeling;
- what can serve as a prototype for modeling;
- what is the place of modeling in human activity;
- what are the main stages of modeling;
- what is a computer model;
- what is a computer experiment.

The place of modeling in human activity

In the "Understanding an Object Model" topic, we defined what a model is. The model can be an abstract or physical object, the study of which allows one to cognize the essential features of another object - the original. Building and studying models is a field of human activity called modeling.

Modeling - the study of objects by building and studying their models.

Why not investigate the original itself, why create a model?

Firstly, the original may not exist in the present: it is an object of the past or the future. For modeling, time is not a hindrance. Based on known facts, using the method of hypotheses and analogies, you can build a model of events or natural disasters in the distant past. So, for example, theories of the extinction of dinosaurs, the origin of life on Earth were created. Using the same method, one can look into the future. Physicists have built a theoretical model of the "nuclear winter" that will occur on our planet in the event of a nuclear war. This model is a warning to humanity. 

Secondly, the original can have many properties and relationships. On the model, which is a simplified representation of the object, it is possible to study some properties of interest to the researcher, without considering others. For example, when studying the most complex human organism in biology lessons, its various models are used.

Thirdly, often the model is an abstract generalization of real-life objects. A fashion model (model), demonstrating a new style of clothing, does not represent some real person with his features and shortcomings, but some generalized ideal image, a standard. Speaking about natural phenomena in geography lessons, we do not mean any specific natural phenomenon, for example, an earthquake, but some generalization, a model of this phenomenon. In such cases, the prototype of the model is a whole class of objects with some common properties.

Fourth, the original may not be available to the researcher for any reason: a model of the hydrogen atom, the relief of the lunar surface, parliamentary power in the country.

What can be modeled? The object of modeling can be a material object, phenomenon, process or system.

Models material objects visual aids in the classroom, drawings of architectural structures, reduced or enlarged copies of the objects themselves can serve.

To prevent disasters and use natural forces for the benefit of man, models of the phenomena of living nature are created and studied. Academician Georg Richman, associate and friend of the great Lomonosov, back in the first half of the 18th century, simulated magnetic and electrical phenomena for the purpose of their study and further application.

You can also create process models: course, sequential change of states, stage of development of an object or system. You have probably heard about models of economic or ecological processes, models of the development of the Universe, society, etc.

If the object is considered as a system, then a model of the system is built and investigated. Before the construction of a residential area, architects create a full-scale model of the development area, taking into account the location of buildings, squares, parks and roads.

Modeling is one of the key types of human activity and always in one form or another precedes its other types.

Before taking on any work, you need to clearly understand the starting and ending points of the activity, as well as its approximate stages. The same can be said for modeling.

The starting point here is the prototype (Figure 11.1). As mentioned earlier, it can be an existing or projected object, phenomenon, process or system.

Rice. 11.1. Generalized stages of human activity in the study of an object

The final stage of modeling is decision making... As a result of modeling, new information is acquired and a decision is made to create a new object or to modify and use an existing one.

An example of modeling in the creation of new technical means is the history of the development of space technology. To implement a space flight, it was necessary to solve two problems: to overcome gravity and to ensure progress in airless space. Even Newton spoke about the possibility of overcoming the Earth's gravity in the 17th century. K.E. Tsiolkovsky suggested using a jet engine for movement in space. He compiled a fairly accurate descriptive model of the future interplanetary spacecraft with drawings, calculations and justifications.

Less than half a century later, Tsiolkovsky's descriptive model became the basis for real modeling in S.P.Korolev's design bureau. In full-scale experiments, various types of liquid propellants, the shape of the rocket, control and life support systems, instruments for scientific research, etc. were tested. The result of versatile modeling was powerful rockets that put artificial earth satellites, ships with astronauts on board and space stations into near-earth orbit ...

Let's look at another example. The famous chemist of the 18th century Antoine Lavoisier, studying the combustion process, conducted numerous experiments. He simulated combustion processes with various substances, which he heated and weighed before and after the experiment. At the same time, it turned out that some substances become heavier after heating. Lavoisier suggested that something is added to these substances during the heating process. So the modeling and subsequent analysis of the results led to the definition of a new substance - oxygen, to the generalization of the concept of "combustion". This provided an explanation for many well-known phenomena and opened new horizons in other fields of science, in particular in biology. Oxygen turned out to be one of the main components of respiration and energy exchange in animals and plants.

The diagram in Figure 11.1 shows that simulation is central to object research. Building a model allows you to reasonably make decisions on improving existing objects and creating new ones, changing their management processes and, ultimately, changing the world around us for the better.

Modeling is a creative process and therefore it is very difficult to put it in a formal framework. In its most general form, it can be represented in stages, as shown in Figure 11.2.

Rice. 11.2. Simulation steps

Each time when solving a specific problem, such a scheme may undergo some changes: some block will be excluded or improved, some will be added. All stages are determined by the task and the goals of the simulation.

Formulation of the problem

Life constantly presents a person with problems that need to be resolved. In terms of their complexity, these problems cannot be compared with any, even the most difficult task from school textbooks. In school problems it is clearly indicated to you what is given and what is required to be obtained, and in the section where the problem is given, possible methods of solving it are recommended. As a rule, in real life, a person deals with tasks (problems), where this is not explicitly. Therefore, the most important sign of a competent specialist is the ability to set a task, that is, to formulate it in such a way and in such a language that anyone who will participate in its solution can unambiguously understand it.

Stage of setting the problem characterized by three main points: description of the problem, definition of modeling goals and formalization of the problem.

Description of the task

The statement of the problem, as a rule, begins with its description... This is done in ordinary language, in the most common phrases. At the same time, the initial object, the conditions in which it is located, and the desired result, in other words, the starting and ending points of modeling, are described in detail.

By the nature of the setting, all tasks can be divided into two main groups .

TO first group can be attributed to tasks in which it is required to investigate how the characteristics of an object will change with some impact on it. This formulation of the problem is usually called “what will happen if? ..”. For example, would it be sweet if you put two teaspoons of sugar in your tea? Or: what will happen if the utility bills are doubled?

Some tasks are formulated somewhat broader. What happens if you change the characteristics of an object in a given range with a certain step? Such a study helps to trace the dependence of the parameters of the object on the initial data. For example, the information explosion model: “One person saw HJIO and told his friends about it. Those, in turn, spread the news further, etc. " It is necessary to track how many will be notified at specified intervals.

Second group tasks has the following generalized formulation: what effect should be made on the object so that its parameters satisfy a certain given condition? This formulation of the problem is often called “as soelat, which is, for example, how large should a balloon filled with helium be in order for it to rise upward with a load of 100 kg?

Most of the modeling tasks are usually complex. Solving such problems begins with building a model for one set of input data. In other words, first of all, the problem is solved “what will happen if? ..”. In rare cases, but still it happens that the final goal is achieved after the very first experiment. More often this does not happen, and then the object is examined when the parameters are changed in a certain range. And finally, according to the results of the study, the parameters are selected so that the model satisfies some of the projected properties. It is important to understand that the more experienced the researcher, the more accurately he will choose the range of input data and the step with which this range will be checked, and, as a consequence, the sooner he will achieve the predicted result.

An example of such an integrated approach is the solution of the problem of obtaining a chemical solution of a given concentration: “A chemical solution with a volume of 5 parts has an initial concentration of 70%. How many parts of water must be added to obtain a solution of a given concentration? "

First, the concentration is calculated when 1 part of water is added. Then a table of concentrations is built by adding 2, 3, 4 ... parts of water. The result obtained allows you to quickly recalculate the model with different initial data. According to the calculation tables, you can give an answer to the question posed: how many parts of water must be added to obtain the required concentration.

Let's consider three simple tasks, by the example of which we will follow the stages of modeling in the future.

Objective 1. Typing.

Type and prepare text for printing.

This problem often arises when creating compound documents in which one of the elements is text. This problem refers to the setting "what if?..".

Objective 2. Vehicle movement.

How does the vehicle speed change while driving?

In this task, it is supposed to trace how the speed of the car will change in a certain range of time. This is an extended statement of the problem. "what if?..".

Objective 3. Arrangement of furniture.

Find the most comfortable arrangement of a teenage furniture set in the room.

This problem refers to the setting "How to do that? ..".

Purpose of modeling

An important point at the stage of setting the problem is to determine the goal of modeling. The chosen goal determines which characteristics of the object under study are considered essential and which are discarded. In accordance with the set goal, the toolkit can be selected, methods for solving the problem, the forms of displaying the results can be determined.

Let's consider the possible goals of modeling.

Primitive people studied the surrounding nature in order to learn how to resist natural elements, enjoy natural benefits, just survive.

The accumulated knowledge was passed on from generation to generation orally, later in writing and, finally, with the help of subject models. This is how the globe was created - a model of the Earth, which allows you to get a visual idea of ​​the shape of our planet, its rotation around its own axis and the location of the continents. Such models help to understand how a specific object is arranged, to find out its basic properties, to establish the laws of its development and interaction with the surrounding world. In this case, the goal of building a model is to understand the surrounding world.

Having accumulated enough knowledge, the person asked himself the question: "Is it possible to create an object with given properties and capabilities in order to counteract the elements and put natural phenomena at his service?" Man began to build models of objects that did not yet exist. This is how the ideas of creating windmills, various mechanisms, even an ordinary umbrella were born. Many of these models have now become reality. These are objects created by human hands.

Thus, another important goal of modeling is the creation of objects with specified properties. This goal corresponds to the formulation of the problem and how to do it to ... ”.

Purpose of modeling tasks like "what will happen if .." - determining the consequences of the impact on the object and making the right decision. Simulations like these are important when considering social and environmental issues: what happens if the fare increases, or what happens if nuclear waste is buried in an area?

For example, in order to save St. Petersburg from constant floods, causing enormous damage, it was decided to build a dam. When designing it, many models were built, including natural ones, with the aim of predicting the consequences of interference in nature.

Often, the goal of modeling is the efficiency of object (or process) management. Since the management criteria are very contradictory, it will only be effective if "the wolves are fed and the sheep are safe."

For example, you need to establish food in the school cafeteria. On the one hand, food should correspond to age requirements (high-calorie, containing vitamins and mineral salts), on the other hand, most children should like it and be “affordable” for their parents, and on the third, the cooking technology should correspond to the capabilities of the school canteen. How to reconcile the incompatible? Building a model helps you find the right solution.

Let's return to the previously described tasks and define the goals of the simulation.

Objective 1. Typing.

Target: get a literate, readable document.

Objective 2. Vehicle movement.

Target: explore the process of movement.

Objective 3. Arrangement of furniture.

Target: find the best option for arranging furniture from the point of view of the resident.

Determining the purpose of modeling allows you to clearly establish which data are the source, which are irrelevant in the modeling process and what you want to get at the output.

Formalization of the task

In everyday life, we are constantly faced with the manifestation of formalism, which means strict order. And although we often talk about formalism with a negative assessment, in some cases it is indispensable. Is it possible to organize accounting and storage of drugs in a hospital or dispatch control in aviation, if these processes are not subject to strict formalization? In such cases, it means clear rules and their common understanding by everyone, strict accounting, uniform reporting forms, etc.

Usually they talk about formalization when the collected data is supposed to be processed by mathematical means.

Those of you who participated in the census may have noticed what forms the inspectors filled out after interviewing family members. In these forms, no room was allocated for emotions, they contained formalized survey data - units in strictly defined columns. This data was then processed using mathematical methods. It is impossible not to mention that the processing was carried out using a computer. A computer is a universal tool for processing information, but to solve any problem with its use, it must be stated in a strict, formalized language. No matter how miracle of technology the computer may seem, it does not understand human language.

When formalizing the tasks, they start from its general description. This makes it possible to clearly highlight the prototype of the simulation and its main properties. As a rule, there are quite a few of these properties, and some of them cannot be described in quantitative ratios. In addition, in accordance with the set goal, it is necessary to select the parameters that are known (initial data) and which should be found (results).

As mentioned above, the prototype for modeling can be an object, process, or system. If a system is modeled, it is analyzed: the components of the system (elementary objects) are identified and the connections between them are determined. When analyzing, it is also necessary to decide the question of the degree of detail of the system.

Formalization is carried out in the form of searching for answers to questions that clarify the general description of the problem.

Let's formalize the previously described tasks.

Objective 1. Typing.

What is being modeled? Object "text" Where can I get the content of the text? Available as a draft What is the intended print type? Black and white What are the options for the text? Indentation, right and left borders, typeface, font size and weight, color (black) What do you need to get? Typed, edited and formatted text

Objective 2. Vehicle movement.

What is being modeled? The process of movement of the object "car" Type of movement Equally accelerated What is known about the movement? Initial speed (V 0), acceleration (∝), maximum vehicle speed (V Max) What should be found? Velocity (V i) at given times (t i) How are times specified? From zero at regular intervals (A t) What limits the calculation? V i х V Max

Such characteristics of the object as color, body type, year of manufacture and total mileage, tire wear and many others, will not be taken into account in this setting.

Task 3. Arrangement of furniture.

What is being modeled? System ROOM-FURNITURE Room - is the System viewed as an object or as a system? What elements of the system Walls, doors, ROOM windows are important in this task? Furniture - is the System viewed as an object or as a system? What is included in the furniture? A sofa, a desk, a wardrobe, a general-purpose wardrobe (for books, a music center, toys, etc.), a wall-mounted sports complex What are the parameters of the furniture Length, width, height are specified? What are the parameters of the room in the form of a sketch are set: is it geometric? shape, size, location of the window and door What do you need to get? The variant of the most convenient furniture arrangement, presented in the form of a drawing (sketch)

In this task, it is inappropriate to divide pieces of furniture into components. For example, it makes no sense to consider a set of objects instead of a table - a table top, drawers, legs.

When arranging furniture, the following relationships should be considered:

♦ the height of the furniture is less than the height of the room; ♦ pieces of furniture should be placed with the front side inside the room; ♦ pieces of furniture should not obstruct the door and window; ♦ There must be enough free space around the sports complex.

When arranging furniture, the following connections should also be taken into account:

♦ all pieces of furniture must be close to the wall; ♦ The writing desk should be either near the window or close to the window against the wall so that the light falls from the left.

We will not take into account the connections between the pieces of furniture themselves. This means that all objects can be positioned in relation to each other as desired. This greatly simplifies the task.

The stage of setting the problem moves the researcher from describing the problem through understanding the goals of modeling to its formalization.

It is fundamental to modeling. A person goes through this stage independently, without the help of a computer. Further successful work on the development of the model depends on the correct formulation of the problem.

Model development

The stage of model development begins with the construction of an information model in various symbolic forms, which at the final stage are embodied in a computer model. In information models, the problem takes on a form that allows you to make a decision on the choice of a software environment and clearly present an algorithm for constructing a computer model.

Information model

The choice of the most essential data in the formation of an information model and its complexity are determined by the purpose of modeling. The parameters of the objects defined during the formalization of the task are arranged in decreasing order of importance. When modeling, not all are taken into account, but only some of the properties of interest to the researcher.

If we discard the essential factors, then the model will incorrectly reflect the original (prototype). Leaving too many of them can make the model difficult to build and explore. In many studies, several models of one object are created, starting from the simplest ones, with a minimum set of defining parameters. Then the model is gradually refined by adding some of the discarded characteristics.

Sometimes the task can already be formulated in a simplified form, the goal is clearly stated, and the parameters of the model that must be taken into account are defined. Problems of this kind you had to solve repeatedly in the lessons of mathematics and physics. However, in ordinary life, the selection of information has to be done independently.

The result of building an information model is a well-known table of object characteristics. Depending on the type of task, the table can be modified.

Consider the information models of the tasks described above.

Objective 1. Typing.

Information model

When building a computer figurative-sign model (text or graphic document), the information model will describe objects, their parameters, as well as preliminary initial values, which the researcher determines in accordance with his experience and ideas, and then refines it in the course of a computer experiment.

Objective 2. Vehicle movement.

Information model

In computational problems, the table contains a list of input, computational and resulting parameters.

Objective 3. Arrangement of furniture.

Information model

The information model, as a rule, is presented in one or another symbolic form. The table is one example of iconic patterns.

Sometimes it is useful to supplement the idea of ​​the object with other symbolic forms (diagram, drawing, formulas), if this contributes to a better understanding of the problem.

Consider sign models for the tasks described above.

Objective 1. Typing.

The iconic model is the result of solving a problem.

Objective 2. Vehicle movement.

The problem of car movement becomes clearer if you give a picture indicating the symbols used in the problem (Figure 11.3).

Rice. 11.3. Illustration for the problem of car movement

The mathematical model of the car movement is as follows:

T i + 1 = t 1 + V i + 1 = V 0 + ∝t 1

A correctly compiled mathematical model is simply necessary in tasks where it is required to calculate the values ​​of the object's parameters.

For systems, the information model is supplemented by a diagram of the connections identified during the analysis. Examples of such schemes are given in clause 8.4. The connection diagram can be as shown in Figure 11.4. In this diagram, connections are depicted by arrows pointing from one object to another. One-way arrows show the direction of the link - from the defining object to the defined one. Double-headed arrows indicate that objects mutually influence each other. Relationships in the construction of such schemes are depicted by dotted arrows.

Near the arrow, you can explain the nature of the connection.

Rice. 11.4. An example of a diagram of connections between system objects

Objective 3. Arrangement of furniture.

A diagram of connections and relationships is shown in Figure 11.5.

Rice. 11.5. Diagram of connections and relationships to the problem of arranging furniture

Sign forms can also have a different look.

For example, when creating geographic or historical maps, a legend system is developed.

Sign models are not required only for simple, familiar tasks.

The process of creativity and research always presupposes a painful search for a symbolic and figurative form of representing a model. Previously, this process was accompanied by baskets of discarded drafts. Nowadays, when the computer has become the main tool of the researcher, many people prefer to compose and write down preliminary sketches, formulas directly on the computer, while saving time and mountains of paper.

Computer model

Now that the informational sign model has been formed, one can proceed to the actual computer modeling - the creation of a computer model. The question immediately arises about the means that are needed for this, that is, about the modeling tools.

A computer model is a model implemented by means of a software environment.

There are many software packages that allow you to build and study models (modeling). Each software environment has its own tools and allows you to work with certain types of information models. Therefore, the researcher faces the difficult question of choosing the most convenient and effective environment for solving the problem. I must say that the same problem can be solved using different environments.

Originally, many years ago, computers were only used to solve computational problems. To do this, it was necessary to compose programs in special programming languages. With the development of software and hardware, the range of tasks that can be solved using a computer has expanded significantly.

In the programming environment, it is now possible not only to carry out the traditional calculation of the parameters of an object, but also to build a figurative model (drawing, diagram, animation plot) using the graphic means of the language.

In the process of developing a computer model, the initial informational sign model will undergo some changes in the form of presentation, since it should be guided by a certain software environment and tools. You learned the capabilities of specific software environments in practical exercises. The choice of the software environment in accordance with the type of information was discussed in topics 9, 10.

The algorithm for constructing a computer model, as well as the form of its presentation, depends on the choice of the software environment.

For example, it could be a block diagram. Figure 11.6 shows the algorithm for the problem of car movement in the form of a block diagram. Based on the flowchart, the problem can be solved in different environments. In a programming environment, it is a program written in an algorithmic language. In applied environments, this is a sequence of technological methods leading to a solution of a problem.

Rice. 11.6. Algorithm presentation in the form of a flowchart

For example, when simulating in the environment of a graphics editor or word processor, the algorithm can be presented in verbal form, describing the sequence of actions for creating objects and, if required, technological techniques. When developing an algorithm for building a model in spreadsheets, special attention is paid to the selection of areas of initial and calculated data and the rules for writing formulas connecting data from different areas.

Based on the foregoing, we can conclude that when modeling on a computer, it is necessary to have an idea of ​​the classes of software tools, their purpose, tools and technological methods of work. A variety of software allows you to transform the original informational sign model into a computer model and conduct a computer experiment.

Let's consider the possible options for choosing a computer environment for the above examples. For the sake of fairness, it should be noted that the problems proposed as illustrations can be solved and are often solved without the use of a computer.

Objective 1. Typing.

Traditionally, a word processor environment is used to model text documents.

Objective 2. Vehicle movement.

For tasks that require calculated values, a spreadsheet environment is suitable. In this environment, information and mathematical models are combined into a table containing three areas: raw data, intermediate calculations, and results. The spreadsheet allows you not only to calculate the required speeds, but also to build a car schedule.

A similar problem can be solved no less successfully in a programming environment. For example, the LogoWorld environment allows you to calculate the values ​​of the car's speed at regular intervals, as well as create an accompanying animation plot in which the car will move and the calculated values ​​will appear at regular intervals.

Objective 3. Arrangement of furniture.

The result of solving the problem is the most convenient option for arranging furniture, presented in one form or another: mentally, in the form of a drawing (sketch), in the form of a description. Very often a similar problem is solved “in the mind”. But if you want to clothe the reasoning in a symbolic form, then any environment that allows you to work with graphics will do. It can be a graphics editor, an embedded vector graphics toolkit in a word processor, or a programming environment.

The main stages of information modeling

Information Modeling is a creative process. There is no universal recipe for building models suitable for all occasions, but you can highlight the main stages and patterns that are typical for the creation of a variety of models.

First stage - formulation of the problem. First of all, you should understand the purpose of the simulation. Based on the purpose of modeling, the type and form of presentation of the information model, as well as the degree of detail and formalization of the model, are determined. In accordance with the purpose of modeling, the boundaries of applicability of the created model are predetermined. At this stage, it is also necessary to select the tools that will be used in the simulation (for example, a computer program).

Second phase - actual modeling, building a model. At this stage, it is important to correctly identify the objects that make up the system, their properties and relationships, and present all this information in the already selected form. The created model must be periodically subjected to critical analysis in order to timely identify redundancy, inconsistency and inconsistency with the goals of modeling.

Third stage - model quality assessment, which consists in checking the conformity of the model to the modeling goals. Such a check can be carried out by logical reasoning, as well as experiments, including computer ones. In this case, the limits of applicability of the model can be refined. If the model is found to be inconsistent with the goals of modeling, it is subject to partial or complete rework.

Fourth stage - operation of the model, its application for solving practical problems in accordance with the goals of modeling.

Fifth stage - analysis of the results obtained and correction of the investigated model.

Practical work in 3dsMax

First meeting. Facility management

Working with standard primitives

Creation of structures from primitives, management of views, rendering

Units, Grid, Snap to Grid, Arrays

Splines, spline vertex types, bodies of revolution

Extrude, bevel, loft, simple terrain

Working with materials

Composite materials

Lighting

Subtraction. Creation of a wall system. Organization of openings by subtraction

ALGORITHMIZATION AND PROGRAMMING

Algorithms

The emergence of algorithms is associated with the birth of mathematics. More than 1000 years ago (in 825), a scientist from the city of Khorezm Abdullah (or Abu Jafar) Muhammad bin Musa al-Khorezmi created a book on mathematics, in which he described how to perform arithmetic operations on multi-digit numbers. The word algorithm itself arose in Europe after the translation of the book of this mathematician into Latin.

Algorithm - a description of the sequence of actions (plan), the strict implementation of which leads to the solution of the task in a finite number of steps.

During its existence, mankind has developed rules of behavior in certain situations to achieve its goals. Often these rules can be presented in the form of instructions consisting of sequentially executed items (steps). So, for example, in a primitive society, an instruction for hunters to replenish the food reserves of a tribe might look like this:

Find a path that mammoths often walk along.

Dig a large deep hole on it and mask it with branches.

Hide and wait until the mammoth falls into the hole.

Throw spears and stones at a failed mammoth.

Butcher the carcass and deliver it to the tribe's huts.

It is possible that some of the rock paintings, made before the advent of writing, represented a kind of record of such instructions.

Lists of alternately performed actions are used in a wide variety of areas of human activity. Examples include the rules for multiplying and dividing numbers with a “column” in arithmetic, step-by-step instructions for performing physical or chemical experiments, assembling furniture, and preparing a camera for operation.

Algorithm properties:
1. Discreteness (the algorithm should consist of specific actions, following in a specific order);
2. Determinism (any action must be strictly and unequivocally defined in each case);
3. Finiteness (each action and the algorithm as a whole must be able to complete);
4. Massiveness (the same algorithm can be used with different input data);
5. Effectiveness (no errors, the algorithm should lead to the correct result for all valid input values).

Algorithm types:
1. Linear algorithm (description of actions that are performed once in a given order);
2. Cyclic algorithm (description of actions that must be repeated a specified number of times or until the task is completed);
3. A branching algorithm (an algorithm in which, depending on the condition, either one or the other sequence of actions is performed)
4. Auxiliary algorithm (an algorithm that can be used in other algorithms by specifying only its name).

For a more visual representation of the algorithm, it is widely used graphic form - block diagram, which is composed of standard graphic objects.

Algorithm development stages:
1. The algorithm should be presented in a form understandable to the person who develops it.
2. The algorithm should be presented in a form understandable to the object (including a person) who will perform the actions described in the algorithm.

Executor - the object that executes the algorithm.

The ideal performers are machines, robots, computers ...

The performer is only able to execute a limited number of commands. Therefore, the algorithm is developed and detailed so that it contains only those commands and constructions that can be performed by the performer.

The performer, like any object, is in a certain environment and can only perform actions that are allowed in it. If the executor encounters a command unknown to him in the algorithm, then the execution of the algorithm will stop.

A computer is an automatic executor of algorithms.

An algorithm written in a programming language "understandable" by a computer is called program .

Programming - the process of compiling a program for a computer. For the first computers, programs were written in the form of a sequence of elementary operations. It was a very time consuming and ineffective job. Therefore, later on, special programming languages ​​were developed. There are many artificial programming languages ​​nowadays. However, it was never possible to create an ideal language that would suit everyone.

Linear Algorithm

There are a large number of algorithms in which commands must be executed one after another. Such algorithms are called linear .

P A program has a linear structure if all statements (commands) are executed sequentially one after another.

Forking algorithm

Forking algorithm Is an algorithm in which, depending on the condition, either one or another sequence of actions is performed.

In many cases, it is required that under some conditions one sequence of actions is performed, and under others, another.

V The entire program consists of commands (operators). Commands can be simple and compound (commands within which other commands are found). Compound commands are often referred to as control constructs. This emphasizes that these operators control the further flow of the program.

Algorithmic structure "cycle". Counter and conditional loops

The best qualities of computers appear not when they calculate the values ​​of complex expressions, but when they repeat relatively simple operations many times, with minor changes. Even very simple calculations can confuse a person if they have to be repeated thousands of times, and a person is completely unable to repeat operations millions of times.

Programmers are constantly faced with the need for repetitive calculations. For example, if you need to count how many times the letter "o" occurs in the text, you need to iterate over all the letters. For all the simplicity of this program, it is very difficult for a person to execute it, but for a computer it is a task for a few seconds.

Cyclic algorithm - a description of actions that must be repeated a specified number of times or until a specified condition is met.

The list of repetitive actions is called body of the cycle .

For example, in a physical education class, you should run a number of laps around the stadium.

Such loops are called - cycles with a counter.

You watch TV on Saturday night. From time to time you glance at your watch and if the time is less than midnight, then you continue to watch TV, if this is not the case, then you stop watching TV.

Cycles of this kind are called - loops with a precondition.

You need to sharpen all the pencils in the box. You sharpen one pencil and set it aside. Then you check to see if the pencils are still in the box. If the condition is false, then the "sharpen pencil" action is performed again. As soon as the condition becomes true, the cycle ends.

Cycles of this kind are called - loops with postcondition.

Programming

Object-oriented is currently the most popular programming technology. Object-oriented programming languages ​​are Visual Basic, Pascal, Visual Basic for Application (VBA), Delphi, etc.

The basic unit in object oriented programming is an object , which contains (encapsulates) both the data describing it ( properties ), and the means of processing this data ( methods ).

Objects containing the same list of properties and methods are combined into classes ... Each individual object is an instance of the class ... Instances of the class can have different property values.
For example, in Windows & Office, Word has a document object class, which is denoted as follows: Documents ()
An object class can contain many different documents (class instances), each of which has its own name. For example, one of the documents might be named flpo6a.doc: Documents ("npo6a.doc")
Objects in applications form some kind of hierarchy. At the top of the object hierarchy is the application. So, the hierarchy of objects of the Word application includes the following objects: application (Aplication), document (Documents), document fragment (Selection), symbol (Character), etc.
A complete reference to an object consists of a series of names of objects nested one after another. The separators of the names of objects in this row are dots, the row begins with the highest-level object and ends with the name of the object of interest to us.
For example, a link to a flpo6a.doc document in Word would look like this: Application. Documents ("Sample. Doc")
For an object to perform any operation, a method must be set. Many methods have arguments that allow you to set parameters for the actions to be performed. To assign specific values ​​to arguments, a colon and an equal sign are used, and the arguments are separated by a comma. The command syntax for applying an object method is as follows: Object.Method: = value, arg2: = value
For example, the operation of opening a document flpo6a.doc in Word must contain not only the name of the Open method, but also an indication of the path to the file being opened (the argument of the FileName method must be assigned a specific value): Documents () .Open FileName: = "С: DocumentsProb. Doc "
To change the state of an object, you need to define new values ​​for its properties. To assign a specific value to a property, use the equal sign. The syntax for setting an object property value is as follows: Object.Property = PropertyValue
One of the object classes is the Characters () character class. Instances of the class are numbered: Characters (I), Characters (2), etc. Set the text fragment (Selection object) for the first character (Characters (1) object) to boldface (Bold property).
The Bold property has two values ​​and can be set (True) or unset (False). True and False are the keywords of the language. Set the Bold property to True: Selection.Characters (1). Bold = True
Object-oriented programming is essentially about building applications from objects, just like houses are built from blocks and various parts. Some objects have to be completely created independently, while others can be borrowed ready-made from a variety of software libraries.

Practical work in QBasic

Introducing QBasic. Text output.

Displaying text and characters

Color management in text mode

Solving math problems

Entering data from the keyboard. INPUT statement

Condition Operators

Loop Operators

Text and Graphics Modes of Monitors

Graphic primitives

Arrays

Practical work in Pascal

Language structure, basic operators

Location of symbols

Arithmetic operations and expressions

Introducing the concept of a variable

Variable types

Division Operators

Read statement

Condition statement if… then

Arrays

Graphics

INFORMATION TECHNOLOGY

TEXT PROCESSING TECHNOLOGY

Text any sequence of symbols is called, which include letters, space, punctuation marks, numbers, signs of arithmetic and relation operations, etc.

Text input hardware includes a keyboard, scanner, light pencil, etc.

Text editor - a software tool designed to create (enter, type), edit and design texts.

The main functions of a text editor:

providing text input from the keyboard or from an existing file;

editing text (adding, changing, deleting or copying fragments of text, symbols, words, etc.);

text design (choice of fonts, alignment method, setting line spacing, spacing between paragraphs, etc.);

placement of text on the page (setting the page size, margins, indents; breaking into columns; arranging page numbers, headers and footers, etc.);

saving text to a file on an external medium or receiving a hard copy (printing the text);

spell checking, selection of synonyms, contextual search and replacement;

issuing tips and so on.

If we consider the text as a system, then its elements will be individual characters, words, lines, sentences, paragraphs.

Paragraph in ordinary text, a part of the text is called from one red line to another.

In a text editor paragraph - this is a part of the text from one line end sign to another (most often the line end sign is inserted into the text automatically when you press the enter key).

Above paragraphs in text editors, such operations are performed as alignment, setting line spacing, setting the indentation of a red line.

In text editors, operations on individual text elements are allowed, even if they are not selected, for example, operations on characters (delete, insert, replace), paragraphs (alignment, indents), but the basic principle of text design in a text editor "you-divide and transform ”.

In text editors, most operations for transforming text are carried out on selected text fragments, for example, such operations as copying and transferring.

The most common text editors: Lek-Sikon, Edit, Word and Deed, Ched, NotePad, Write.

Word processor differs from a text editor in wider functionality, such as:

user-configurable menu;

using the context menu;

accompanying the text with tables and carrying out the simplest calculations in them;

insert graphic objects (pictures, diagrams, titles, etc.) or create pictures using built-in tools;

inserting formulas, graphs, diagrams;

formatting the text with lists, drop caps;

using the tool for auto-correction of text and its auto-abstraction;

creating and using macros;

background check for spelling, syntax and more.

Most common word processors: Word (Microsoft Office), Word Pro (Lotus SmartSuite), WordPerfect (Perfect Office), WordExpress, Accent.

Practical work in a text editor WordPad

Getting to know WordPad. Entering text

Text formatting

Lists

Insert a picture

Practical work in a word processor MS Word

Familiarity with MSWord. Entering text

Selection of fragments of text. Indent.

Text formatting

Lists

Insert a picture

Working with tables

Drawing in Word

Headers and footers. Pagination

Inserting formulas

GRAPHIC INFORMATION PROCESSING TECHNOLOGY

To process images on a computer, special programs are used - graphic editors. Graphics editors can also be divided into two categories: raster and vector.

Bitmap graphic editors are the best means of processing photographs and drawings, since bitmaps provide high accuracy in reproducing color gradations and halftones.

Among the raster graphics editors there are simple ones, for example, the standard Paint application, and powerful professional graphics systems, such as Adobe Photoshop.

Vector graphic editors include a graphic editor built into the Word text editor. CorelDRAW is the most widely used professional vector graphics system.

Graphics editor is a program for creating, editing and viewing graphic images.

To create a drawing using traditional methods, you need to choose a drawing tool (these can be flo-masters, a brush with paints, pencils, pastels and much more). Graphic editors also provide the ability to select tools for creating and editing graphic images, combining them in the toolbar.

Practical work in the graphics editor Paint

Explore Paint Editor Features

Creation of the simplest drawings.

Duplicate items. Symmetry.

Practical work in the graphics editor Photoshop

Star

Flower

gold chain

Golden text

Wood textureDocument

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It is advisable to divide the simulation execution process into phases, each of which should end with a specific measurable result:

■ phase 0 - establishing the subject of research and the boundaries of the model;

■ phase 1 - defining entity classes;

■ Phase 2 - defining the classes of relations that exist between the classes of entities established in the previous phase;

■ Phase 3 - defining key classes for each entity class and each attribute class that is used by the key class.

■ Phase 4 - Allocation of non-key attribute classes to entity classes and a complete description of such attribute classes.

The creation of an information model is represented as a cyclical iterative process, consisting of collecting data, building a model on their basis, and eliminating comments from reviewers. As the subject of study is examined and additional information is obtained, the modeler can repeatedly return to previous design phases to make changes, refinements, and additions. An information model must undergo a comprehensive review before conclusions and decisions can be made from its analysis.

On the phase 0 the main organizational issues are resolved: the subject, goals and boundaries of modeling, methods of collecting and sources of information, a plan for performing work and their distribution among performers are determined, which are recorded in the relevant documents. Information about data sources and specific data are recorded in tabular forms.

The task phase 1 is the definition and description of classes of entities of the information model. Studying the documents that are used in the processes of the organization's activities and polling employees, the analyst forms a pool of entity classes. Once the entity classes are defined, they must be described, so the next step in this modeling phase is to build a glossary, or vocabulary, of entity classes.

On the phase 2 defines the classes of relationships that exist between the entity classes of the model. Relationships between entity classes are depicted in the form of diagrams. Next, entity class diagrams are created. IDEF1 diagrams contain images of a number of entity classes connected by lines that represent their mutual relationships. Entity class diagrams create a graphical representation of information used in an organization. The model represents the structure of information in two ways - as a set of instances of entities within each class of entities and as a set of instances of relationships between classes of entities.

The purpose phase 3 is the definition of key classes for each entity class. Attribute class sets are grouped by the modeler into a pool of attribute classes. Attribute classes, just like the entity and relationship classes previously, need to be detailed. By examining the properties of the attribute classes, the modeler determines the ones that will be used in the key class. Once the key classes are defined, the developer moves on to building attribute class diagrams. As with entity class diagrams, attribute class diagrams focus on one of the entity classes, the image of which is placed in the center of the diagram form. The attribute class diagram can be considered as a further development of the entity class diagram, since they differ only in the information contained within the block depicting the entity class - key classes and other attribute classes are used as the content of the entity class block.

On the phase 4 the distribution of attribute classes that cannot be used in the classes of keys is carried out according to the corresponding classes of entities. The activities performed in this phase of model development are very similar to those in the previous phase. As a result of Phase 4 work, the developer receives a structured information model.

If the actions in all phases were performed correctly, then each entity class will be represented by an optimal set of information and each pair of entity classes sharing a relationship class will accurately reflect the data interdependencies in the model.

Thus, the IDEFl-model is a form of data presentation that facilitates the development of a control system database. Nevertheless, it cannot be said that the development of the IDEFl information model is the development of a database. The IDEFl model represents only a stable information structure and a stable set of rules and definitions, taking into account which the development of a database can be carried out.

The IDEF1X methodology is a relational database development tool. As noted earlier, IDEF1X is designed to build a conceptual diagram of the logical structure of a relational database, which would be independent of the software platform of its final implementation.

IDEF1X, like IDEF1, uses the concepts of entities, attributes, relationships, and keys. The model graphics languages ​​used by these methodologies are also very similar. However, IDEF1X does not consider objects of the real world, but only their information display, since by the time the database is developed, all the organization's IR must be studied, the necessary data set to reflect its activities has been determined and checked for completeness. Since IDEF1X is intended for the development of relational databases, it additionally operates with a number of concepts, rules and constraints, such as domains, views, primary, foreign and surrogate keys, and others that come from relational algebra and which are not necessary at the stages of studying and describing the activities of an organization. ...

The listed methodologies and standards are the basis of numerous tools for creating an information model for IS, called CASE tools.

In this paper, we propose to analyze in detail the topic of modeling in computer science. This section is of great importance for the training of future specialists in the field of information technology.

To solve any problem (industrial or scientific), informatics uses the following chain:

It should pay special attention to the concept of "model". Without the presence of this link, the solution of the problem will not be possible. Why is the model used and what is meant by this term? We will talk about this in the next section.

Model

Modeling in computer science is the compilation of an image of a real-life object that reflects all the essential features and properties. A model for solving a problem is necessary, since it is, in fact, used in the solution process.

In the school computer science course, the topic of modeling begins to be studied in the sixth grade. At the very beginning, children need to be introduced to the concept of a model. What it is?

• Simplified likeness of an object;
• Reduced copy of a real object;
• Scheme of a phenomenon or process;
• An image of a phenomenon or process;
• Description of the phenomenon or process;
• Physical analogue of the object;
• Informational analogue;
• A placeholder object that reflects the properties of a real object, and so on.

A model is a very broad concept, as it has already become clear from the above. It is important to note that all models are usually divided into groups:

• material;
• perfect.

A material model is understood as an object based on a real-life object. It can be a body or a process. This group is usually subdivided into two more types:

• physical;
• analog.

This classification is conditional, because it is very difficult to draw a clear line between these two subspecies.

The ideal model is even more difficult to characterize. She is associated with:

• thinking;
• imagination;
• perception.

It includes works of art (theater, painting, literature, and so on).

Modeling goals

Modeling in computer science is a very important step as it has many goals. Now we invite you to get to know them.

First of all, modeling helps to know the world around us. From time immemorial, people have accumulated the acquired knowledge and passed it on to their descendants. Thus, a model of our planet (globe) appeared.

In past centuries, modeling of non-existent objects was carried out, which are now firmly entrenched in our life (umbrella, mill, and so on). At the present time, modeling is aimed at:

• identification of the consequences of any process (increase in the cost of travel or disposal of chemical waste underground);
• ensuring the effectiveness of the decisions made.

Modeling tasks

Information model

Now let's talk about another type of models studied in the school computer science course. Computer modeling, which must be mastered by every future IT specialist, includes the process of implementing an information model using computer tools. But what is this information model?

It is a whole list of information about any object. What does this model describe and what useful information it carries:

• properties of the modeled object;
• his condition;
• connections with the outside world;
• relationships with external objects.

What can serve as an information model:

• verbal description;
• text;
• drawing;
• table;
• scheme;
• drawing;
• formula and so on.

A distinctive feature of the information model is that it cannot be touched, tasted, and so on. It does not carry material embodiment, as it is presented in the form of information.

A systematic approach to creating a model

In which class of the school curriculum is modeling studied? Informatics in grade 9 introduces students to this topic in more detail. It is in this class that the child learns about the systems approach to modeling. We propose to talk about this in a little more detail.

Let's start with the concept of "system". It is a group of interrelated elements that work together to accomplish a given task. To build a model, a systematic approach is often used, since an object is considered as a system that functions in a certain environment. If any complex object is modeled, then the system is usually divided into smaller parts - subsystems.

Purpose of use

Now we will consider the goals of modeling (informatics grade 11). Earlier it was said that all models are divided into some types and classes, but the boundaries between them are conditional. There are several signs by which it is customary to classify models: purpose, area of ​​knowledge, time factor, way of presentation.

As for the goals, it is customary to distinguish the following types:

• educational;
• experienced;
• imitation;
• gaming;
• scientific and technical.

The first type includes teaching materials. To the second, reduced or enlarged copies of real objects (a model of a structure, an airplane wing, and so on). allows you to predict the outcome of an event. Simulation is often used in medicine and the social field. For example, does the model help you understand how people will react to a particular reform? Before doing a serious operation on a human organ transplant, many experiments were carried out. In other words, the simulation model solves the problem by trial and error. A game model is a kind of economic, business, or military game. Using this model, you can predict the behavior of an object in different situations. A scientific and technical model is used to study a process or phenomenon (a device that simulates a lightning discharge, a model of the motion of the planets of the solar system, and so on).

Field of knowledge

In which class is the student more familiar with modeling? Grade 9 computer science focuses on preparing its students for university entrance exams. Since the USE and GIA tickets contain modeling questions, now it is necessary to consider this topic in as much detail as possible. So, how is the classification by area of ​​expertise done? On this basis, the following types are distinguished:

• biological (for example, diseases artificially caused in animals, genetic disorders, malignant neoplasms);
• the behavior of the firm, the model of the formation of the market price, and so on);
• historical (family tree, models of historical events, model of the Roman army, etc.);
• sociological (the model of personal interest, the behavior of bankers when adapting to new economic conditions) and so on.

Time factor

According to this characteristic, two types of models are distinguished:

• dynamic;
• static.

Already, judging by the name alone, it is not difficult to guess that the first type reflects the functioning, development and change of an object in time. Static, on the contrary, is capable of describing an object at a particular moment in time. This type is sometimes called structural, since the model reflects the structure and parameters of the object, that is, it gives a slice of information about it.

Examples are:

• a set of formulas reflecting the motion of the planets of the solar system;
• air temperature change graph;
• video footage of a volcanic eruption and so on.

Examples of a statistical model are:

• a list of the planets of the solar system;
• a map of the area and so on.

Presentation method

To begin with, it is very important to say that all models have a form and form, they are always made of something, somehow presented or described. On this basis, it is accepted in this way:

• material;
• intangible.

The first type includes material copies of existing objects. You can touch them, smell them, and so on. They reflect external or internal properties, actions of an object. What are material models for? They are used for the experimental method of cognition (empirical method).

We have also addressed immaterial models earlier. They use the theoretical method of cognition. Such models are usually called ideal or abstract. This category is divided into several more subspecies: imaginary models and informational ones.

Information models provide a list of various information about an object. Tables, figures, verbal descriptions, diagrams and so on can act as an information model. Why is this model called intangible? The thing is that it cannot be touched, since it has no material embodiment. Significant and visual models are distinguished among information models.

The imaginary model is one of the This is a creative process that takes place in the imagination of a person, which precedes the creation of a material object.

Simulation steps

The 9th grade informatics topic "Modeling and formalization" has a lot of weight. It is a must to learn. In grades 9-11, the teacher is obliged to acquaint students with the stages of creating models. This is what we are going to do now. So, the following stages of modeling are distinguished:

• meaningful statement of the problem;
• mathematical formulation of the problem;
• development using computers;
• operation of the model;
• getting the result.

It is important to note that in the study of everything that surrounds us, the processes of modeling and formalization are used. Computer science is a subject devoted to modern methods of studying and solving any problems. Consequently, the emphasis is on models that can be implemented with a computer. Particular attention in this topic should be paid to the point of developing a solution algorithm using electronic computers.

Relationships between objects

Now let's talk a little about relationships between objects. In total, there are three types:

• one to one (such a connection is indicated by a one-way arrow in one direction or the other);
• one-to-many (multiple relationship is indicated by a double arrow);
• many-to-many (this is indicated by a double arrow).

It is important to note that links can be conditional and unconditional. An unconditional link involves the use of every instance of an object. And in the conditional, only individual elements are involved.

Practical work No. 14

Completed by a student of group number ___________ Full name ______________________

Topic Designing programs based on the development of algorithms for processes of various nature.

Target: get familiar with the concepts of modeling and modeling, learn how to create computer models.

Theoretical information

Model - itan artificially created object that replaces some object of the real world (object of modeling) and reproduces a limited number of its properties. The concept of a model refers to fundamental general scientific concepts, and modeling is a method of cognizing reality used by various sciences.

The object of modeling is a broad concept that includes objects of animate or inanimate nature, processes and phenomena of reality. The model itself can be either a physical or an ideal object. The former are called full-scale models, the latter are called information models. For example, a building model is a full-scale model of a building, and a drawing of the same building is its information model presented in graphic form (graphic model).

In experimental scientific research, full-scale models are used that allow one to study the patterns of the phenomenon or process under study. For example, in a wind tunnel, the flight process of an aircraft is simulated by blowing a model of an aircraft with an air stream. This determines, for example, the loads on the aircraft body that will take place in a real flight.

Information models are used in theoretical studies of modeling objects. Nowadays, the main tool for information modeling is computer technology and information technology.

Computer modelling includes the progress of the realism of the information model on a computer and the study with the help of this model of the object of modeling - a computational experiment.

Formalization
The subject area of ​​computer science includes tools and methods of computer modeling. A computer model can only be created on the basis of a well-formalized information model. What is formalization?

Formalization of information about some object is its reflection in a certainform. You can also say this: formalization is the reduction of content to form. Formulas describing physical processes are the formalization of these processes. The radio circuit of an electronic device is a formalization of the functioning of this device. The notes written on a sheet of music are the formalization of music, etc.

A formalized information model is a certain set of signs (symbols) that exist separately from the modeling object and can be transmitted and processed. Implementation of an information model on a computer comes down to its formalization into data formats that a computer can "handle" with.

But we can talk about the other side of formalization as applied to a computer. A program in a certain programming language is a formalized representation of the data processing process. This does not contradict the above definition of a formalized information model as a set of signs, since a machine program has a sign representation. A computer program is a model of human activity in information processing, reduced to a sequence of elementary operations that a computer processor can perform. Therefore, computer programming is the formalization of the information processing process. And the computer acts as the formal executor of the program.

Information Modeling Stages

Building an information model starts with system analysis object of modeling (see. "System Analysis"). Imagine a rapidly growing firm whose management is faced with the problem of decreasing the efficiency of the firm as it grows (which is a common situation) and decided to streamline management activities.

The first thing that needs to be done on this path is to conduct a systematic analysis of the firm's activities. A systems analyst invited to a firm should study its activities, identify the participants in the management process and their business relationships, i.e. the modeling object is analyzed as a system. The results of such an analysis are formalized: they are presented in the form of tables, graphs, formulas, equations, inequalities, etc. theoretical model of the system.

The next stage of formalization - the theoretical model is translated into the format of computer data and programs. For this, "either ready-made software is used, or programmers are involved to develop it. In the end, it turns out computer information model, which will be used for its intended purpose.

For an example with a firm, using a computer model, the optimal management option can be found, in which the highest efficiency of the firm will be achieved according to the criterion laid down in the model (for example, obtaining the maximum profit per unit of investment).

Classification of information models can be based on different principles. If we classify them according to the dominant technology in the modeling process, then we can distinguish mathematical models, graphic models, simulation models, tabular models, statistical models, etc. (biological) systems and processes, models of processes of optimal economic planning, models of educational activities, models of knowledge, etc. Classification issues are important for science, because they allow you to form a systematic view of the problem, but their importance should not be overestimated. Different approaches to classifying models can be equally useful. In addition, a specific model can by no means always be attributed to one class, even if we limit ourselves to the list above.

Let us dwell on this classification in more detail and explain it with examples.

Modeling the motion of a comet that invaded the solar system, we describe the situation (predict the trajectory of the comet's flight, the distance at which it will pass from the Earth, etc.), i.e. set purely descriptive goals. We do not have any possibilities to influence the motion of the comet, to change something during the modeling process.

In optimization models, we can influence processes, trying to achieve some goal. In this case, the model includes one or several parameters available to our influence. For example, by changing the thermal regime in the grain storage, we can strive to select one in order to achieve maximum grain safety, that is, we optimize the process.

It is often necessary to optimize the process by several parameters at once, and the goals can be very contradictory. For example, knowing the prices of food and a person's need for food, organize meals for large groups of people (in the army, summer camp, etc.) as useful as possible and as cheaply as possible. It is clear that these goals, generally speaking, do not coincide at all, i.e. when modeling, there will be several criteria between which a balance must be sought. In this case, we speak of multi-criteria models.

Game models can be related not only to children's games (including computer games), but also to very serious things. For example, a commander before a battle in the presence of incomplete information about the opposing army must develop a plan in which order to enter into battle certain units, etc., taking into account the possible reaction of the enemy. In modern mathematics, there is a special section - game theory, which studies decision-making methods in conditions of incomplete information.

Finally, it happens that the model largely imitates the real process, i.e. imitates it. For example, modeling the dynamics of the number of microorganisms in a colony, one can consider a set of individual objects and monitor the fate of each of them, setting certain conditions for its survival, reproduction, etc. In this case, sometimes an explicit mathematical description of the process is not used, being replaced by some verbal conditions (for example, after a certain period of time, the microorganism is divided into two parts, and the other segment dies). Another example is modeling the motion of molecules in a gas, when each molecule is represented in the form of a ball, and the conditions for the behavior of these balls when they collide with each other and with walls are set (for example, an absolutely elastic impact); you do not need to use any equations of motion.

We can say that most often simulation is used in an attempt to describe the properties of a large system, provided that the behavior of its constituent objects is very simple and clearly formulated. The mathematical description is then made at the level of statistical processing of the simulation results while finding the macroscopic characteristics of the system. Such a computer experiment actually pretends to reproduce a natural experiment. To the question "why do this?" the following answer can be given: imitation modeling allows us to single out "in a pure form" the consequences of the hypotheses inherent in our ideas about microevents, clearing them from the influence of other factors inevitable in a natural experiment, which we may not even be aware of. If such modeling also includes elements of a mathematical description of events at the micro level, and if the researcher does not set the task of finding a strategy for regulating the results (for example, managing the number of microorganisms colony), then the difference between the simulation model and the descriptive one is rather arbitrary; it is rather a question of terminology.

Another approach to the classification of mathematical models subdivides them into deterministic and stochastic (probabilistic) ones. In deterministic models, the input parameters are measurable unambiguously and with any degree of accuracy, i.e. are deterministic values. Accordingly, the process of evolution of such a system is deterministic. In stochastic models, the values ​​of the input parameters are known only with a certain degree of probability, i.e. these parameters are stochastic; accordingly, the process of evolution of the system will also be random. At the same time, the output parameters of the stochastic model can be both probabilistic values ​​and uniquely determined ones.