Modeling And Formalization
Modeling
Modeling- a method of cognition, consisting in the creation and study of models.
Those. study of objects by building and studying models
The concept of the model
Model –
The model saves the most important characteristics and properties of the original.
The model "copies" the real object.
Model - any analogue, image (mental or conditional: image, description, diagram, symbol, formula, drawing, graph, plan, map, table, etc.) of any object of study.
The same object may have many models , A different objects can be described one model .
Examples models
The model is needed in order to:
- understand how arranged real object: what is its structure, basic properties, laws of development and interaction with the outside world;
- teach manage object or process: define best ways management under given goals and criteria ( optimization);
- predict direct or indirect consequences of the implementation of the specified methods and forms of impact on the object.
Model representation forms
Model classes
Subject (material)– reproduce geometric, physical and other properties of objects in material form (globe, anatomical dummies, models of buildings, etc.)
Informational– represent objects and processes in figurative And iconic form
Classification of models by area of use
Training Models - used in teaching
Scientific and technical - created to study processes and phenomena
Experienced - These are reduced or enlarged copies of the designed object. Used to study and predict its future characteristics
Gaming – rehearsal of the behavior of the object in different conditions
simulation - a reflection of reality to one degree or another (this is a trial and error method)
Formalization
Formalization – the process of building information models using formal languages.
With the help of formal languages, formal information models(mathematical, physical, logical, etc.)
physical
informational
1 question
1 option
Option 2
A) subject model
B) information model
2 question
What class does the model in the picture belong to?
1 option
Option 2
A) subject model
B) information model
A) information model
B) subject model
3 question
1 option
some simplified similarity of a real object, which reflects the essential features (properties) of the studied real object, phenomenon or process
Option 2
A) model
B) modeling
B) formalization
A) formalization
B) modeling
B) model
4 question
Definitions are given, choose the correct answer
1 option
Option 2
some simplified similarity of a real object, which reflects the essential features (properties) of the studied real object, phenomenon or process
A) formalization
B) modeling
A) model
B) modeling
B) model
B) formalization
5 question
Definitions are given, choose the correct answer
1 option
Option 2
method of knowledge, consisting in the creation and study of models
the process of building information models using formal languages
A) formalization
B) modeling
A) model
B) modeling
B) model
B) formalization
6 question
1 option
Option 2
A) figurative models
B) mixed models
A) mixed models
B) figurative models
C) iconic models
C) iconic models
7 question
The pictures show information models, what form do they belong to?
1 option
Option 2
A) figurative models
B) mixed models
A) mixed models
B) figurative models
C) iconic models
C) iconic models
8 question
Insert missing word
1 option
One and the same object can have many models, and different objects can be described by ………….. model
Option 2
A) many
The same object can have …………… models, and different objects can be described by one model
A) many
Answers:
1 option
Option 2
question number
question number
Correct answer
Correct answer
Rating scale
grade
Number of correct answers
System approach in modeling
The concept of the system
System is a set of interrelated objects, which are called elements of the system.
An important feature of the system is its holistic functioning.
The state of the system is characterized by its structure , that is, the composition and properties of the elements, their relationships and connections with each other.
Classification of models by time factor:
Dynamic– models describing the processes of change and development of the system
Static– models describing the state of the system at a certain point in time (the growth of students in the class on the day of the study)
Discrete (growth of class students over 10 years, algorithms)
Continuous (measurement of atmospheric pressure during the day)
Types of Information Models
Tabular
Hierarchical
Network
Tabular Information Models
In a tabular information model, the list of objects or properties of the same type is placed in the first column (or row) of the table, and the values of their properties are placed in the following columns (or rows) of the table
Hierarchical Information Models
In a hierarchical information model, objects are distributed by levels.
Each element
more high level may consist of lower-level elements, and a lower-level element may be part of only one higher-level element.
Network Information Models are used to reflect systems with a complex structure, in which the connections between elements are of an arbitrary nature.
static
Dynamic
Performed:
Ashurova O.A.
computer science teacher
You can choose: Modeling as a method of scientific knowledge. Model. Modeling as a method of scientific knowledge. Model. Classification of models Material models. information models. Formalization of models. System approach in modeling Statistical and dynamic models. Graphic information models. Tabular models. hierarchical models. Network information models. Object-information models.
Modeling as a method of scientific knowledge. Model. Modeling as a method of scientific knowledge. Model. Model: - this is some simplified similarity of a real object, phenomenon or process; - this is such a material or mentally represented object that replaces the original object for the purpose of its study, while retaining some of the typical features and properties of the original that are important for this study.
Contents The model is necessary in order to: The model is necessary in order to: learn how to manage an object or process and determine the best ways to manage for given goals and criteria (optimization); predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object, process. understand how a particular object works, what are its structure, basic properties, laws of development and interaction with the outside world;
Main stages of modeling Main stages of modeling I stage. Statement of the problem Description of the problem The purpose of modeling Analysis of the object Stage II. Model development Information model Sign model Computer model Stage III. Computer experiment IV stage. Analysis of simulation results Results fit the purpose Results don't fit the purpose Contents
information models. information models. Information models represent objects and processes in figurative or symbolic form. Figurative models (drawings, photographs, etc.) are visual images objects fixed on any information carrier (paper, photographic and film) Sign information models are built using different languages (sign systems). Sign information can be presented in the form of a text (for example, a program in a programming language), a formula (for example, Newton's second law F=m*a), a table (for example, D.I. Mendeleev's periodic table of elements), etc.
Throughout history, mankind has used various ways and tools for creating information models. These methods have been constantly improved. Thus, the first information models were created in the form of rock paintings, while at the present time information models are usually built and studied using modern computer technologies. Contents Information models.
Formalization of models. Formalization of models. To represent information models in one form or another, natural and formal languages are used. Natural languages are used to create descriptive information models. With the help of formal languages, formal information models (mathematical, logical, etc.) are built. One of the most widely used formal languages is mathematics. The language of mathematics is a collection of formal languages. You will get acquainted with some of them (algebra, geometry, trigonometry) at school, with others (set theory, probability theory, etc.) you will be able to get acquainted with in the process of further education.
The language of algebra allows one to formalize functional dependencies between quantities. Thus, Newton formalized the heliocentric system of the world by discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In the school course of physics, many various functional dependencies are considered, expressed in the language of algebra, which are mathematical models of the phenomena or processes being studied. The language of logic algebra (propositional algebra) allows building formal logical models. With the help of propositional algebra, one can formalize (write in the form of logical expressions) simple and complex propositions expressed in natural language. Building logical models allows you to solve logical problems, build logical models of computer devices (adder, trigger), and so on. Formalization of models. Formalization of models.
The process of building information models using formal languages is called formalization. In the process of cognition of the surrounding world, mankind constantly uses modeling and formalization. When studying a new object, its descriptive information model is usually built in natural language, then it is formalized, that is, it is expressed using formal languages (mathematics, logic, etc.). Contents Formalization of models. Formalization of models.
System approach in modeling. System approach in modeling. The concept of the system. The world around us consists of many different objects, each of which has various properties, and at the same time objects interact with each other. For example, the planets of our solar system have different properties (mass, geometric dimensions, etc.) and, according to the law of universal gravitation, interact with the Sun and with each other. The planets are part of a larger object - the solar system, and the solar system is part of our galaxy "Milky Way". On the other hand, the planets are made up of atoms of various chemical elements, while atoms are made up of elementary particles. Thus, we can conclude that almost every object consists of other objects, that is, it is a system. Content A system is a whole, consisting of objects interconnected with each other, which are called elements of the system. For example, a computer is a system consisting of various devices, while the devices are interconnected both in hardware (physically connected to each other) and functionally (information is exchanged between devices. An important feature of the system is its holistic functioning.
System analysis To describe a system, it is not enough just to list its elements. You must specify how these elements are related to each other. It is the presence of connections that turns a set of elements into a system. When you describe the elements of the system and indicate their relationships, you will conduct a system analysis. Systematization Systematization is the process of turning a set of objects into a system. Systematization is of great importance. In everyday life, each of us is engaged in systematization - he divides clothes into winter and summer, dishes into glasses, plates, pots. The systematization of knowledge in various sciences is invaluable. System analysis. Systematization System analysis. Systematization
Static Information Models At each point in time, the system is in a certain state, which is characterized by the composition of the elements, the values of their properties, the magnitude and nature of the interaction between the elements, and so on. Thus, the state of the solar system at any moment of time is characterized by the composition of its constituent objects (the Sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of the interaction between them (gravitational forces, with the help of electromagnetic waves and etc.). Models that describe the state of the system at a certain point in time are called static information models. In physics, an example of static information models are models that describe simple mechanisms, in biology - models of the structure of plants and animals, in chemistry - models of the structure of molecules and crystal lattices, and so on. Static and dynamic models Static and dynamic models
Dynamic Information Models The state of systems changes over time, that is, there are processes of change and development of systems. So, the planets move, their position relative to the Sun and each other changes; The sun, like any other star, evolves, its chemical composition, radiation, and so on change. Models that describe the processes of change and development of systems are called dynamic information models. In physics, dynamic information models describe the movement of bodies, in biology - the development of organisms or animal populations, in chemistry - the processes of chemical reactions, and so on. Static and dynamic models Static and dynamic models
Static information model "Price of individual computer devices" Static information model "Price of individual computer devices" 350 MHz) 100 System board Price (in USD) Device name
Dynamic information model "Change in the price of a computer" Dynamic information model "Change in the price of a computer" Price of a Pentium II computer Years Contents
Graphic information models. Graphic information models. Graphical information models are the simplest type of models that convey the external features of an object: size, shape, color. Graphic models are more informative than verbal ones. Graphic models are: Maps - without maps it is difficult to imagine botany and biology, geography, military affairs, shipping, etc.; Blueprints technical devices, buildings; Electrical and radio circuits - physics, radio electronics; Graphs and charts (visual form of presentation of numerical information)
Tabular models. Tabular models. Another common form of information model representation is a rectangular table consisting of rows and columns. In a tabular information model, objects or their properties are represented as a list, and their values are placed in the cells of a rectangular table. Tables can be used to express both static and dynamic information models. staticdynamic With the help of tables, information models are built in various subject areas. The presentation of mathematical functions, statistical data, schedules of trains, planes and lessons, etc. is widely known. The information presented in the form of tables is very convenient and understandable for perception. Basic concepts of a table Basic concepts of a table How to format a table correctly How to format a table correctly What types of tables are divided into? What types are tables divided into?
The table may reflect some process occurring over time. In mathematics, a rectangular table made up of numbers is called a matrix. If the matrix contains only zeros and ones, then it is called a binary matrix. The tables, which are binary matrices, reflect the qualitative nature of the relationship between objects (there is a road there is no road; visits does not visit, etc.). Tabular models. Complete practical tasks
Matrix example. Matrix example. Student RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Progress
An example of a binary matrix. An example of a binary matrix. Student RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Subjects studied A unit indicates a subject being studied, and a non-studied subject is marked with zero.
Hierarchical information models. Hierarchical information models. We are surrounded by many different objects, each of which has certain properties. However, some groups of objects have the same general properties that distinguish them from objects in other groups. A group of objects that have the same general properties is called an object class. Within a class of objects, subclasses can be distinguished, the objects of which have some special properties, in turn, subclasses can be divided into even smaller groups, and so on. This process of systematization of objects is called the process of classification.
Hierarchical information models. Hierarchical information models. In the process of classifying objects, information models are often built that have a hierarchical structure. In biology, the entire animal world is considered as a hierarchical system (type, class, order, family, genus, species), in computer science, a hierarchical system is used. file system and so on. In a hierarchical information model, objects are distributed by levels, from the first (upper) level to the lower (last) level. Each higher-level element can be composed of lower-level elements, and a lower-level element can be part of only one higher-level element.
Static hierarchical model. Consider the process of constructing an information hierarchical model in the form of a graph, which allows you to classify modern computers. The graph class Computers can be divided into three subclasses: Supercomputers, Supercomputers, Servers and Personal computers computers. Hierarchical information models. Hierarchical information models.
There are three levels in the considered hierarchical model that classifies computers. On the first, upper level, there is the element Computers, it includes three elements of the second level - Supercomputers, Servers and Personal Computers. The structure of the latter includes three elements of the third, lower, level Desktop, Portable and Pocket computers. The subclass Personal computers is divided, in turn, into Desktop, Notebook and Pocket computers.
A graph is a convenient way to visualize the structure of information models. The vertices of the graph (ovals) represent the elements of the system. Relationships between elements are depicted on the graph by lines. If the line is directed (i.e. with an arrow), then it is called an arc. If there is no arrow, then it is an edge. Two vertices connected by an edge or arc are called adjacent. Relations that are valid in both directions are called symmetric. Symmetrical connections on a graph are edges. Graphs in this case are called undirected. Graphs in which the links between objects are not symmetrical (displayed by arcs) are called directed. Hierarchical graphs are sometimes called trees. Information models on graphs. Information models on graphs. Complete practical tasks
Another example of a directed graph is flowcharts of algorithms. The block diagram of the algorithm is a graph of the control process of some executor. The vertex blocks of this graph indicate individual commands that are given to the performer, and the arcs indicate the sequence of transitions from one command to another. The geometric shapes that are used to indicate the vertices are as follows: --condition (a question that can only be answered "Yes" or "No") Information models on graphs. Information models on graphs. Complete practical tasks
Dynamic hierarchical model. To describe the historical process of family generation change, dynamic information models in the form of a genealogical tree are used. As an example, consider a fragment (X-XI century) of the family tree of the Rurik dynasty. A fragment (X-XI century) of the family tree of the Rurik dynasty. Information models on graphs. Information models on graphs. Dynamic Hierarchical Model". Dynamic Hierarchical Model".
Network information models. A many-to-many relationship. Network information models. A many-to-many relationship. Network information models are used to reflect systems with a complex structure, in which the links between elements are of an arbitrary nature. For example, the various regional parts of the global computer network The Internet (see figure) (American, European, Russian, Australian, and so on) are interconnected by high-speed communication lines. At the same time, some parts (for example, the American one) have direct connections with all regional parts of the Internet, while others can exchange information with each other only through the American part (for example, Russian and Australian). Contents Let's build a graph that reflects the structure global network Internet. The vertices of the graph are the regional networks. The connections between the vertices are two-way and therefore are depicted as non-directed lines (edges), and the graph itself is therefore called undirected.
Object-information models. Object-information models. Now consider another approach to information modeling which is called the object-oriented approach. The main concept here is "object". An object is a part of the reality around us. From the point of view of human perception, objects can be divided into the following groups: tangible or visible objects (for example: chair, car, bridge); images created by thinking (for example: a poem, musical composition, mathematical theorem). The information model of an object should reflect a certain set of its properties. Object Properties An object's properties are a set of attributes that distinguish it from other objects.
Examples of objects and their properties. Examples of objects and their properties. Object nameProperties My teacherName, Length of service, Course taught My hard diskAmount, Amount of memory used Important documentName, Creation date Amount of memory used, Location
Objects that have the same properties and behavior form an object class. Every object is an instance of some class. An instance of a class (object) is a specific object or image, and a class defines a set of objects with the same properties and behavior. A class can generate an arbitrary number of objects, but any object belongs to a strictly fixed class. Content
Goals:
give students a general idea of the formalization of the object;
form the concept of formalization;
to develop the research competence of students in the formalization of the model, logical thinking, broaden their horizons;
develop cognitive interest, cultivate an information culture.
Software and didactic support
computer type IBM, operating system Windows, RFP MS Office XP and above,
Presentation Formalization . pps .
Theoretical material
Formalization as milestone modeling
Slide #1
In his activity - artistic, scientific, practical - a person very often creates a certain image of the object (process or phenomenon) with which he has or will have to deal - a model of this object. The creation of this image always pursues a goal. The model is important not in itself, but as a tool that facilitates cognition or visual representation.
In the process of learning about the world around us and communicating, we are faced with formalization at almost every step: we formulate thoughts, draw up reports, fill out all kinds of forms and forms, transform formulas. When studying a new object, first its descriptive information model is usually built in natural language, then it is formalized, that is, it is expressed using formal languages (mathematics, logic, etc.).
Thus, before building a model of an object (phenomenon, process), it is necessary to single out its constituent elements and the connections between them (to conduct a system analysis) and “translate” (display) the resulting structure into some predetermined form - formalize information.
Slide #2
Formalization - this is the process of highlighting and translating the internal structure of an object, phenomenon or process into a certain information structure - a form. Modeling of any system is impossible without preliminary formalization. In fact, formalization is the first and very important step in the modeling process.
Formalization is a replacement for a real object or process formal description, i.e. its information model.
Slide #3
Having built an information model, a person uses it instead of the original object to study the properties of this object, predict its behavior, etc. Before building some kind of complex structure, such as a bridge, designers make its drawings, calculate strength, allowable loads. Thus, instead of a real bridge, they deal with its model description in the form of drawings, mathematical formulas. If the designers wish to reproduce the bridge in a reduced size, then this will already be a full-scale model - a model of the bridge.
Slide #4
Natural languages are used to create descriptive information models. Numerous descriptive information models are known in the history of science; for example, the heliocentric model of the world proposed by Copernicus was formulated as follows:
The earth rotates on its axis and around the sun;
All planets orbit around the Sun.
Slide #5
With the help of formal languages, formal information models(mathematical, logical, etc.). One of the most widely used formal languages is mathematics. Models built using mathematical concepts and formulas are called mathematical models. The language of mathematics is a collection of formal languages.
Slides #6-8
The language of algebra (propositional algebra) makes it possible to formalize functional dependencies between quantities. Thus, Newton formalized the heliocentric system of the world by discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In the school course of physics, many various functional dependencies are considered, expressed in the language of algebra, which are mathematical models of the phenomena or processes being studied.
The language of the algebra of logic allows one to construct formal logical models. With the help of propositional algebra, one can formalize (write in the form of logical expressions) simple and complex propositions expressed in natural language. Building logical models allows you to solve logical problems, build logical models of computer devices (adder, trigger), and so on.
The encyclopedic dictionary gives the following interpretation of this concept: “ Formalization- this is the presentation and study of any meaningful area of knowledge (scientific theory, reasoning, search procedures, etc.) in the form of a formal system or calculus.
Slide #9
In the context of modeling under formalization we will understand the process of translating the task description into general view(general problem statement) into a formal representation language in order to create computer model and explore it. From the point of view of information processing, it is necessary to define the source data (what needs to be processed) and describe the processing rules (how to process).
Slide #10
Formalization- one of the main tools of mathematics. Because mathematics operates with really non-existent entities, abstract concepts, describes laws, theorems, rules, hypotheses, etc., it is impossible to do without agreements on the representation of all this.
slide 2
A model is a simplified representation of a real object, process or phenomenon.
2 The model retains the most important characteristics and properties of the original. Model - any analogue, image (mental or conditional: image, description, diagram, symbol, formula, drawing, plan, table, map, etc.) of any object of study.
slide 3
3 The model is necessary in order to: understand how a real object works: what is its structure, basic properties, laws of development and interaction with the surrounding world; learn to manage an object or process: determine the best methods of management for given goals and criteria (optimization); predict direct or indirect consequences of the implementation of the specified methods and forms of impact on the object.
slide 4
Modeling:
4 building and studying models in order to obtain new knowledge and further improve the characteristics of the objects of study; method of scientific knowledge of the objective world with the help of models.
slide 5
Model classification
5 By area of use
slide 6
6 TAKING INTO ACCOUNT THE TIME FACTOR MODELS DYNAMIC STATIC DISCRETE CONTINUOUS GROWTH OF STUDENTS IN A CLASS DURING THE DAY OF RESEARCH GROWTH OF STUDENTS IN THIS CLASS OVER 10 YEARS ALGORITHMS CHANGE IN ATMOSPHERIC PRESSURE DURING THE DAY
Slide 7
Task number 1
7 Give examples of statistical and dynamic models.
Slide 8
Model classification
8 IN THE FIELD OF KNOWLEDGE MODELS BIOLOGICAL SOCIOLOGICAL HISTORICAL MATHEMATICAL Task №2. Give examples of models from different fields of knowledge.
Slide 9
9 ACCORDING TO THE METHOD OF REPRESENTATION OF THE MODEL MATERIAL INFORMATIONAL VERBAL SIGN MENTALLY ORAL IN ANY LANGUAGE TOYS GLOBE STICKED BIRD PHYSICAL OR CHEMICAL EXPERIMENTS
Slide 10
INFORMATION MODELS
10 Information model is a description of a real object (process, phenomenon) in one of the languages (colloquial or formal).
slide 11
11 IN THE FORM OF REPRESENTATION INFORMATION MODELS GEOMETRIC COMPUTER STRUCTURAL SPECIAL VERBAL LOGICAL MATHEMATICAL
slide 12
12 Geometric models - graphic forms and three-dimensional structures. Word models are oral and written descriptions using illustrations. Mathematical models - mathematical formulas, inequalities, systems, etc. Structural models - diagrams, graphs, tables, etc. Logical models are models in which decisions are made based on the analysis of various conditions. Special models - notes, chemical formulas and so on.
slide 13
13 Any information model is a system. A system is a whole, consisting of elements interconnected with each other. System = elements + links between them Systems are: material (man, plane, tree); intangible (human language, mathematics); mixed (school system).
Slide 14
The main property of any system is the emergence of a “system effect”, or the “emergence principle”: when elements are combined into a system, the system acquires new properties that none of the elements of the system possessed.
14 An example is an airplane. Its main property is the ability to fly. None of its constituent parts individually possesses this property. But if you put them all together and connect them in a strictly defined way, the plane will fly.
slide 15
15 Task number 3. Give examples: biological systems ___________ technical systems _____________ systems in computer science ___________ Task No. 4. List the elements of the "computer" system.
slide 16
Systematization (classification) is the process of turning a set of objects into a system.
16 The structure of the system is a certain order of combining the elements of the system. Structural information models ALGORITHMS TABLE DIAGRAM (GRAPHS) HIERARCHICAL NETWORK
Slide 17
Task number 5
17 Draw a network model. In the first row, write the names of friends, in the second - their hobbies. Depict links with arcs: name - hobby.
Slide 18
18 The structure of the information model: characteristics (parameters) of the object of communication between them Example: model of uniform rectilinear motion. Parameters: speed v, time t, path S. Relationship between them: S=v t. Task number 6. Specify parameters and relationships for the Triangle model. Parameters: _________________________ Links: ______________________________
Slide 19
Task number 7
19 The model of a chemical reaction is the equation of this reaction: 2KOH + H2SO4 = K2SO4 + 2H2O Is this model informational? _________________ Why? ___________________ Specify the parameters of this model. ___________________________ Provide links. _______________
slide 23
The main stages of computer simulation
23 Building a model (usually a description of the information model). Formalization of the model (record in some formal language). Building a computer model (in a programming language or using an application program). Carrying out a computer experiment. Analysis of simulation results.
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Slides captions:
Modeling and formalization Completed by the teacher of computer science MBOU secondary school No. 108 Samara Gazizova Ekaterina Aleksandrovna
Models and modeling One of the methods of cognition of objects of the surrounding world is modeling, which consists in the creation and study of simplified substitutes for real objects. The replacement object is usually called a model, and the original object is called a prototype or original.
Models and Simulation Modeling is used when the object under study is too large (solar system) or too small (atom), when the process is very fast (fuel processing in an internal combustion engine) or very slow (geological processes), when the study of the object may turn out to be dangerous to others (atomic explosion), lead to the destruction of itself (checking the seismic properties of a high-rise building) or when the creation of a real object is very expensive (new architectural solution), etc.
Stages of building an information model Analysis highlights the properties of formalization Formalization is the replacement of a real object with its formal description, i.e. its information model.
Types of models Model Natural (material) Informational Descriptions of the original object in information coding languages Real objects, in a reduced or enlarged form, reproducing appearance, structure or behavior of the simulation object
Classification of information models
Figurative models Figurative models are visual images of objects fixed on some information carrier.
Sign models Sign information models are built using different languages (sign systems). program lab; var a, b, s, p: integer; begin write(" Enter length: "); readln(a); write(" Enter width: "); readln(b); s:= a*b; p:= 2 * (a + b); writeln("Area is: ", s); writeln("Perimeter is: ", p); end. Take care of our language, our beautiful Russian language is a treasure, it is a property handed down to us by our predecessors! I.S. Turgenev
Mixed models Mixed information models simultaneously use figurative and symbolic elements.
Verbal Information Models Verbal models are descriptions of objects, phenomena, events, processes in natural languages. For example, the heliocentric model of the world proposed by Copernicus was verbally described as follows: - The Earth rotates around its axis and around the Sun; All planets orbit around the Sun. Many verbal models are contained in your school textbooks: a history textbook presents models of historical events, a geography textbook - models of geographical objects and natural processes, a biology textbook - models of objects of the animal and plant world.
Mathematical Models Information models built using mathematical concepts and formulas are called mathematical models. With the help of the language of algebra of logic, logical models are built - simple and complex statements expressed in natural language are formalized (written in the form of logical expressions). By constructing logical models, it is possible to solve logical problems, create logical models of devices, etc. Computer mathematical models At present, the most complex mathematical models can be implemented on a computer. In this case, such means are used as: - programming systems; - spreadsheets; - specialized mathematical packages and software for modeling. Simulation modeling is an artificial experiment in which, instead of conducting full-scale tests with real equipment, experiments are carried out using computer models.
Graphic information models Drawing - conditional graphic image object with the exact ratio of its dimensions, obtained by the projection method. Diagram - a graphical representation that gives a visual representation of the ratio of any values or several values of one value, the change in their values. Graph - a line that gives a visual representation of the nature of the dependence of one value. A schema is a representation of some object in general, main terms using symbols. With the help of schemes, both the appearance of an object and its structure can be represented.
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