Presentation on the topic of modeling and formalization.
News
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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 is any analogue, image (mental or conventional: image, description, diagram, symbol, formula, drawing, plan, table, map, etc.) of any research object.
management with given goals and criteria (optimization); predict direct or indirect consequences of the implementation of specified methods and forms of influence on the object.
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Modeling:
4 construction and study of models in order to obtain new knowledge and further improve the characteristics of research objects; method of scientific knowledge of the objective world using models.
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Model classification
5 By area of use
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6 TAKEN INTO ACCOUNT OF THE TIME FACTOR MODELS DYNAMIC STATIC DISCRETE CONTINUOUS GROWTH OF CLASS STUDENTS ON THE DAY OF RESEARCH GROWTH OF STUDENTS IN THIS CLASS OVER 10 YEARS ALGORITHMS CHANGE IN ATMOSPHERIC PRESSURE DURING THE DAY
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Task No. 1
7 Give examples of statistical and dynamic models.
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8 BY AREA OF KNOWLEDGE MODELS BIOLOGICAL SOCIOLOGICAL HISTORICAL MATHEMATICAL Task No. 2. Give examples of models from different fields of knowledge.
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9 BY WAY OF REPRESENTING THE MODEL MATERIAL INFORMATION VERBAL SIGN MENTAL ORAL IN ANY LANGUAGE TOYS GLOBE STOCKED BIRDS PHYSICAL OR CHEMICAL EXPERIMENTS
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INFORMATION MODELS
10 Information model is a description of a real object (process, phenomenon) in one of the languages (colloquial or formal).
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11 BY FORM OF REPRESENTATION INFORMATION MODELS GEOMETRIC COMPUTER STRUCTURAL SPECIAL WORDAL LOGICAL MATHEMATICAL
12 Geometric models – graphic forms and volumetric structures. Verbal models – 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, etc.
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13 Any information model is a system. A system is a whole consisting of interconnected elements. System = elements + connections between them Systems are: material (man, plane, tree); intangible (human language, mathematics); mixed (school system).
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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.
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15 Task No. 3. Give examples: biological systems ___________ technical systems _____________ systems in computer science ___________ Task No. 4. List the elements of the computer system.
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Systematization (classification) is the process of transforming a set of objects into a system.
16 System structure – a certain order of combining system elements. Structural information models ALGORITHMS TABLE CHARTS (GRAPHS) HIERARCHICAL NETWORK
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Task No. 5
17 Create a network model. In the first row, indicate the names of your friends, in the second - their hobbies. Draw connections with arcs: name – hobby.
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18 Structure of the information model: characteristics (parameters) of the communication object between them Example: model of uniform rectilinear motion. Parameters: speedv, timet, path S. Relationship between them: S=v·t. Task No. 6. Specify the parameters and connections for the Triangle model. Parameters: _________________________ Connections: ______________________________
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Task No. 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. ___________________________ Indicate connections. _______________
Slide 23
Main stages of computer modeling
23 Model building (usually a description of the information model). Formalization of the model (recording in some formal language). Construction of a computer model (in a programming language or using an application program). Conducting a computer experiment. Analysis of simulation results.
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Modeling and formalization Performed by computer science teacher MBOU Secondary School No. 108 Samara Gazizova Ekaterina Aleksandrovna
Models and modeling One of the methods of understanding objects in the surrounding world is modeling, which consists of creating and studying 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 modeling Models are resorted to when the object under study is too large (solar system) or too small (atom), when the process proceeds very quickly (fuel processing in an internal combustion engine) or very slowly (geological processes), when the study of the object may turn out to be dangerous for others (atomic explosion), lead to the destruction of itself (testing 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, properties are highlighted Formalization Formalization is the replacement of a real object with its formal description, i.e., its information model.
Types of models Model Full-scale (material) Information Descriptions of the original object in information coding languages Real objects that reproduce in a reduced or enlarged form appearance, structure or behavior of the modeling object
Classification information models
Imaginative models Imaginative models are visual images of objects recorded on any storage medium.
Sign models Sign information models are built using various 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, this is an asset passed on 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, which Copernicus proposed, 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 contains models of geographical objects and natural processes, and a biology textbook contains models of objects of the animal and plant world.
Mathematical Models Information models built using mathematical concepts and formulas are called mathematical models. Using the language of logic algebra, logical models are built - formalized (written in the form logical expressions) simple and complex statements expressed in natural language. By constructing logical models, it is possible to solve logical problems, create logical models of devices, etc. Computer mathematical models are currently the most complex mathematical models can be implemented on a computer. In this case, such tools 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 an object with an exact ratio of its dimensions, obtained by projection. A diagram is a graphic image that gives a visual representation of the relationship between any quantities or several values of one quantity, and the change in their values. A graph is a line that gives a visual representation of the nature of the dependence of one quantity. A diagram is a representation of some object in general, main features using symbols. With the help of diagrams, both the appearance of an object and its structure can be represented.
Modeling And Formalization
Modeling
Modeling– a method of cognition consisting in the creation and study of models.
Those. research of objects by building and studying models
Concept of the model
Model –
The model saves the most important characteristics and properties of the original.
The model “copies” the real object.
Model is any analogue, image (mental or conditional: image, description, diagram, symbol, formula, drawing, graph, plan, map, table, etc.) of any research object.
The same the 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: determine the best methods of management given the goals and criteria ( optimization);
- predict direct or indirect consequences of the implementation of specified methods and forms of influence on the object.
Model representation forms
Model classes
Subject (material)– reproduce geometric, physical and other properties of objects in material form (globe, anatomical models, building models, etc.)
Information– represent objects and processes in figurative And iconic form
Classification of models by area of use
Training models – used in training
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 an object’s behavior in various conditions
Imitation – 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.
Formal information models (mathematical, physical, logical, etc.) are built using formal languages.
physical
informational
1 question
1 option
Option 2
A) subject model
B) information model
Question 2
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
Question 3
1 option
some simplified resemblance of a real object, which reflects the essential features (properties) of the real object, phenomenon or process being studied
Option 2
A) model
B) modeling
B) formalization
A) formalization
B) modeling
B) model
Question 4
Definitions are given, choose the correct answer
1 option
Option 2
some simplified resemblance of a real object, which reflects the essential features (properties) of the real object, phenomenon or process being studied
A) formalization
B) modeling
A) model
B) modeling
B) model
B) formalization
Question 5
Definitions are given, choose the correct answer
1 option
Option 2
a method of cognition 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
Question 6
1 option
Option 2
A) figurative models
B) mixed models
A) mixed models
B) figurative models
B) iconic models
B) iconic models
Question 7
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
B) iconic models
B) iconic models
Question 8
Fill in the missing word
1 option
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 no.
Question no.
Correct answer
Correct answer
Grading scale
grade
Number of correct answers
Systematic approach to modeling
Concept of the system
System is a collection of interconnected objects called system elements.
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 class students on the day of the study)
Discrete (growth of class students over 10 years, algorithms)
Continuous (measuring atmospheric pressure throughout the day)
Types of Information Models
Tabular
Hierarchical
Network
Tabular Information Models
In a tabular information model, a list of similar objects or properties 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 across levels.
Each element
a higher level can be composed of elements at a lower level, and an element at a lower level can be part of only one element at a higher level.
Network information models are used to reflect systems with a complex structure, in which connections between elements are arbitrary.
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. Systematic approach to 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 resemblance of a real object, phenomenon or process; - this is such a material or mentally imagined object that replaces the original object for the purpose of its study, preserving some typical features and properties of the original that are important for this study.
Contents A model is necessary in order to: A model is necessary in order to: learn to manage an object or process and determine the best management methods for given goals and criteria (optimization); predict direct and indirect consequences of implementing specified methods and forms of influence on an object or process. understand how a specific object works, what its structure, basic properties, laws of development and interaction with the outside world are;
Main stages of modeling Main stages of modeling Stage I. Statement of the problem Description of the problem Purpose of modeling Analysis of the object Stage II. Model development Information model Sign model Computer model Stage III. Computer experiment Stage IV. Analysis of simulation results Results meet the goal Results do not meet the goal Contents
Information models. Information models. Information models represent objects and processes in figurative or symbolic form. Figurative models (drawings, photographs, etc.) are visual images of objects recorded on some information medium (paper, photo and film). Sign information models are constructed using various languages (sign systems). Sign information can be presented in the form of 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, humanity 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, but nowadays information models are usually built and studied using modern computer technologies. Contents Information models.
Formalization of models. Formalization of models. Natural and formal languages are used to represent information models in one form or another. 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 become familiar with some of them (algebra, geometry, trigonometry) at school, others (set theory, probability theory, etc.) you can become familiar 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, discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In a school physics course, many different 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 you to build formal logical models. Using propositional algebra, you can formalize (write in the form of logical expressions) simple and complex statements 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 understanding the world around us, humanity constantly uses modeling and formalization. When studying a new object, first, its descriptive information model is usually built in natural language, then it is formalized, that is, expressed using formal languages (mathematics, logic, etc.). Contents Formalization of models. Formalization of models.
Systematic approach to modeling. Systematic approach to modeling. Concept of the system. The world around us consists of many different objects, each of which has various properties, and at the same time the objects interact with each other. For example, our planet 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 Milky Way galaxy. On the other hand, planets are made up of different atoms chemical elements, and atoms are made from elementary particles. Thus, we can conclude that almost every object consists of other objects, that is, it is a system. Contents A system is a whole consisting of interconnected objects, which are called system elements. For example, a computer is a system consisting of various devices, while the devices are interconnected both 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. It is necessary to indicate how these elements relate 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 thereby conduct system analysis. Systematization Systematization is the process of transforming many objects into a system. Systematization is of great importance. In everyday life, each of us is engaged in systematization - dividing 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 moment 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 in time is characterized by the composition of the objects included in it (the Sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of the interaction with each other (gravitational forces, with the help of electromagnetic waves, etc.). Models that describe the state of a system at a certain point in time are called static information models. In physics, examples 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, processes of change and development of systems occur. So, the planets move, their position relative to the Sun and each other changes; The Sun, like any other star, develops, 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” 5 Mouse 10 Keyboard 25 Case 50 CD-ROM drive x32 30 Sound card 16 bit 200 Monitor 15 30 Video card 4 MB 150 Hard drive 4 GB 20 Drive 3.5 30 Memory 16 MB 200 Pentium II processor ( 350 MHz) 100 Motherboard 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 simplest form models that convey the external characteristics 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 diagrams (visual form of presenting numerical information)
Tabular models. Tabular models. Another common form of representing an information model is a rectangular table consisting of rows and columns. In a tabular information model, objects or their properties are presented as a list, and their values are placed in the cells of a rectangular table. Both static and dynamic information models can be expressed using tables. staticdynamic Using tables, information models are built in various subject areas. The presentation of mathematical functions, statistical data, train, plane and lesson schedules, etc. is widely known. Information presented in the form of tables is very convenient and understandable. Basic concepts of a tableBasic concepts of a table How to properly format a tableHow to correctly format a table 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 a matrix contains only 0s and 1s, then it is called a binary matrix. The tables, which are binary matrices, reflect the qualitative nature of the connection between objects (there is a road, there is no road; visits do not visit, etc.). matrix binary matrix Contents Tabular models. Tabular models. Complete practical tasks
Matrix example. Matrix example. Student RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Academic Progress
An example of a binary matrix. Example of a binary matrix. Student RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Subjects studied The unit indicates the subject being studied, and the unstudied 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 common properties that distinguish them from objects in other groups. A group of objects that have the same common 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 systematizing objects is called the classification process.
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 (phylum, 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 into levels, from the first (top) level to the bottom (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. Let's consider the process of constructing an information hierarchical model in the form of a graph, which allows us to classify modern computers. Graph Class Computers can be divided into three subclasses: Supercomputers, Supercomputers, Servers and Personal computers computers. Hierarchical information models. Hierarchical information models.
In the considered hierarchical model classifying computers, there are three levels. At the first, top level there is the Computers element, which includes three elements of the second level - Supercomputers, Servers and Personal Computers. The latter includes three elements of the third, lower, level: Tabletop, Portable and Pocket computers. The subclass Personal computers is divided, in turn, into Desktop, Portable and Pocket computers.
The graph is in a convenient way visual representation of the structure of information models. The vertices of the graph (ovals) display the elements of the system. The connections 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. Relationships that are valid in both directions are called symmetric. Symmetric connections in a graph are edges. Graphs in this case are called undirected. Graphs in which the connections between objects are asymmetrical (displayed as arcs) are called oriented. Hierarchical graphs are sometimes called trees. Information models on graphs. Information models on graphs. Complete practical tasks
Another example of a directed graph is algorithm flowcharts. The flowchart of the algorithm is a graph of the control process of some executor. The blocks at the top 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 Geometric figures, which are used to designate vertices, are the following: - the beginning and end of a sequence of actions - - initial data and result - - Actions - - 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 changing generations of a family, dynamic information models in the form of a family tree are used. As an example, we can consider a fragment (X-XI centuries) of the family tree of the Rurik dynasty. fragment (X-XI centuries) 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. Many-to-many relationship. Network information models. Many-to-many relationship. Network information models are used to reflect systems with a complex structure, in which connections between elements are arbitrary. For example, various regional parts of the global computer network The Internet (see figure) (American, European, Russian, Australian, and so on) is connected to each other 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, the Russian and Australian ones). Contents Let's build a graph that reflects the structure global network Internet. The vertices of the graph are regional networks. The connections between the vertices are two-way in nature and therefore are depicted by undirected lines (edges), and the graph itself is therefore called undirected
Object information models. Object information models. Now let's look at 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: a chair, a car, a bridge); images created by thinking (for example: a poem, a piece of music, a mathematical theorem). The information model of an object must reflect a certain set of its properties. Properties of an object Properties of an object are a set of characteristics that distinguish it from other objects.
Examples of objects and their properties. Examples of objects and their properties. Object nameProperties My teacherName, Work experience, Course taught My hard drive Volume, Quantity used memory Important documentName, Creation date Memory footprint, 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 general idea about the formalization of the object;
form the concept of formalization;
develop students’ research competence in formalizing the model, logical thinking, and broaden their horizons;
develop cognitive interest, cultivate information culture.
Software and teaching software
Computer type IBM, operating Windows system, PPP MS Office XP and higher,
Presentation Formalization . pps .
Theoretical material
Formalization as the most important stage of modeling
Slide No. 1
In his activities - artistic, scientific, practical - a person very often creates some 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 certain 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 encounter 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, expressed using formal languages (mathematics, logic, etc.).
Thus, before building a model of an object (phenomenon, process), it is necessary to identify its constituent elements and the connections between them (carry out a system analysis) and “translate” (display) the resulting structure into some predetermined form - formalize information.
Slide No. 2
Formalization - is the process of identifying and translating the internal structure of an object, phenomenon or process into a certain information structure- form. Modeling of any system is impossible without preliminary formalization. In fact, formalization is the first and very important stage of the modeling process.
Formalization - this is the replacement of a real object or process with its formal description, i.e., its information model.
Slide No. 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 complex structure, such as a bridge, designers make its drawings, carry out calculations of strength and permissible loads. Thus, instead of a real bridge, they deal with its model description in the form of drawings and mathematical formulas. If the designers wish to reproduce the bridge in a reduced size, then this will already be a full-scale model - a mock-up of the bridge.
Slide No. 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 that Copernicus proposed was formulated as follows:
The Earth rotates on its axis and around the Sun;
All planets orbit around the Sun.
Slide No. 5
Formal languages are used to build 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 No. 6-8
The language of algebra (propositional algebra) allows one to formalize functional dependencies between quantities. Thus, Newton formalized the heliocentric system of the world, discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In a school physics course, many different functional dependencies are considered, expressed in the language of algebra, which are mathematical models of the phenomena or processes being studied.
The language of algebra logic allows you to build formal logical models. Using propositional algebra, you can formalize (write in the form of logical expressions) simple and complex statements 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 provides the following interpretation of this concept: “ Formalization- 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 No. 9
In the context of modeling under formalization we will understand the process of translating the task description into general view(general formulation of the problem) into the language of formal representation in order to create computer model and explore it. From an information processing perspective, the input data (what needs to be processed) should be defined and the processing rules (how to be processed) should be described.
Slide No. 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., then it is impossible to do without agreements on the presentation of all this.