**Type of lesson:** repeating and summarizing lesson.

**Objectives:**

1. Educational: To repeat and generalize knowledge on the topic “Mathematics in science, technology, economics, information technology and practical activities”; to systematize the acquired knowledge.

2. Developing – to develop the ability to apply knowledge in practice, to promote the development of logical thinking, will and independence, the development of skills of learning work (the ability to work at a pace).

3. Educational – to create conditions for education of interest to the studied topic, education of motives of learning, positive attitude to knowledge, education of discipline, to provide conditions for successful work in the team.

**Objectives:**

1. To consolidate the studied material by changing the types of work on the theme “Mathematics in science, technology, economics, information technology and practical activities”.

2. To develop skills and abilities, to develop logical thinking, correct and competent mathematical speech, to develop independence and confidence in their knowledge and skills in performing different types of work.

3. To foster interest in mathematics by introducing different types of material consolidation: oral work, work with the textbook, work at the board, answering questions and being able to do self-analysis, independent work; stimulating and encouraging students’ activities.

**Plan:**

**I. The organizational moment.**

**II. New topic:**

“Mathematics in Science, Technology, Economics, Information Technology, and Practice”

1. Theoretical part.

**III. Outcome.**

1. On questions.

Lesson progress

I. Organizing moment.

Emotional mood and readiness of the teacher and students for the lesson. Announcement of goals and objectives.

**II. New topic:** “Mathematics in science, engineering, economics, information technology and practice” 1.

1.Theoretical part.

Mathematics plays an important role in natural science, engineering and technology, and humanities research. It has become for many branches of knowledge not only a tool for quantitative calculation, but also a method of precise research and a means of extremely clear formulation of concepts and problems. Without modern mathematics, with its advanced logical and computational apparatus, progress in various fields of human activity would be impossible.

– Mathematics is the basis of fundamental research in the natural sciences and humanities. Because of this its importance in the general system of human knowledge is constantly increasing. Mathematical ideas and methods penetrate into the management of very complex and large systems of different nature: flights of spacecraft, industries, extensive transportation systems and other activities. New theories are emerging in mathematics in response to the demands of practice and the internal development of mathematics itself. Applications of various fields of mathematics have become an integral part of science, including: physics, chemistry, geology, biology, medicine, linguistics, economics, sociology, etc.

– Mathematics is not only a powerful tool for solving applied problems and a universal language of science, but also an element of general culture. Therefore, mathematical education should be regarded as an important component in the system of fundamental training of modern specialist-humanitarian.

– In modern economics, mathematical methods act as a necessary tool, which are used, first of all, when solving problems of economic content. These include complex interest calculation problems, linear programming problems, optimization problems. In solving percentage problems, students are introduced to economic concepts such as cost, cost, labor productivity, material output, and profitability of production. Linear programming problems are widely used in justifying economic decisions related to labor productivity, volume, and profitability of production. Optimization problems are used in economics to select optimal economic solutions, especially important in the allocation of resources in a particular economic activity. It should be noted that economics uses not only the mathematical apparatus in connection with specific economic problems, but also the organization of information processes of processing economic information.

**SYMBOLS AND IMAGES. **

The binary system of calculus in information technology is the Stone Age. By any evaluation criteria: Information Storage, Information Processing, Information Transmission, Information Displaying, etc.

To understand this I propose to replace theory and logic with image and analysis. I am not going to talk about the advantages and disadvantages of these approaches. These are different fields of cognition. Like the round and the red. But the connection between the round and the red exists and is realized through symbols.

No one will doubt that the lettering of the alphabet and the numbering of the natural number have nothing in common. They do not. The connection is direct and unambiguous. Moreover, already indicated by ancient knowledge. Suffice it to refer to the Vedas or the Old Slavonic language Old Slavonic alphabet contains symbols (letters) and image (number + letter). If in conversation the Englishman does not understand the word he hears, he asks, “How do you spell that?” When communicating in Old Slavonic, the appropriate question is: “Say a number.” The connection of symbols and images is obvious. Old Slavic language and writing is figurative-symbolic.

All computer science is based on a flawed theory and a cumbersome binary system of calculus, which has nothing to do with the alphabet and the alphabet. But in teaching the alphabet we use images: watermelons, houses, etc. The image is easier to comprehend and remember. A symbol is easier to display and transmit. These are the basic issues of computer science, which are not reflected by the existing computer science. To exclude this disadvantage it is necessary to shift from theory and logic to image and analysis.

For example, the letter “P” is a root symbol for an infinite number of words. If after P stands the first letter (symbol), we get the word RA. Its semantic meaning is the source of light – the Sun. If the last letter (symbol) is after RA, we get the word YAR, the source of heat – the Sun. There are an infinite number of words between these words. To understand the meaning of which is possible only through analysis of images displayed by symbols.

Obviously, knowing the symbol, through the definition and the image we know the full information of this symbol. A symbol is easier to memorize, write down and transmit through communication channels. One symbol contains many sine programs. Why is a sine wave a program? Because it contains the initial element. Transformation function. Final element. All program attributes are present.

This is a typical example for functionals. Functionals of functions is a nonequilibrium, unstable system. Everything strives for stability based on self-organization. Consequently, there should be a stable structure inside the functional. These stable structures are displayed by functionals of structures.

**MODERN MATHEMATICS IS THE BASIS FOR CREATIVITY**

It is about creativity in science. Writing theories for the needs of science is not creativity. In the simplest sense, creativity in science should be seen as solving problems in cognition of the world around us. In what can knowledge about the world around us be expressed? Knowledge of the surrounding world can be expressed only in the difference of these or those phenomena of nature or in their unity and interrelation. To understand the categories of difference, unity, and interrelation is possible only through the properties of the observable or obtained by experience. If there are no properties, there is no knowledge, for there is no difference of one from another. Everything is cognized through properties. Consequently, the task of science is reduced to the determination of properties in any area of the world around us.

Creativity in science is not reduced only to problem solving. The most significant criterion of creativity is the ways leading to the solution of a particular cognitive task. Only through the ways of solving the problem of cognition, sometimes by trial and error, can properties be expressed.

For example. I promulgated the properties of natural electricity. But I did not indicate what experiments and observations I used to determine these properties. The task of knowing natural electricity is solved. There are properties of natural electricity. Now, natural electricity, based on its properties, can be distinguished from any other natural phenomenon. At first glance, the result of cognition is obtained, and creativity has acquired a finished form. But this is far from being the case. Prospects for creativity are just opening up. Sometimes it happens so, the experiment was conducted, but the result was not noticed. The result of a particular experiment will be noticed in conjunction with other experiments and realized as a separate property. Searching for ways of certain properties already leads to questions of applicability of properties as technologies. There are seven properties of natural electricity. But I have already identified 10 ways of obtaining it.

To solve G. Kantor’s problem I applied axioms taken from natural phenomena, such as the motion of light. The speed of light per unit time increases in volume eight times. During the same time the linear velocity of light increases twofold. It is known that a mathematical problem is solvable when all the initial data of that problem are used.

All recent mathematics is based on these solutions and discoveries. It took a long time to find a way to convey the knowledge that was contained in the newest mathematics. Every attempt to write a theory did not lead to a positive result. I was simply drowning in the abundance of connections and interrelations of natural phenomena.

All variety of natural phenomena managed to reflect through the functionals of natural phenomena. The common property of natural phenomena is vibration.

– Properties of vibrations.

– Properties of functionals of functions.

– Properties of functionals of structures.

The unity of these properties in natural phenomena is considered by the newest mathematics. The newest mathematics is a universal formalized language for all natural phenomena without exception. It is the basis for all creative processes.

**III. Reflexion.**

1. Recall how information is presented in statistics? (tables and charts)

2. Do you think it is possible to separate mathematics from economics? Justify your answer.