Application of mathematical knowledge in life. Lesson on the topic "the importance of mathematics in human life"

Many people often ask why do you need math?. Often the very fact that this discipline is included in the mandatory curriculum of universities and schools, puts people at a loss. This bewilderment is expressed in the following: Like, why should I, a person whose future (or current) profession will not be connected with making calculations and applying mathematical methods, know mathematics?

How can this be useful to me in life? Thus, a large number of people do not see any sense for themselves in mastering this science, even on an elementary basis. But I'm sure the math, more precisely mathematical thinking skills needed by everyone and everyone. In this article I will explain why I am so sure of this. First, I will tell you why this discipline, how scientific knowledge and the method is needed in general and where is its place in the system of all natural sciences and how it is applied in practice.

If you already know this, but still wonder why you personally need to study this discipline, then go straight to the second part of the article. There I will talk about what personal qualities mathematics helps to develop, and what you will lose if you refuse to master this subject, at least at a basic level.

The place of mathematics in the system of sciences

Mathematics is a fundamental science, whose methods are actively used in many natural disciplines, such as physics, chemistry and even biology. By itself, this area of ​​knowledge operates with abstract relationships and relationships, that is, with such entities that in themselves are not something material.

But nevertheless, as soon as mathematics enters the field of any science about the world, it is immediately embodied in the description, modeling and prediction of quite specific and real natural processes. Here she finds flesh and blood, coming out from under the cover of idealized formulas and calculations cut off from life.

Mathematics is a tool for understanding the world

It is an exact science that does not tolerate arbitrariness in interpretation and various speculations. This is the embodiment of order and rigid logic. It helps to understand the world around us, to learn more about its laws, since these laws are subject to the same order that reigns in mathematics!

We can successfully translate the language spoken by nature into the language of mathematics and understand the structure of the relationships of a phenomenon. And, after we formalize these connections, we can build models, predict the future states of the phenomena that these models describe, only on paper or inside the memory of computers!

Einstein, in response to a question where his laboratory was located, smiled and pointed to a pencil and paper sheet.

His formulas of the theory of relativity have become an important step towards understanding the universe in which we live. And this happened before man began to explore space and only then experimentally confirmed the correctness of the equations of the great scientist!

Application in modeling and forecasting

Thanks to the application of mathematics, we do not need to conduct costly and life-threatening experiments before realizing any complex project, for example, in space exploration. We can calculate in advance the parameters of the orbit of a spacecraft launched from the earth to deliver astronauts to the orbital station. Mathematical calculations will make it possible not to risk people's lives, but to estimate in advance all the parameters necessary for launching a rocket, ensuring a safe flight.

Of course, a model is a model because it cannot take into account all possible variables, which is why disasters happen, but it still provides fairly reliable forecasts.

You can see the embodiment of mathematical calculation everywhere: in the car you drive, in the computer or portable device from which you are currently reading this article. All buildings, buildings do not collapse under their own weight due to the fact that all the data necessary for the construction were calculated in advance using formulas.

Medicine and healthcare also exist thanks to mathematics, which is used, firstly, in the design of medical devices, and secondly, in the analysis of data on the effectiveness of a particular treatment.

Even the weather forecast is not complete without the use of mathematical models.

In short, thanks to mathematics, we have all the technologies available to us today, do not expose our lives to senseless danger, build cities, explore space and develop culture! Without her, the world would be very different.

Why do people need mathematics? What skills does she develop?

So, we found out that mathematics is one of the most important achievements of culture and civilization. Without it, the development of technology and the knowledge of nature would be unthinkable things! Well, you say, let's say this exact science is really extremely important for humanity as a whole, but why do I need it personally? What will she give me?

Mathematics develops mental abilities

Mathematics allows you to develop some important mental qualities, which I wrote about in an article about the development of intelligence (). These are analytical, deductive (ability to generalize), critical, prognostic (ability to predict, think several steps ahead) abilities.

Also, this discipline improves the possibilities of abstract thinking (after all, this is an abstract science), the ability to concentrate, trains memory and enhances the speed of thinking. That's how much you get! But at the same time, you or your children can lose a lot if you do not pay due attention to this subject.

Speaking in more detail and operating with specific skills, then mathematics will help a person develop the following intellectual abilities

• The ability to generalize. Consider a particular event as a manifestation of a general order. The ability to find the role of the particular in the general.
• Ability to analyze difficult life situations, the ability to make the right decision of problems and be determined in the face of difficult choices.
• Ability to find patterns.
• Ability to think and reason logically, competently and clearly formulate thoughts, draw correct logical conclusions.
• Ability to think quickly and make decisions.
• Planning ahead skill, the ability to keep several consecutive steps in mind.
• Conceptual and abstract thinking skills: the ability to consistently and logically build complex concepts or operations and keep them in mind.

An important point: I have already received a number of questions from readers, so I want to clarify something here right away. The above qualities are developed not only by solving problems from different areas of mathematics: trigonometry, probability theory, etc. You do not have to find dusty school textbooks in these subjects at all if you want to improve these abilities.

Here I am talking not only about mathematics as a specific science, but rather about all those areas of knowledge where the mathematical method is applied and precision, order and logic prevail. So for the development of some qualities of intelligence, the study of the exact sciences is suitable, the decision logic puzzles and even some.

Take what is closer and more interesting to you, there is no need to force yourself to study boring textbooks, the main thing is that the head works, so that the tasks require you to search for non-trivial solutions and the accuracy of the analysis. I write about it right away so that it will be clear what I'm talking about.

Mathematics is essential for the development of a child!

Mathematics is especially important for the development of a child! It sets the standards for correct, rational thinking for the rest of your life! Gives a huge boost to mental development.

I don't even know which one school subject capable of raising the mental level of the growing individual to such an extent and serving as such a good help for intellectual development later, already in adulthood. I do not mean mathematics only as a subject, algebra or arithmetic, I am talking about the application of mathematical methods in general, including physics, geometry, computer science, etc.

Mathematics Organizes, Organizes, and Optimizes Your Thinking

I will begin this paragraph with the famous saying of Lomonosov, the great scientist who achieved success both in the natural sciences and in the field of the humanities - the rarest case of a universal mind. He said: “Mathematics only then needs to be taught, that it puts the mind in order.”

Mathematics trains, such mental qualities that form the framework and skeleton of all your thinking! This is, first of all, logical ability. This is all that organizes all your thoughts into a coherent system of concepts and ideas and the connections between them.

Mathematics itself is the epitome of natural order, and it is not surprising that it orders your mind. And without this notorious logic in the head, a person is not able to draw correct logical conclusions, compare concepts of various kinds, he loses the ability for sound analysis and reasoning. What can lead to the phenomenon of "porridge in the head", confusion in thoughts and reasoning, indistinctness of the argument.

It is easy to mislead such a person, which actually usually happens, since he is not able to identify a clear violation of logic in the statements of all schemers and charlatans (Already the second paid experience with financial pyramids in our country suggests that a huge part of people believe that they don't need math. Knowledge of mathematics does not allow you to deceive!

So it's not only calculations and formulas, it's primarily logic and order! It is a set of rules and functions that make your thinking consistent and logical. This is reflected in your ability to reason, formulate thoughts, hold complex concepts in your head and build intricate relationships.

Why do humanities need mathematics?

Which will certainly come in handy for you, even if you are going to succeed on the basis of some humanitarian discipline, since logic, systemic thinking skills and the ability to formulate complex theories are very necessary there too. Without this, it will not become science, but verbiage.

I heard about brilliant lawyers who, in addition to legal education, received, in addition, physical and mathematical education. This helped them, like good chess players, build complex combinations of defense options in court, or invent clever ways to interact with legislative framework and come up with all sorts of ingenious and non-trivial solutions.

Of course, it is not at all necessary to receive a specialized specialized education in mathematics, even, in my opinion, redundant if you are not going to work in this area. But to master this discipline at a basic level school education and the initial courses of the university, I think everyone should and is capable.

You should not think that this is not given to you by nature, that your vocation is the humanities and you are not able to teach exact subjects. When someone says that he humanitarian mindset and, therefore, he cannot, in principle, count, read formulas and solve problems, no matter how much he wants to, then know that this is such an elegant attempt to justify the fact of the lack of development of mathematical abilities. Not their absence! But only the fact that these skills, for some reason, have not received proper development.

The human mind is a universal thing designed to solve a variety of problems. Of course, this statement has its limits: everyone, due to the peculiarities of their innate and acquired properties of thinking, has certain inclinations to master different sciences. In addition, specialization most often requires knowledge of one thing: it is difficult to be an excellent mathematician, chemist, lawyer, teacher in one (not all of us are Lomonosovs). There will always be something to choose from.

But everyone can master the basic skills of mathematical thinking! For some, it will simply be more difficult, for others it will be easier. But this is for everyone. And as I said, this is necessary for balanced development of your mind. From what you are interested in, for example, literature or psychology, it does not follow that you do not need mathematics and you are simply not capable of mastering it somehow by nature!

One does not exclude the other, but, on the contrary, harmoniously complements. "Humanitarian mentality" in the context of the impossibility of mastering the exact sciences is just one big nonsense and an attempt to justify the reluctance to master those skills that are given with more difficulty than others.

Why is mathematics important in life and work?

Math is useful in business. But maybe the profession that you consider as your future calling will not be related to calculations, formulas, computer science or analytics. Or you don't use it in your current job.

But still, this does not mean that it will always be so. Perhaps you want to change your profession. Or you get so bored with hired work that you decide to start your own business (and this happens quite often). The organization of an independent enterprise always requires calculations, forecasting and analysis. You, as the head of a new business, will need to have the appropriate skills, not everything is possible to delegate to hired employees, their work in any case needs to be controlled.

Without support in the form of mathematical methods of forecasting, modeling and analysis (at least at a primitive level, depending on what kind of business you have), it is difficult to achieve success in organizing your own business. Based on personal statistics, I can say that, as a rule, graduates of technical and mathematical universities achieve the greatest success in business.

It is not only a matter of knowing some special calculation methods, because it is never too late to master this if necessary. The key is in a certain organization of the mind. Business is a highly ordered system, the construction of which requires from its creator certain intellectual skills, structured thinking, the ability to generalize and derive relationships. The study of the exact sciences, as you know, develops these skills.

Conclusion

Mathematics and other exact sciences are very important both for the development of mankind as a whole and for the intellectual improvement of a particular individual. Of course, a balanced mental development of a person implies the development of not only exact subjects, but also humanitarian disciplines. Reading quality literature, for example, is also essential if you want to develop.

But, this alone is not enough. I would like to supplement the wording of the well-known statement: "if you want to become smart, you need to read a lot", adding to this: "- and doing mathematics." Otherwise, the effect of just reading books will be like a body without a skeleton or a building without a frame. It's hard for one without the other.

That is why many humanists, no matter how well they understand their subject area, suffer from confusion of thinking and lack of sober judgment, and many avid mathematicians and techies become isolated in the world of abstract formulas and calculations, losing touch with the real world.

The golden rule is everything is good in moderation, the destiny of a harmoniously developed mind, universality at the most basic level! All together and books and mathematics! This is not a sermon for the glory of amateurism, no, in your specialization you must be a professional and narrow specialist, an expert in his field. But as for your basic erudition and knowledge, there should be a little bit of everything.

I believe that the idea of ​​school education and teaching in the primary courses of universities meets this principle of universality (only an idea, I don’t presume to discuss how this is implemented in practice). I would be extremely negative about strengthening the specialization of primary and secondary education, believing that the growing individual should be given as much as possible from different areas, and when he receives it, let him choose what is closer to him!

"Why do we need mathematics?" - such a question can often be heard from schoolchildren and students of all ages. A great many people around the world sincerely believe that in their entire lives, mathematics has never been useful to them. The problem is that even in primary school, where the basic knowledge of arithmetic is laid, they do not explain to us for what purpose we are doing all this. Apparently, the main thing is to learn, and for what to teach, the students will guess for themselves. It's just that not everyone guesses. And when you don’t understand what to teach for, you lose interest in the subject and the motivation to do anything at all. The only thing that can motivate a student in this case is grades, for which very superficial knowledge is enough, or even simple copying of ready-made answers. If we consider modern system secondary education, it seems that the most important thing is successfully passed exams. It is logical that an increased interest in mathematics arises during the period of preparation for them, when teachers urgently begin to “train” students on typical tasks. Now the students know why they have been teaching mathematics all these years - in order to successfully pass the OGE and the Unified State Examination, after which they can safely forget everything they were taught, because mathematics is no longer useful anyway, so why "clog" your bright heads? Few of them at this moment think about what awaits yesterday's schoolchildren and students outside the walls of their educational institutions. So let's see what math is all about. Mathematics teaches us to think logically and consistently, to easily and reasonably prove our point of view. Yes, our young friend, geometry will still help you in life. After all, the main reason why you were forced to solve tedious problems is not memorizing the theorems of Pythagoras and Thales (although they will still serve you well). No, all this is necessary in order to develop your brains in the right direction. What does it take to solve a math problem? Knowledge of all theorems, axioms, definitions and rules? Or maybe the possession of some cunning tricks? No. All you need is the ability to see the goal, choose the right path to it and plan this path correctly. Isn't this quality important in real life ? By doing mathematics, we force the brain to develop - to instantly structure all incoming information, "stitch" it into "magazines" and "books", "sort it into order". Moreover, the more trained the brain, the more “shelves” in it, the more accurately they are “numbered” and, therefore, the easier it is to put in place or find the necessary information. Therefore, people who are "friends" with the exact sciences and all other sciences are easier, because mathematics teaches us to analyze and simulate various situations. It introduces us to the methods of induction and deduction. With it, we learn to know the world through the prism of logical reasoning. It remains to understand one thing - at what exact moment do we "miss" our children? After all, everything went so well: an inquisitive first-grader readily sat down for lessons, why is it now impossible to even force him to do this? When did he get disappointed? When a child comes to first grade, everything is interesting to him, and when something else turns out well, it is doubly interesting. And since they prepare for elementary school in kindergarten, there are no problems with mathematics in the first four grades. After all, the child succeeds, and it is this success that stimulates his interest in learning something new. But, as we all know, in the fifth grade there is a revolution - the transition from primary to secondary school, where the teacher is no longer one - there are many of them. This period is characterized by a difficult psychological state of the child - adaptation. It is at this point that parents need to closely monitor that interest in mathematics does not disappear. Indeed, in the fifth grade, the first topic of mathematics is “Fractions”. "Fractions" in itself is a very difficult topic to understand, and given that a small person at this moment continues the period of adaptation, it is easy to guess that it is at this moment that a misunderstanding appears between the student and mathematics. It is at this moment that the student needs the help of parents or professional tutors who will help restore faith in themselves and interest the student. If you put everything on the shelves in time, then there should not be any problems in the future. The next crisis period is grade 6, the topic is "Numbers with different signs." Again, if the student does not understand this topic, he will have difficulties with mathematics in the future. After all, this topic is fundamental. Then everything will “wind up” like a snowball. Mathematics will become more complicated and no one will return to these “childish” topics, more precisely, no one will explain them again, but they will give more complex tasks with elements of these topics. In the fifth or sixth grades, it is necessary to closely, but unobtrusively, monitor the progress of the student, since it is in these classes that he receives basic knowledge that will be 100% useful; it is here that he may have difficulties; it is here that the child begins to understand whether he likes this subject or not. At such moments, it is worth supporting your child, explaining why and why he needs it, and then, he will definitely have no illusions about how much mathematics will be useful to him in life. Remember that before the ninth grade you can still fix everything, after - no longer. At this age, the child already has his own opinion on everything that surrounds him and, most often, it is unshakable. Imagine that mathematics is an ancient city, multifaceted and amazing with its expanses. Exploring the nooks and crannies of this city, people learn to think logically, consistently and efficiently, find their way wherever they go and streamline the knowledge gained in the process - otherwise they won’t know it. And all these invaluable skills lie on the surface - come and take it! But what are we doing? And we seem to be saying, “Why should I explore the city? I can get to work anyway, what else do I need? And then we spend hours wandering through the back streets to visit relatives ... That is why it is worth returning and looking into these missed back streets, suddenly there is something interesting left; something important? Many justify their attitude to the exact sciences like this: “After all, this is not mine! I am a humanist, why should I know this? But doesn't the humanities really need to think logically and consistently? The highest, as it seems to us, manifestation of a humanist is a writer. But would anyone really read a story that starts in the middle, continues to the end of the story, and then follows incoherent snippets of text? But how often now one can meet precisely such attempts to "create" ... The lack of coherence of presentation can ruin even the best works. So we are able to ruin our “best works” - our lives, only without realizing in time what is really important for us, and what is secondary. And paramount for us is the knowledge of mathematics, which, over the years of study at school, evolves from a simple method of counting into a complex, many-sided system that overlaps each of the possible areas of knowledge and systematizes disparate facts into a complete and comprehensive picture of the world. That is why the study of mathematics is one of the most important skills acquired by a child at school, which will allow him to adapt in a dynamically changing environment and take his rightful place in life.

The meaning of life - mathematical models. Part 1

1. Introduction.

Around 1998, I tried, on the basis of elements of control theory known to me, and system analysis to formulate some limitations of the life strategy in mathematical formulas. Even earlier, in 1991-1994. I gave a course of lectures at the Institute of Instrumentation on Control in Biological and Medical Systems and introduced into these lectures some mathematical descriptions of control algorithms and life strategies. Elements of these lectures I have also introduced into this essay. Naturally, I did not pretend to give recipes for a life strategy - for this there are professional philosophers, founders of philosophical and religious teachings, prophets, mystics, etc. My goal was much more modest - to see how these problems look from the mathematical side. Accordingly, the result is quite modest - one should not look for a direct correspondence between mathematical formulas and life categories - mathematics is not well adapted for the correct description of these categories. I added here a number of literary digressions, some of which I used in my time for the entertainment of students.

2. Preliminary agreements and restrictions.

The concept of "Meaning of life" is ambiguous - it includes explanations of its biological and social mechanisms (how?), its causal relationships (why?), its goals (why?). Most often, when asking this question, it is associated with the latter (why?), i.e. the concepts of "meaning" and "goal" become synonymous in the everyday sense (although this is not at all the case in the mathematical sense). The main part of the further presentation will be devoted to the last understanding - "The Meaning of Life" as "The Purpose of Life".

Literary digression 1.

<<Ситуация очень схожа со сценой из «Фауста» Гете - при попытке перевода Библии на немецкий язык Фауст с первых же строк сталкивается с затруднением: «В начале было Слово». Дело в том, что в древнееврейском и древнегреческом (повидимому, Библию Фауст переводил с одного из этих классических языков, т.е. с подлинника или «Септуагинты») эта строка читается по-разному и в нее вкладывается многозначный смысл.

In ancient Greek, this is "Logos" - the concept includes the cosmic mind of the Universe, the Main Idea and much more. This concept is closest to the translation "Creative Thought". The most clear presentation of the concept is in Plato. The Supreme Being is conceived as the chief architect of the universe.

In Hebrew, this is in one of the variants of "Kabbalah" - for a sage-Kabbalist, the ability to literally create worlds with the "Word" is an absolute truth - you just need to pronounce it correctly, with all the aspirations and rituals. In contrast to the ancient Greek, here the “Word” is given the mystical meaning of direct creation (by the way, historically this precedes the concept of “Logos”). The Supreme Being is conceived as the main master - the demiurge, who creates the Universe.

When trying to find a German analogue of this concept, Faust sorts through the concepts of "Word", "Thought", "Deed" (in Russian translation, and in German also "Will" - a very important addition).

It is quite obvious that in the concept of "The Meaning of Life" there are all these options - and the main idea, and the main thought, and the main thing, as well as the main goal and the will to achieve it, and in addition, for esotericists (initiates) - also mystical understanding.>>

From the foregoing, it is clear that “words correspond to concepts” (also from “Faust”), and if we want to put our research on a scientific basis, then for each quite obvious (in the everyday sense) word, we need to define the concept that we have in mind, from the set of possible concepts corresponding to the given word. Wittgenstein defines the process of association between a word and a concept as a "language game”: “The whole process of using words in a language can also be represented as one of those games with the help of which children master their native language. I will call these games"language games" and sometimes speak of some primitive language as language game».

The correspondence between a word and a concept can be done most simply, although not very clearly, at the mathematical level - at the level of models. Abstract mathematical models, of course, will be homeomorphic in relation to the described phenomena of life, but not isomorphic, i.e. the model is the likeness of life, but life is not the likeness of the model. Since we are studying the concept of “Goal”, then in the model for us its predictive value will be the main thing - if the forecast made according to the model allows us to correctly plan the trajectory of movement, strategy and tactics of behavior, then this model will be considered satisfactory. Therefore, the most common objection is mathematics, but in life everything is not so - it turns out to be untenable - the model does not claim to be a complete description, but only serves to predict.

Descriptions of phenomena in terms and categories of culture and morality are, in essence, a list of restrictions imposed on behavior patterns that can also be described mathematically, but are more concise, although less formally accurate. The degree of correspondence of these descriptions to real life phenomena in the prognostic sense is approximately the same as that of purely mathematical models, that is, these descriptions are quite pragmatic.

Another significant limitation: in order not to multiply entities beyond the necessary (Pluralitas non est ponenda sine necessitate - Occam's razor), we will not involve the Creator, aliens, the fourth dimension, the aura, midi-chlorians and the Force (from Star Wars) and so on when describing mathematical models. (the list can be continued indefinitely).

A remark about the list of references - the list of sources is too long for the traditional list of printed publications (from Herodotus and Hegel to the Strugatskys and Spinoza); it focuses on Internet sources inon- line- a query in any search engine by the name of the author gives links to dozens of sites.

3. Formation of a hierarchy of goals at the individual level.

In cybernetics, the main feature of a living organism is the property of homeostasis, i.e. retention within the specified limits of the basic parameters of life due to adaptive behavior.

The electromechanical model of the homeostatic system is Walter's famous turtles, held on the edge of the table, the mathematical model is given, in particular, by Ashby:

Since the step functions change in jumps, the analytical integration of these differential equations impossible, but nevertheless these equations uniquely determine the behavior of the system if the initial conditions (state of the system) are given, and the solution can be found with any degree of accuracy using numerical methods.

Living systems, determined by the equations of homeostasis, correspond to organisms that fully implement adaptation due to unconditioned reflexes. The adaptation program is fully recorded on genetic level(in the structure of DNA). The amount of information an organism can pass on to its offspring is entirely determined by the size of its genome.

Literary digression 2.

<< Рассмотрение организма как машины имеет очень давнюю традицию, хотя принято связывать эту аналогию с 18-м веком (веком Просвещения). Любопытно, что уже в то время делались небезуспешные попытки ввести для простейших организмов - машин понятия нравственности. У Потоцкого в «Рукописи, найденной в Сарагосе» один из героев (математик) рассуждает, имеет ли моллюск в раковине понятие о добре и зле. Первичная дихотомия добра и зла у него отождествляется с дихотомией «съедобно - несъедобно»: моллюск открывает свою раковину и поглощает съедобную частицу или закрывает раковину и отвергает несъедобную. Рост сложности системы (и, соответственно, усложнение нравственности) достигается за счет увеличения числа возможных выборов поведения. Таким образом, по Потоцкому, моллюск оперирует 2 понятиями, а гений на уровне Исаака Ньютона - 10 000 понятий - вот пример чистой математической индукции, без учета качественного изменения системы.>>

The next stage of more perfect adaptive behavior is associated with the introduction of the concept of a conditioned reflex. Modeling of the conditioned reflex has also been carried out for Walter's turtles, but the most popular mathematical model of systems with a conditioned reflex is Rosenblatt's perceptron. The main idea of ​​the perceptron is the ability to change the coefficients feedback and distribution of step functions from homeostasis equations in the learning process. Learning outcomes (positive or negative) serve to reinforce or weaken the feedback of individual blocks of the system. Then the process in the homeostatic system is determined not only by its initial state, but also by the process of its learning, i.e. the structure of the system adapts to the environment in the learning process. The amount of information that is transmitted to descendants, in this case, significantly exceeds the volume of the genome.

The main drawback of control at these 2 stages is the delay of control - control uses only information about the current state of the environment, when the environmental parameters change, there is a time lag between obtaining new information and forming a new control, which reduces the organism's chances of survival.

The next step in improving adaptive behavior is the construction by the bodymodels environment, predicting the future state of the environment using the model and planning their behavior using this model. Here we first encounter the conceptgoals because planning involves solving some problem. The question of understanding this task is key here, since without setting this task there is no concept of a goal. Whether the concept of purpose is inherent only to man, or to other higher animals, is a debatable question and is of no fundamental importance for our study.

The mathematical model of purposeful systems is described in general theory systems (Mesarovic and Takahara) as follows:

and the pair (x, y) belongs Sif and only ifyis a solution to the decision problem given by the element X . Multiple inputsXis called the set of solutions, the setY- a set of output quantities that can be obtained in response to input actions X. The complication of the mathematical model of goal-oriented systems leads to the concepts of the satisfaction problem, the model of the control object and the decision-making system. To describe and analyze these models, a deeper knowledge of set theory is required. Moreover, any system that converts inputs into outputs can be described as a decision-making system. The phenomenological and purposeful approaches here depend on what the researcher's interest is aimed at. We will naturally take a focused approach.

If we introduce a set of restrictions into the equations of the systemNassociated with moral and cultural taboos, the equations will take the form:

With the advent of the concept goals associated with the introduction of the objective function, the search for the extremum of which is a control problem. Note that with adaptive control, reaching the extremum of the objective function is not necessary. The target function represents a functional of type

t- time, T - the time interval over which the integration is performed (for example, the duration of life). The search for the extremum of the objective function is performed on the space of input variablesxn. The solution with any degree of accuracy to achieve the extremum of the objective function is found by numerical methods.

F value corresponds to the degree of satisfaction of the totality of some human needs - both material and emotional.

Here, two types of tasks are traditionally distinguished: target planning tasks and operational control tasks (although at the modern level of computer technology, the line between these two types of tasks is blurred, since the solution of target planning problems can be carried out in real time with a sufficiently large computing power).

For target planning tasks, depending on the type of objective function, the following are used:

linear programming (Kantorovich) - it is required to find the maximum of the function

2. dynamic programming (Bellman) - a typical problem solved by this method is the traveling salesman problem: there isn+1 cities A 0 , A 1 ,… Anwith given distances between themdij; it is required to choose such a route of movementA 0 , Ai 1 , Ai 2 ,… Ain, A 0 , at which the total path is minimal;

3. heuristic programming (Newell, Shaw, Minsky) - at the same time, information about the control object is incomplete and, in particular, expert decision-making systems are used;

4. game methods applied to conflict situations and stochastic control objects - this group of methods, in particular, includes the so-called "business games".

For operational control tasks, various methods of automatic control in real time are used:

1. For deterministic systems, extremum search methods: Gauss-Seidel method, steepest descent method (according to the gradient maximum);

2. For stochastic systems - correlation-extreme method (Miller, Tarasenko, Melik-Shakhnazarov, Markatun) - while determining the optimal location coordinates or their derivatives is carried out by finding the extremum of the correlation functionRijor its varieties.

Of course, the above lists of methods for solving problems of target planning and operational management are far from complete and include only the most traditional and well-mastered methods.

We summarize the above: the goal of life in the traditional interpretation is modeled as finding the maximum of the objective function F (happiness) during life T (note that T - inconstant and depends on the search strategy). Here, for the first time, we introduced the concept of happiness into our study. It (continuing the language game again according to Wittgenstein) is very complex and, strictly speaking, cannot be fully disclosed. However, in order to be able to move on, let us assume in our language game that in the formula for F can be taken into account with certain weighting factors, both material and emotional incentives to satisfy the individual. Mathematization of the concepts of morality and emotions will be considered in Sections 8 and 9 of this study.

Since in the objective function F must be taken into account with the sign “-“ the misfortunes and sufferings of life, then the result F may be negative. With a pessimistic approach (if the weights of suffering are taken higher than the weights of pleasure), the most profitable strategy is the complete absence of control (action) so as not to increase the amount of suffering (the ideal is nirvana). It is easy to understand that with such a strategy, the existence of both the individual and society is impossible. Therefore, in what follows we will not consider such a strategy, since the result is trivial.

Literary digression 3.

<<Религиозные мыслители рассматривают T , as a value tending to infinity (taking into account the existence beyond the grave). Then the objective function search strategy takes on a completely different form. Here is Pascal's proof of the existence of God, based on the theory of probability:

Atheist strategy - T1 = T - the time of earthly life, the final value, F1 - the amount of goods acquired by a person in earthly life, the possible gain - F1 - does not depend on the probability of the existence of God r b .

The believer's strategy T2 -> “infinity”( afterlife duration), F1 -> 0 - zero amount of benefits received by a believer in earthly life with righteous behavior, F2 -> “infinity” (an infinite amount of benefits received by a believer in the afterlife, i.e. eternal bliss), a possible gain - F2 * r b .

Comparing the possible payoffs, we find that the believer's strategy gives a larger payoff for an arbitrarily small r b . Note that if we try to define r b according to the principle of a scientific experiment, then this probability should be defined as the ratio of the number of successful (confirming the existence of God) experiments to the total number of experiments. The whole problem is that the scientific validity of successful experiments is unprovable because of the fundamentally different interpretation of their results by an atheist observer and a religious observer. >>

Search for the maximum F is considered as a strategic task of long-term planning, or a tactical task of operational management, and there is a logical paradox - the type of the objective function is determined by the subject himself, implementing the search strategy, while the objectivity of the choice is lost - the correctness can only be assessed by an outside observer (or a group of observers representing society ). Which of the types of happiness is objectively optimal - health and longevity, wealth, power, social prestige, wisdom, self-satisfaction from drugs, alcohol and debauchery - cannot be determined at the level of the individual.

Literary digression 4.

<< Одно из древнейших доказательств субъективности определения счастья мы находим в рассказе о Солоне и Крезе (Геродот, Плутарх, Ксенофонт). Лидийский царь Крез, накопивший несметные богатства, показал их афинскому мудрецу Солону и спросил, кто, по его мнению, является счастливейшим человеком на земле. Солон привел в пример афинских граждан - одни пали смертью героев на войне за отечество, другие после праведной жизни умерли в святилище богини. Крез с возмущением спросил его - не знает ли он счастливых среди живущих, на что Солон сказал, что объявлять счастливым того, кто еще живет - то же, что объявлять победителем в беге того, кто еще не закончил дистанцию. Через некоторое время царство Креза было разорено завоевателями, а сам он приговорен к смерти на костре и на себе ощутил справедливость суждения Солона. Здесь в основе понимания счастья две системы ценностей: у Креза - материальные блага; у Солона - авторитет в обществе на основе высокого уровня Платоновского «тимоса». «Тимос» понимается как врожденное чувство справедливости, порождающее жажду общественного признания (Фукуяма).>>

Literary digression 5.

<<Насколько далеко мы ушли от понимания счастья во времена Солона и Креза, покажем на следующем отрывке из Кристофера Лога (цитируется по сказке Стругацких):

"You are asking:

What do I think

Am I the highest happiness on earth?

Two things:

Change the state of mind in the same way,

How would I exchange a penny for a shilling,

young girl

Hear the singing

Out of my way, but following

How did you find out the way for me?

Perhaps, paradoxically, this passage is closest to the modern understanding of happiness.

It remains to add the following quotation from the Strugatskys:

“Are such things algorithmized?!”

But the Strugatskys are not Holy Scripture, and we will continue this hopeless cause.>>

The source of the paradox when choosing the objective function is the construction of a hierarchy of goals using the method of mathematical induction: to solve a small tactical problem (for example, conducting a commercial operation), a tactical goal is determined lower level(getting a certain amount of money), the tactical task of the next level (achieving well-being) determines the next goal by induction (complete financial well-being), the next level (the conquest of power in society on this basis) puts forward the next tactical goal. There is an illusion that the method of induction is applicable to human life in general. However, Gödel's theorem comes into force here: those tasks that were formulated within individual segments of human life cannot be formulated by an individual for human life as a whole. For an objective statement of the task of optimizing the objective function, it is necessary to move to the next system level - to consider not an individual, but society.

4. Formation of goals at the level of society .

Unlike the previous section, the system for which the tasks of survival, adaptation and optimization of the objective function are solved is not a single individual, but a society or part of it. At different stages of development, the part of the society that set and solved these tasks for itself was the clan (family), tribe, people (ethnos), humanity as a whole (the latter is still only in the future).

The choice of the objective function here is also quite arbitrary, but the correctness of this choice is determined over the observable historical periods according to the state of this part of the society. A management strategy for society is, on the one hand, a certain set of restrictions that set the rules for the social behavior of individuals (morality, religion, morality, cultural taboos, jurisdiction, etc.), on the other hand, an idea that unites part of society, in particular, a national idea ( world domination, freedom and unlimited possibilities for the development of the personality of individuals, guaranteed bliss in the afterlife, improvement of the race and the creation of a superman, high level welfare for all, etc.).

The correctness of the choice of strategy can be judged from a historical perspective, on the basis of an analysis of what is the stability of the society with the chosen strategy, what is the amount of happiness and unhappiness received by members of the society. Note that when analyzing the correctness of the strategy, we must again go beyond the analyzed system and consider a system that includes society and society as components. environment(the planet, and in the future the whole space).

Retrospective (historical) analysis of the correctness of the society's strategy on individual historical stages has also the limitation that the attitude of individuals on various stages civilization is incomparable, and therefore, the definition of happiness and unhappiness of a member of society is impossible. For us, the worldview of the ancient Hellenes, the Chinese of the era of Confucius, the Aztecs and the Mayans is incomprehensible. Attempts to reconstruct this attitude have literary, but not objective, value.

Therefore, when developing a national idea or a code of morality and morality, one can only be guided by clearly negative examples (the short-lived existence of the Third Reich, an unsuccessful attempt to build a communist society in Russia, etc.).

The maximum that an individual in society can do when planning his personal strategy:

understand the target function of your part of society and bring your personal strategy in line with it (changing part of your personality) - Confucian approach,

to find for oneself a part of the society, the target function of which is more consistent with the personal strategy, to become a member of this part of the society (and endure all the inconveniences and additional efforts necessary to change the environment) - an individualistic approach,

change the target function of your part of society, bringing it into line with your personal target function (transformation of society with minimal chances of success) - a revolutionary approach.

Self-regulating systems .

There is an illusion that it is enough to establish the rules of the game, and with sufficiently good rules, the system itself will develop in a “good” direction and lead society to a prosperous state. In our time, the most indicative here is the idea of ​​a market economy, which itself will regulate everything and improve the economic performance of society. This can be compared with the influence of evolution on the animal world of the planet. Evolution is indeed effective in weeding out less fit organisms, it remains to be seen whether dinosaurs and Neanderthals would have been satisfied with its results. By the way, the Neanderthal brain was larger in brain volume modern man, so perhaps the extinction of the Neanderthals closed the way for humanity to a more intelligent society.

5.information model management.

Another remark concerns the ability of the individual to develop the right tactics and management strategy. The control information model developed by Wiener defines the optimal control condition as:

H(X)>= H(Y) (5),

The above ratio is known as the law of necessary diversity and, translated into ordinary language, means that the information capabilities of the controlling individual must be no less than the information wealth of the controlled object, i.e. optimal control with incomplete information about the object is impossible.

Therefore, when developing a life strategy, it is necessary to take into account:

The fundamental incompleteness of information that an individual can collect during his life.

The need to take into account the total information accumulated in society.

The importance of information filters for assimilation of useful information for management and elimination of harmful information.

The choice is up to the individual. The objectivity of the choice increases with understanding of various aspects of the problem - personal capabilities, lifestyle in certain parts of society, prospects for the development of oneself and society, voluntary acceptance of the restrictions that apply in society (rules of the game). Obviously, a scientific understanding of the problem of building a life strategy sharply narrows the possibility of a personal free choice of life alternatives.

Note that the value of information wealth for management was practically the basis for the selection of officials in ancient China - to be appointed to a post, an official had to pass exams in classical philosophy (according to Confucius), in literature, mathematics (including geometry). The result of the skilled work of officials was success in construction (the Great Chinese Wall), irrigation, the creation of a giant fleet and other industries where Ancient China was far ahead of the surrounding countries.

Literary digression 6.

<<Информационная модель Винера имеет достаточно простой житейский аналог, который по-латыни формулируется так:

Ubi nil vales, ibi nil velis.

Where you can do nothing, there you should not want anything - that is. if your information wealth is significantly less than the information wealth of an object, you cannot manage that object. Submit and do not make plans.

Seneca, from letters to Lucilius:

“Ducunt fata volentem, nolentem trahunt.”

“Fate leads the humble, drags the recalcitrant.”>>

The Stoic philosopher's approach is formulated for a static model, when the functionsH(X) And H(Y) are constant during the solution process. However, in practice, a dynamic approach is more often used - when the managing individual conducts a study of the structure of the managed object. At the same time, the information wealth of the controlling individual increases.H(X) and it becomes possible to fulfill the condition of successful control (5).

True, another option is also possible - when the managing individual, instead of increasing his information wealthH(X) reduces the information richness of the objectH(Y), i.e. remakes the controlled object in order to eliminate obstacles to control (for example, destroys the political opposition) - a dictatorial approach.

Only it will no longer be the same object and not the same controlling subject, and control turns into suppression.

The management information model leads to the task of selecting governing subjects, i.e., to the choice between classical democracy of the “one person - one vote” type and meritocracy (the rule of the worthy, i.e., in our case, the most qualified experts in the art of management). Partially, such a system of two-stage elections is implemented in the United States. In the transition to two-stage elections, the eternal question inevitably arises: “who guards the guards” or “Quis custodiet ipsos custodes?». Selection system experts is a key issue, but not a hopeless one. The community of academic scientists and managers is quite capable of forming a competent expert group.

6. The dependence of the strategy on the age of the ethnic group and the individual

In the previous sections, it was tacitly assumed that the individual's personal strategy is adopted by him somewhere at the beginning of life and then does not change throughout life, i.e. the individual accepts the “rules of the game” and follows them (the type of functionalF(x 1 , x 2 ,… xn) does not change throughout life T ). For strategy 1 (the Confucian approach), this is possible only if the individual is brought up in the “correct” spirit, which is typical for relatively young ethnic groups. Examples: ancient Sparta, Ancient China, Samurai Japan, Chivalry In Medieval Europe. The knight's motto is "without fear and reproach" (chevalierSanspeuretSansreproche) - "do what you must, and let it be what will be." Even in the conditions of one closed type of civilization, this type of strategy was rarely fully maintained during the life of an individual. For example, Socrates was raised as a warrior, in his youth he was an exemplary warrior, then he became a philosopher. Social dynamics (social “elevators”) made kings out of ordinary knights, shoguns out of ordinary samurai; at the same time, the strategy of behavior changed radically from strategy (1) (the Confucian approach) to strategy (2) (the individualistic approach). Freelancers appeared instead of knights “without fear and reproach” (freelancers) - free spearmen who were looking for their happiness, choosing for a short time the next overlord. At present, freelancers (albeit in a completely different sense) are one of the main groups of the active population, especially in creative, creative professions - programmers, designers, etc. At the same time, clerks who are true to the "corporate" spirit, i.e. e. following Confucian ethics. Such is the general dynamics of groups characteristic of post-industrial society.

On the other hand, such dynamics is also characteristic of the development of an individual. At first life path the individual is basically brought up and accepts the ideology of life “according to the rules”; as one grows up and assimilates more and more information about one's capabilities (knowledge of oneself) and about the external environment (knowledge of life) (see Wiener's management model in the previous section), individualistic or revolutionary traits intensify; at the end of his life, when his strength dries up, he goes back to the Confucian way of life.

Taking into account the change in the chosen strategy during the lifetime, the formula for the objective function takes the form:

Where k+1 - the number of strategies used by the individual during life;

Fi- functional determined by the type of strategyi.

Literary digression 7 (and last).

<<” SiJeunessesavait, sivieillessepouvait”(Etienne, 1594) -“If youth knew, if old age could.” >>

Still, there are quite accurate analogies between mathematical formulas and worldly wisdom, you just need to dig.

culture art society science meaning of life, target planning, information model

It is known that mathematics is never alone, it is always applied to something! This suggests that no other science can exist without mathematics. Therefore, if humanity had not created the world of mathematics, it would never have been able to possess SCIENCE! Let's take technological progress as an example. In order for some new apparatus to be born, many scientists and developers are needed. Among them there will definitely be a mathematician, because there is undoubtedly a need for this! Hence follows the important role of mathematics in the development of the world around us and humanity in general.

The development of methods of computational mathematics and the increase in the power of computers make it possible today to perform accurate calculations in the field of the dynamics of the most complex living and non-living systems in order to predict their behavior. Real success along this path depends on the readiness of mathematicians and programmers to work with data obtained in traditional ways in the natural and human sciences: observation, description, survey, experiment.

The position of mathematics in the modern world is far from what it was one hundred or even only forty years ago. Mathematics has become a daily tool of research in physics, astronomy, biology, engineering, production organization and many other areas of theoretical and applied activity. Many prominent physicians, economists and specialists in the field social studies consider that the further progress of their disciplines is closely connected with a wider and fuller use of mathematical methods than has been hitherto. No wonder the Greek scientists said that mathematics is the key to all sciences.

Of course, the above once again proves how important mathematics is not just in itself, but how other sciences need it, rely on mathematical facts and, thereby, help humanity develop further and further! Mathematics has always been an integral and essential part of human culture, it is the key to understanding the world around us, the basis of scientific and technological progress and an important component of personality development.

Mathematics contains features of volitional activity, speculative reasoning and striving for aesthetic perfection. Its main and mutually opposite elements are logic and intuition, analysis and construction, generality and concreteness.

We have already considered many reasons why mathematics is considered not even one of, but the most important science. Let us now try to give a number of facts proving this. They are simple, they are faced by any person, and every day.

1. Mathematics is found and used in everyday life, therefore, every person needs certain mathematical skills.

Isn't it true that we have to count in life (for example, money), we constantly use (often without noticing it) knowledge about the quantities that characterize the length, area, volume, time intervals, speeds and much more. All this came to us in the lessons of arithmetic and geometry and came in handy for orientation in the world around us.

Mathematics is needed for children to form a spiritual image, develop the necessary character traits (patience, diligence). A girl can take into account the fact that mathematics will help her to be a good mother (to help her children, to conduct developmental work with them). For some, doing this science gives self-confidence, someone is glad that he learns about interesting people (for example, about Archimedes). For some, mathematics is pleasant as a science, the majority is aware of its need for a future profession.

Mathematical knowledge and skills are required in almost all professions. First of all, of course, in those related to the natural sciences, technology and economics. Mathematics is the language of natural science and technology, and therefore the profession of a natural scientist and engineer requires a serious mastery of many professional information based on mathematics. Galileo said very well about this: ``Philosophy (we are talking about natural philosophy, in our modern language- about physics) is written in a majestic book that is constantly open to your gaze, but only those who first learn to understand its language and interpret the signs with which it is written can understand it. It is written in the language of mathematics. But now there is no doubt the need to use mathematical knowledge and mathematical thinking to a doctor, linguist, historian, and it is difficult to cut off this list, mathematical education is so important for professional activity in our time. Therefore, mathematics and mathematical education are needed to prepare for a future profession. This requires knowledge of algebra, mathematical analysis, probability theory and statistics.

Another major reason for the need of mankind in mathematics is the education in a person of the ability to understand the meaning of the task assigned to him, the ability to correctly, logically reason, and learn the skills of algorithmic thinking. Everyone needs to learn how to analyze, distinguish a hypothesis from a fact, criticize, understand the meaning of the task, schematize, clearly express their thoughts, etc., and on the other hand, develop imagination and intuition (spatial representation, the ability to foresee the result and predict the solution path and etc.). In other words, mathematics is necessary for the intellectual development of the individual. In 1267 the famous English philosopher Roger Bacon said: ``He who does not know mathematics cannot know any other science and cannot even show his ignorance.''

The military security, economic and technological independence of the country depend on the mathematical literacy of its citizens, and the bulk, and not the elite group. It is difficult to overestimate the importance of mathematics, mathematical education and mathematical culture in the modern world. All modern science permeated with mathematical methods and mathematical ideas.

Poor mathematical education violates the basic rights of a citizen, in particular the right to free choice of profession. People who do not know what mathematical proof, mathematical reasoning is, are easily manipulated by shameless politicians, as well as financial tycoons and criminal authorities through the media controlled by them. Mathematically uneducated people are ready to dutifully follow any false prophet, they listen with delight to demon-possessed clairvoyants and illiterate astrologers. Mathematically illiterate leaders of states, large industrial and financial corporations, surrounded by insufficiently mathematically educated advisers and consultants, today pose a huge danger to humanity. They are not able to think systematically, they cannot even calculate the immediate consequences of their actions, which more and more often lead to military conflicts, economic crises, financial upheavals, environmental and humanitarian disasters, which very quickly lose their local character.

Mathematical modeling should become an obligatory stage preceding the adoption of any responsible decision. Achievements of the Soviet-Russian mathematical science and mathematical education are well known and generally recognized. It was they who became the basis of many of the real successes of Russia in the Soviet period. The Russian mathematical school had a serious impact on the development of world science and education in the second half of the 20th century. Her students can be found in all major scientific centers of the planet. But today we are bitterly witnessing a significant decline in the mathematical education of our society, the fall of its mathematical culture. Numerous so-called innovations destroy traditions Russian education, offering the worst Western examples as benchmarks. The economic ruin, which has become the main sign of the reforms taking place in our country, has pushed the problems of education to the last place. In the education system itself, it was mathematics that found itself in the most difficult position, as a subject that does not correspond well to market ideology. Recently, there has been a constant reduction in hours for mathematical subjects, reduction and simplification of programs. Practically no modern scientific literature in mathematics, without which it is impossible to educate highly qualified specialists. The ongoing emigration and semi-emigration of leading scientists and teachers, and now of the best students, is greatly accelerating this process of decay.

Concern about the state of mathematical education in Russia is expressed today by many foreign scientists. Russian mathematical education has been and still remains a model for the whole world, and its destruction can be the beginning of the destruction of the mathematical education of all civilized mankind.

Mathematics is a phenomenon of global culture, it reflects the history of the development of human thought. Destroying mathematics, mathematical education, we are destroying human culture, destroying the history of mankind. Universal computerization not only did not reduce the importance of mathematical education, but, on the contrary, set new tasks for it. A decrease in the level of mathematical education and mathematical culture of society can turn a person from the owner of a computer into his servant and even slave.

In the process of cognition of reality, mathematics plays an ever-increasing role. Today there is no such field of knowledge where mathematical concepts and methods would not be used to one degree or another. Problems that were previously considered impossible to solve are successfully solved through the use of mathematics, thereby expanding the possibilities scientific knowledge. Modern mathematics combines very different areas of knowledge in single system. This process of synthesis of sciences, carried out in the bosom of mathematization, is also reflected in the dynamics of the conceptual apparatus. In order for humanity to develop, and develop fruitfully, not only "the best minds" are needed, but also fresh ideas. And this requires creative people with unusual thinking, a broad outlook, a flexible mind. For all this to be in a person, it is necessary that he perfect himself. Mathematics makes us think, analyze. In the process of searching for information for the message I prepared, I found one interesting site. On it, people of different ages, education, worldviews shared their opinions about mathematics, namely: they left their votes for and against mathematics, for love or hatred in relation to it. Here is what one of the participants in the discussion wrote: “There are no lies in mathematics. All formulas and theorems have a rigorous proof. Mathematics develops the ability to think logically, which allows a person to live interestingly and never be bored. I read a lot of textbooks on higher mathematics. Through the study higher mathematics a philosophical analytical mind and the ability to think independently are acquired. The conclusion from this can be drawn as follows: the development of human intellect is necessary for the development of civilization. This is possible thanks to the "philosophical analytical mind and the ability to think independently", which is achieved as a result of "brain warm-up".

Can you clearly explain to the child why he needs to do math? After all, the study of concepts, laws of mathematics and logic, the solution of mathematical and logical tasks requires mental effort. And why is it needed at all?

We reviewed a number of scientific studies and identified real evidence for the benefits of doing math.

Even if you are convinced that your child’s life will not be connected with mathematics, we recommend that you still read our article in order to at least easily answer the questions of the little “why”.

1. Mathematics develops thinking

By studying mathematics and solving problems, the child learns:

• summarize and highlight the important;
• analyze and systematize;
• find patterns and establish cause-and-effect relationships;
• reason and draw conclusions;
• think logically, strategically and abstractly.

Just as regular sports training “pumps” the body, makes it healthy, strong and resilient, so regular math exercises “pump” the brain - develop intelligence and cognitive abilities, expand their horizons.

2. Mathematics trains memory

Scientists from Stanford University in the USA studied the process of solving mathematical problems by a person and found out that adults use thinking and the skill, brought to automatism, to “get” the answers already there from memory.

Children under 7 often resort to the help of fingers and toes, as well as various substitutes (real objects, counting sticks). In the "transitional period", at the age of 7 to 9, schoolchildren form the "adult" skill of "thinking", comprehending and remembering information.

An interesting study was published in the journal Nature Neuroscience in 2014. First of all, it was devoted to the study of the role of the hippocampus (an area in the brain) in the development of cognitive activity in children. But his indirect conclusions are as follows:

• if you want your child to have no problems with math at school, train your memory in early age;
• solving mathematical problems develops memory.

3. Math builds character

For the correct solution of mathematical and logical problems, attentiveness, perseverance, responsibility, accuracy and accuracy are needed.

The more regularly a child trains these "muscles of character", the stronger they become, the more often they help the child in solving not only educational problems, but also life problems.

LogicLike is the right training platform for 20-60 minutes a day. Solve problems, participate in olympiads in logic and mathematics, develop the will to win and the ability to win!

We create both simple and Olympiad problems that you want to solve:

• assignments for grade 1;
• assignments for grade 2;
• assignments for grade 3.

4. Music for mathematics, mathematics for music

A comprehensive study by Barbara H. Helmrich of the College of Notre Dame in Baltimore found that children who played musical instruments in middle school did significantly better in math in high school.

Scientists have found that the same part of the brain is responsible for solving algebraic problems and processing musical information.

"The largest average difference in algebra scores between any two groups of subjects was found between African-American 'instrumental' groups and groups of 'non-musical' students."

Paradoxically, scientists didn't seem to be interested in feedback.
After all, if the same part of the brain is responsible for the development of mathematical and musical abilities, it is possible that doing mathematics improves musical abilities.

I remember Sherlock Holmes, who was both an excellent detective and a talented violinist. Many will say that the famous English detective is just a fiction, but he had his own real prototype, a mentor and friend of Arthur Conan Doyle. The greatest physicist Albert Einstein was also a passionate violinist.

5. Math Helps You Succeed in the Humanities

It is the early mathematical ability- a sure premise that in the future the child will not only understand mathematics well, but also succeed in other school disciplines. Next in importance for contributing to academic success are reading skills and the ability to manage one's attention.

Such conclusions were reached by scientists in the field of education and social policy at Northwestern University in Evanston. During the study, they assessed the relationship of key elements of school readiness (basic skills for school admission - "academic" readiness, attention, social-emotional skills) with further academic success.

Mathematics is an interdisciplinary science, it is closely related to physics, geography, geology, and chemistry. Sociology and economics are inseparable from mathematics, and many of the conclusions of even the usual humanities, such as linguistics, journalism, are based on mathematical models and concepts, mathematical and logical laws.

6. Develops skills for solving everyday problems

Barbara Oakley, Dr. technical sciences, brain stem cell researcher and author of Think Like a Mathematician, emphasizes:

“Mathematics saves us from “magical thinking” - we strive to delve into the essence of things and do not rely on chance and higher powers.”

The more difficult the math problems become, the more skills are required to solve them. The child learns to reason, build sequences, think through algorithms, juggle several concepts at once, and these skills become a habit.

Thanks to mathematics, we get rid of bad habits:

• we do not speculate, but operate only in exact terms;
• we do not just memorize information and rules mechanically, but evaluate it, analyze it, reflect in order to understand and learn new material, a new life lesson.

7. Mathematics is the basis of a successful career

If 10-15 years ago it was considered promising to study foreign languages, then now you will not surprise anyone with fluency in several languages. Now professional demand largely depends on the understanding of technology, the ability to think, abstract and the ability to solve non-standard problems. It is extremely difficult to do without knowledge of mathematics for those who want to work in the field of IT.

Abstract, critical and strategic thinking, analytical skills, the ability to build algorithms are a “must-have” for a good developer.

TOP 5 soft skills.