home / Business/ How mathematics teaches critical thinking. Preschoolers' use of mathematical knowledge in everyday life and games Mathematical knowledge and what it gives me

How math teaches critical thinking. Preschoolers' use of mathematical knowledge in everyday life and games Mathematical knowledge and what it gives me

Many people often wonder why do we need mathematics?. Often the very fact that this discipline is included in the compulsory curriculum of universities and schools confuses people. This bewilderment is expressed in the following: Like, why should I, a person whose future (or current) profession will not be related to calculations and the use of 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 that mathematics, more precisely mathematical thinking skills, needed by everyone. In this article I will explain why I am so sure of this. First, I will tell you why this discipline, as scientific knowledge and method, is needed in general and where its place is in the system of all natural sciences and how it is applied in practice.

If you already know this, but are still wondering 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 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, the methods of which are actively used in many natural disciplines, such as physics, chemistry and even biology. In itself, this area of knowledge operates with abstract relationships and interconnections, that is, with entities that in themselves are not something material.

But nevertheless, as soon as mathematics enters the field of any science about the world, it immediately translates into the description, modeling and prediction of very specific and real natural processes. Here she acquires flesh and blood, emerging from under the veil of idealized formulas and calculations divorced 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 that nature speaks into the language of mathematics and understand the structure of the relationships of any 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 the question of where his laboratory was located, smiled and pointed to a pencil and a piece of paper.

His formulas for the theory of relativity became an important step on the path to understanding the universe in which we live. And this happened before man began to explore space and only then did he experimentally confirm the correctness of the great scientist’s equations!

Applications in modeling and forecasting

Thanks to the application of mathematics, we do not need to conduct expensive and life-threatening experiments before implementing some complex project, for example, in space exploration. We can calculate in advance the orbital parameters of a spacecraft launched from the ground to deliver astronauts to the orbital station. Mathematical calculations will allow you 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 just 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 now reading this article. All buildings do not collapse under their own weight due to the fact that all the data necessary for construction was 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 analyzing data on the effectiveness of a particular treatment.

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

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

Why does a person need mathematics? What abilities 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 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 the article about the development of intelligence (). These are analytical, deductive (the ability to generalize), critical, predictive (the ability to predict, think several steps ahead) abilities.

This discipline also improves the capabilities 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 may lose a lot if you do not pay due attention to this subject.

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

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 solutions to problems and make decisions in the face of difficult choices.
Ability to find patterns.
Ability to think logically and reason, formulate thoughts competently and clearly, and draw correct logical conclusions.
Ability to think quickly and make decisions.
Planning ahead skill, the ability to keep several successive steps in mind.
Conceptual and abstract thinking skills: the ability to organize complex concepts or operations in a coherent and logical manner and to hold 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-mentioned qualities are developed not only by solving problems from various fields of mathematics: trigonometry, probability theory, etc. You don't have to find dusty school textbooks on these subjects 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 used and precision, order and logic prevail. So, to develop some qualities of intelligence, studying the exact sciences, solving logical 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 your head works, so that the assignments require you to find non-trivial solutions and accurate analysis. I’m writing about this right away so that further it is clear what I’m talking about.

Mathematics is essential for a child's development!

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

I don’t even know what other school subject is capable of so raising the mental level of a growing individual and serving as such a good aid for intellectual development later, already in adulthood. I don’t mean mathematics only as a subject, algebra or arithmetic, I’m talking about the application of mathematical methods in general, including in physics, geometry, computer science, etc.

Mathematics organizes, streamlines and optimizes your thinking

I will begin this point with the famous saying of Lomonosov, a great scientist who achieved success both in the natural sciences and in the field of humanities - a rare case of a universal mind. He said: “Mathematics should be taught only because 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 abilities. This is all that organizes all your thoughts into a connected system of concepts and ideas and connections between them.

Mathematics itself is the embodiment of natural order and there is nothing surprising in the fact that it organizes your mind. And without this notorious logic in the head, a person is not able to draw correct logical conclusions, compare concepts of different kinds, he loses the ability for sound analysis and reasoning. What can lead to the phenomenon of “mess in the head”, confusion in thoughts and reasoning, vagueness of argumentation.

Such a person is easily misled, which is what usually happens, since he is not able to identify a clear violation of logic in the statements of all sorts of schemers and charlatans (This is the second lamentable experience with financial pyramids in our country, which suggests that a huge part of people believe that they don't need math). Knowledge of mathematics does not allow you to be deceived!

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

Why do humanities students need mathematics?

Which will certainly be useful to you, even if you are going to succeed in some humanities discipline, since logic, systems thinking skills and the ability to formulate complex theories are very necessary there too. Without this, it will not become science, but verbiage.

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

Of course, it is not at all necessary to receive a specially specialized education in mathematics, even, in my opinion, redundant, if you do not intend to work in this field. But I believe everyone should and is capable of mastering this discipline at the basic level of school education and initial university courses.

You should not think that this is not given to you by nature, that your calling is the humanities and you are not able to teach exact subjects. When someone says that he has humanitarian mindset and, therefore, he cannot count, read formulas and solve problems in principle, no matter how much he wants, 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 that these skills, for some reason, were not properly developed.

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 characteristics of their innate and acquired properties of thinking, has certain inclinations to master various sciences. In addition, specialization most often requires knowledge of one thing: it is difficult to be an excellent mathematician, chemist, lawyer, teacher in one thing (we are not all Lomonosovs). You will always have to choose from something.

But Everyone can master basic mathematical thinking skills! For some it will simply be more difficult, for others it will be easier. But everyone can do it. And as I already said, this is necessary for balanced development of your mind. Just because you are interested in, for example, literature or psychology, does not mean that you don’t need mathematics and that you are simply not naturally capable of somehow mastering it!

One does not exclude the other, but, on the contrary, harmoniously complements the other. A “humanitarian mindset” in the context of the impossibility of mastering the exact sciences is simply one huge nonsense and an attempt to justify the reluctance to master those skills that are obtained with more difficulty than others.

Why do you need mathematics in life and work?

Mathematics is useful in business. But maybe the profession that you are considering as your future vocation 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 like this. Perhaps you want to change your profession. Or you will get so tired of hired work that you decide to organize your own business (and this happens quite often). Organizing an independent enterprise always requires calculations, forecasting and analysis. You, as the head of a new business, will need to possess the appropriate skills; not everything can be delegated to hired employees; their work in any case needs supervision.

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’s not just a matter of knowing some special calculation methods, because it’s never too late to master this if necessary. The key is a certain organization of the mind. Business is a highly ordered system, the construction of which requires its creator to have certain intellectual skills, structured thinking, and the ability to generalize and deduce relationships. Studying the exact sciences is known to develop these skills.

Conclusion

Mathematics and other exact sciences are very important both for the development of humanity as a whole and for the intellectual improvement of a particular individual. Of course, balanced mental development of an individual implies mastering not only exact subjects, but also humanitarian disciplines. Reading quality literature, for example, is also necessary for you 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 do mathematics.” Otherwise, the effect of just reading books will be similar to a body without a skeleton or a building without a frame. It’s difficult for one without the other.

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

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

I believe that the idea of school education and teaching in the initial courses of universities meets this principle of universality (just the idea, I do not presume to discuss how this is implemented in practice). I would have an extremely negative attitude towards strengthening the specialization of primary and secondary education, believing that a growing individual should be given as much as possible from different areas, and when he receives this, let him choose what is closest to him!

Ecology of life. How to stop missing deadlines and procrastinating, learn to make important decisions and love yourself with the help of mathematics?

How to stop missing deadlines and procrastination, learn to make important decisions and love yourself with the help of mathematics? We learned the answer from the author of the recently published book “Think Like a Mathematician” and the popular Coursera course “Learning How to Learn,” Barbara Oakley, Ph.D., consulting engineer and brain stem cell researcher.

If you're good at math, it's much harder to fool you

I have been studying the peculiarities of human thinking for a long time. I'm currently working on a book, Mindshift: How Ordinary and Extraordinary People Have Transformed Their Lives Through Learning - And You Can Too. It focuses on amazing stories of people who have changed their lives and careers through new approaches to learning.

There are many ways to overcome your fear of science and science. Outstanding scientists and brilliant minds tend to learn effective learning techniques early because they begin training almost from infancy. In fact, these learning techniques can be mastered by anyone at any age. If I had not studied a foreign language before, I would not have thought that there were specially structured practical techniques.

When you go to the gym, you use machines to develop your muscles. You don't think you can get killer abs by sitting on the sidewalk every day. The same principle can be applied to mathematics. It helps you develop invisible thinking muscles that can help you in unexpected ways. For example, if I need to hire a store manager or develop an online course, I am more likely to give preference to a candidate with developed analytical thinking. The world is changing, and the ability to cope with technical and mathematical challenges is becoming increasingly important.

Knowledge of natural sciences warns people against “magical thinking”

Mathematics and other sciences can help you make important decisions that will affect your life; they will also help you cope with everyday difficulties. Knowledge of mathematics and science warns people against “magical thinking.” When it comes to salary, sometimes I feel like money will just appear out of thin air and I'll get everything I want without putting in any effort. But this doesn't happen. Money will also not magically appear in the state budget, although, of course, the state often makes us believe otherwise. A natural science background simply makes us smarter and allows us to observe things from a detached perspective. For example, we all know how important good ecology is, and we understand that we should fight to make the world clean and green. However, some green initiatives, such as e-cars, are actually bad for the environment. Simply put, people who have no knowledge of mathematics and science are much easier to fool because they do not know how to look at things with skepticism.

Mathematicians love to teach abstract mathematics, which seems detached from reality, but in fact helps to master skills that can be easily transferred to different professional fields. Studying mathematics in relation to one field, such as accounting, is ineffective because it limits the flexibility of your thinking and prevents you from applying new knowledge and skills in a different context. It's the same as refusing to learn a foreign language - then you artificially forever limit your thinking within the framework of one language. If you're afraid of equations and formulas and don't know how to apply your imagination to them, try thinking of them as poetry.

Equations are just a set of coded concepts; in them, as in poetry, there is a deep meaning. Einstein was able to describe the photon using imagination rather than mathematics.

It is known that he was not very strong in mathematics and often turned to other mathematicians for help to continue his research. But he had plenty of imagination: he imagined himself as a flying photon and thought about how another photon would perceive him. People's imaginations are much more developed than they think. If you don't think this is for you, then think about this: if you have the imagination to love and raise your child, then you will have the imagination to create a wonderful new world.

There are many books to help you understand mathematics. My favorites are Calculus Made Easy by Sylvanus Thompson and The World According to Wavelets: The Story of a Mathematical Technique in the Making by Barbara Burke. Hubbard and a three-volume edition of Richard Feynman's lectures on physics. All these works help to get acquainted with mathematics from different sides and explain how it relates to reality.

Your success has nothing to do with your level of genius

I decided to get an engineering degree only at 26 years old. This caused me a lot of hatred and caused me a lot of suffering in my first year; Only rare insights encouraged me. It took about a year and a half before I felt like I “could do this.” Before that, I studied Russian, received a scholarship from the service for non-military training of reserve officers and a bachelor's degree in Slavic languages and literature. I had a chance to become an expert in the signal corps, but I hated mathematics and was afraid of it.

If you too are afraid of math and science, you should know that your brain is constantly performing complex calculations, you just don't know it. Thanks to this, you can catch the ball and avoid road potholes in your car. We solve equations and make complex calculations unconsciously and have no idea that we already know the solution because we all have a knack for math and science. We think that mathematics is more complex than the humanities only because it is encoded in formulas and abstract concepts.

I believe there are thousands of “right” ways to educate children, so I don’t gravitate towards any particular school or system. We too often stress that children should approach learning with passion, when in fact learning itself should be something that makes them passionate. Education should cultivate creativity, curiosity and a desire for discovery in students. However, creativity must be supported by solid knowledge of a particular subject. If you don't have a large set of facts in your mind, you're unlikely to make a creative discovery. Although children attend the same school for many years, their achievements do not level out because people's achievements are highly dependent on their social environment and biological predisposition. But in reality, persistence means much more than intelligence. Many "average" people have gone much further than very gifted people.

Talented people also face many challenges: in childhood they are bullied by their classmates, they begin to suppress their abilities and look for problems where there really are none. Talented people are much more likely to fall into procrastination, because in their youth this approach was effective and, as adults, they simply cannot adapt. Students are constantly competing with their more gifted classmates and trying to catch up with them, as a result, they severely limit themselves in the time they can spend on mastering the material, and fall even further behind. You need to accept yourself and your characteristics. If you feel that you are at a dead end, it is better to ask competent people for advice. Before doing this, try to solve the problem yourself, then you will better accept the other person’s explanations. At university, I was angry with my teachers because I didn’t understand anything, although I only needed to take a few independent steps.

I'm sure stupid people exist! I know this for sure, because I myself have been stupid from time to time. Everyone is different: some students are introduced to useful study techniques and still choose not to use them. This doesn't mean they are stupid, but I feel sorry for them because they often deceive themselves about what they are really capable of. Nobel laureate Richard Feynman liked to talk about his IQ of 125 to prove that success is not just a matter of innate genius. He achieved success precisely through persistent study of physics and mathematics for many years.

Rebuilding your brain is not as difficult as it seems

We think in two different modes: focused and diffuse. There is a hypothesis that this is due to the fact that vertebrates had to solve two important tasks simultaneously: monitor the movement of enemies (dispersed mode) and search for food (focused mode). If each hemisphere is focused on a specific type of perception, the chances of survival increase.

In humans, the left hemisphere is associated with focused attention and specializes in logical thinking; the right is responsible for processing emotions, divided attention and social communication. It is impossible to gain a broad understanding of the world without the participation of the right hemisphere. Successful study of the arts and sciences requires alternating two types of thinking. All the insights known in the history of science, as if whispered by someone from above, are associated precisely with the inclusion of a scattered mode of thinking after a long period of concentrated work. The idea that some people are right-brain dominant and others are left-brain dominant is wrong. The brain is very complex. We deceive ourselves when we try to simplify its work. Michael Anderson's wonderful book After Phrenology explains very clearly why a modular approach to understanding brain function is problematic.

I can't believe that students spend nearly 16 years in college before getting a bachelor's degree and yet they don't have a single course on effective teaching. On the other hand, a course on effective teaching in a traditional educational system would look something like this: three weeks would be spent on the history of education, another three on various educational theories, and another three on a course of lectures on how young children learn. It may be only in the last one or two weeks that students will be able to gain some practical skills. Since most teachers are not familiar with neuroscience, they will not be able to teach you anything about such vital things as focused and distracted thinking modes or the pain centers of the brain that make us procrastinate. I think today's students are very lucky to have access to books like Think Like a Mathematician and courses like Learning How to Learn on Coursera. The information that is given there will be useful for any person who is learning something. It would be great if all these approaches were naturally integrated into school and university education. Fortunately, this is already starting to happen.

All insights, as if whispered by someone from above, are associated with the inclusion of a scattered mode of thinking after a long period of concentrated work

Changing university approaches to teaching is like moving a cemetery to another location. We cannot expect this from the dead themselves. I am confident that universities will only be able to change as a result of external pressure. This is why the disruption of mass online learning is so important. This also applies to my course “Learning How to Learn”, which partially duplicates the content of the book “Think Like a Mathematician”. This is the most popular course in the world, with over a million students signing up for it in the last year alone. And for good reason: it contains powerful, useful, and effective ideas that are scientifically proven. So now all changes depend on the people themselves.

Many students still do not know that taking notes in the margins is more effective than simply underlining in a textbook, and simply rereading cannot replace retrieving data from memory. Constantly re-reading notes or a textbook gives the illusion of competence, although if you close the book or notebook, you will realize that there is nothing left in your mind. Instead, test yourself regularly and mentally review the material you've learned.

It is important to clarify that children do not necessarily learn “wrong” in school. Another thing is that some teaching methods are more effective than others, and specialized courses help you become familiar with them. All people are different from each other, the main thing is to independently integrate these approaches into your own life. The first and most important step is to simply stop procrastinating to reduce your stress levels, improve your learning efficiency, and free up plenty of time for fun and relaxation. We procrastinate when we feel uncomfortable doing something. If you are afraid of mathematics, then the very thought of it is painful for you.

If you need to start doing math, the pain centers in your brain become active. It is important to clarify here that after you start exercising, the pain disappears. N

It is important to introduce changes gradually. If your main problem is procrastination, try the Pomodoro method: set a timer for 25 minutes and focus on your work. This will help you focus your attention for a short period of time. During this time, you cannot check social networks, talk on the phone or search for something on the Internet.

The secret is that 25 minutes is a short period of time, so you can console yourself with the fact that soon it will all be over and you can get some rest. It is useful to support this method with lists of key tasks for the day (5-10 items) and for the week (up to 20 items) in order to track your progress and not miss important things. Remember to “eat your frogs in the morning,” that is, do your most important and unpleasant work early in the day. Associated with learning mathematics and science is a concept called the “attitude effect.” It refers to moments when an initial idea or thought gets in the way of finding a better idea or solution.

Very often this initial impulse leads to the wrong result. When you struggle with a task for a long time, it is this barrier in your thinking that prevents you from finding the right solution. I myself regularly use the methods described in the book - for example, I constantly use the “Pomodoro principle”. Also, when I read non-fiction, I constantly look away and see what I can remember. I think these methods can also help in learning complex abstract concepts, such as philosophy. published

Back forward

Attention! Slide previews are for informational purposes only and may not represent all the features of the presentation. If you are interested in this work, please download the full version.

Participants: 7th grade students.

Goals:

educational: developing a sustainable interest in mathematics;
educational: formation of such personality qualities as cognitive activity.
developing: development of students’ creative abilities (imagination, observation, memory), monologue speech, ability to identify cause-and-effect relationships, development of logical thinking.

Tasks:

study bibliographic sources on this topic;
introduce the history of the emergence and development of mathematics
identify areas of application of mathematical knowledge.

Products: computer presentation.

Necessary equipment: projector, screen, computer.

Progress of the event

Teacher's opening remarks:

1 slide Topic: “Mathematics in human life”

2 slide Fundamental question: Does a person need mathematics?

3 slide Problematic issues:

How and when did mathematics originate?
What professions require mathematics?
What mathematicians do you know?
Do modern people need knowledge of mathematics?

Student performance:

To drive ships
To fly into the sky,
There's a lot to know
And at the same time, and at the same time,
Will you notice?
Very important science
Mathematics!

Why ships
Don't run aground
And they follow the course
Through fog and snowstorm?
Because because,
Will you notice?
Helps captains
Mathematics!

So that as a doctor, a sailor
Or become a pilot.
First of all we must
Know mathematics.
And there are no professions in the world
Will you notice?
Wherever you need it
Mathematics!

4 slide How and when did mathematics originate?

When we are talking about something very simple and understandable, we often say: “The matter is as clear as two and two are four!”

But before they figured out that two and two equal four, people had to study for many, many thousands of years.

Of course, this teaching did not take place at a desk. Man gradually learned to live: to build houses, find his way on long trips, cultivate the land.

Because even in the most distant times, when people lived in caves and dressed in animal skins, they could not do without counting and measuring.

Many rules from school textbooks on arithmetic and geometry were known to the ancient Greeks more than two thousand years ago.

Other ancient peoples - the Egyptians, Babylonians, Chinese, peoples of India - in the third millennium before our era had information on geometry and arithmetic, which some fifth or sixth grade students lack.

With each passing decade, mathematics became more and more necessary for people.

5 slide Pythagoras

The great scientist Pythagoras was born around 570 BC. on the island of Samos. Pythagoras's father was Mnesarchus, a gem cutter.

Pythagorean theorem- one of the fundamental theorems of Euclidean geometry, establishing the relationship between the sides of a right triangle. It is believed that it was proven by the Greek mathematician Pythagoras, after whom it was named.

The theorem goes like this: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs .

6 slide

At the end of the nineteenth century, various speculations were made about the existence of human-like inhabitants of Mars. As a joke, although not entirely without reason, it was decided to send a signal to the inhabitants of Mars in the form of the Pythagorean theorem. It is not known how to do this; but it is obvious to everyone that the mathematical fact expressed by the Pythagorean theorem takes place everywhere and therefore inhabitants of another world similar to us must understand such a signal.

7 slide

Sofia Kovalevskaya

A girl from a noble family loved mathematics and even hid a complex problem book under her pillow at night (her parents did not approve of her hobbies).

At that time, it was not customary for women to go to college, but she went against the wishes of her parents to Germany, to the university, and came to a famous professor. He didn’t want to take her and, in order to get rid of it, he gave several tasks that they had composed themselves, saying that if she decided, he would take her to him.

Even professors could not solve these problems. The girl decided in twenty minutes.

Sofya Kovalevskaya graduated from university and became a world-famous mathematician

8 slide

What can mathematics do?

It helps the astronomer determine the paths of distant stars.
An engineer uses mathematics to calculate a jet plane, a ship, or a new power plant.
For a physicist, mathematics reveals the laws of the atomic nucleus, and for a sailor it shows the path of a ship in the ocean.
In short, mathematics can do everything or almost everything where something needs to be calculated.

But everything begins with mathematics.

The child has just been born, and the first numbers in his life are already heard: height, weight.
The baby is growing up, cannot pronounce the word “mathematics”, but is already doing it, solving small problems of counting toys and cubes.
And parents don’t forget about mathematics and problems. When preparing food for a child, weighing him, they have to use mathematics.
After all, you need to solve basic problems: how much food needs to be prepared for the baby, taking into account his weight.

Slide 9

1 example

You stand at the checkout and pay for the goods. You bought food for 432 rubles, and you have 500 rubles in money in 100 ruble bills. And they give you 40 rubles in change, although they should give you 68 rubles. This means you were shortchanged by 28 rubles!!!

10 slide

2 example

I need to be at the dacha at 15.40. I spend 1.40 hours on the road. Today I need to go to the store. When should I leave? How much time can I spend in the store?

11 slide

12 slide

Solve the problem.

How can you get 100 with one action and five units?

Slide 13

111 - 11 = 100

Slide 14

Where can you do without mathematics?

Here are the builders, building a house. We need to calculate how much cement, how many bricks. Height, width. Make a project.
The dressmaker is about to sew a dress. Measures a person and makes a pattern. Does she need math? Maybe…
The store counts the goods received and the revenue.
The bank counts money, dealing with huge amounts and interest.
Even in music, in poetry, you have to count - rhythm, meter, eighth notes, quarter notes, iambs, trochees.
What can we say about such complex sciences as space (rockets, satellites), computer technology, television, radio! Of course, none of this would have been invented without calculations, without mathematics.
That is, mathematics is our whole life?

15 slide

The task of applying the sign of equality of triangles to measure the distance between two inaccessible objects .

Condition: The road crew needs to make a tunnel, but the distance to cut through the mountain is unknown. What should the team do to find out this distance if the distance from A to C and from B to C is known (Fig. 1)?

Picture 1

Solution: The crew is unable to build a road around the mountain. Therefore, they undertook a little trick: at the entrance to the not yet cut tunnel they placed a person - (A) and at the exit point too - (B), on the side of the mountain they placed a third person - (C), a triangle ABC was formed. Person A draws a straight line through point C, and person B also lays a straight line through point C. Having drawn straight lines and placed two more people on them at a certain distance - (D,E) So CD =AC, A CB = EU.Corner ACB =ECD by the property of vertical angles, therefore triangle DEC is equal to triangle ABC. Now the team connects points D and E with a segment on the ground. The workers just have to measure the distance from E to D, which will be equal to the required distance from A to B.

16 slide

Do modern people need knowledge of mathematics?

The world and life itself are changing rapidly. It includes new technologies. Only mathematics and problem solving in the traditional sense remain true. Mathematical laws have been tested and systematized, so a person can rely on it at important moments and solve any problem. The math won't let you down.

But every year we have more and more wonderful machines: complex machines, various automatic machines. In order to work well on such machines, you need a lot of knowledge. Nowadays mathematics is needed not only by a scientist or an engineer, but also by a craftsman and a factory worker.

However, just a few decades ago there were many problems that were practically impossible to solve, although mathematicians knew how to solve them. It happened that dozens of people worked for several years to solve one single problem. The calculations were slow. The main “tools” of a mathematician were the same as in the days of the ancient Greeks - his own head and a blank sheet of paper with a pencil.

And now mathematics has a new powerful assistant, which is called an electronic computer. Existing high-speed computers work hundreds of thousands of times faster than humans.

Never before has mathematics been so comprehensive and such a necessary science for people as it is today. It is difficult to talk about what mathematics will be like tomorrow. It is now developing so rapidly, new discoveries are being made in it so often, that it is perhaps useless to guess what will happen. One thing is certain: tomorrow mathematics will become even more powerful, more important and more necessary for people than it is today.

There are often conversations in society about why a person needs to study mathematics. Indeed, many people, having received an education, often work in a specialty that is not related to complex calculations. At first glance, mathematics has nothing to do with their lives. However, in the vast majority of countries in the world, for some reason this science is invariably included in the curriculum of schools and universities. Why is this discipline given such great importance?

We study mathematics - we study

This science is based on the natural laws of the surrounding reality. It excludes free interpretations and lengthy reasoning. Its core is order and clear logic. In fact, all processes operating in nature are built on the same principles. Mathematics reflects them like a mirror, while at the same time being a tool for their knowledge.

There are cases when great discoveries literally came off a sheet of paper. Thanks to mathematical calculations, even before the active exploration of space by man, scientists were able to create a fairly accurate picture and describe the processes that operate in it. And the main weapon in their hands became ordinary mathematical formulas.

But what is mathematics for the common man?

Of course, the importance of the science of numbers in the life of society is difficult to overestimate. Without it, technical progress and the development of civilization are impossible. But why does an ordinary person need this item?
The great Russian scientist and thinker M.V. Lomonosov emphasized the importance of mathematics for the formation of personality and called for studying it because “... it puts the mind in order.” You can't say it more precisely! Indeed, this science has a serious impact on the development of intelligence.
It improves analytical, critical, deductive, predictive abilities. Trains the brain to store and process large amounts of information. Its influence on a person’s intellectual potential is expressed in the development of the following personal qualities and skills:

Ability to analyze complex life situations, make informed decisions in the face of difficult choices;
the ability to generalize and the skill of considering a particular event as an integral element of a general order;
ability to find patterns;
the ability to reason and think logically, accurately formulate thoughts and draw logical conclusions.

You can improve your math skills at any age. However, such arithmetic exercises are of particular importance for children. Perhaps there is no other similar subject that has such a strong influence on the development of a child’s intellectual abilities! Working with numbers will help you start thinking rationally from a young age and develop mental acuity.

Organization and orderliness

The qualities developed by mathematical methods form the framework of human thinking. This leads to the organization of all thoughts into a single system of interconnected concepts about the world around us. Representing the embodiment of natural order, mathematics also eliminates chaos in the human head.

It is no longer possible to mislead such a person. She has no confusion in reasoning and uncertainty in behavior. She is not subject to the influence of various kinds of schemers and will not allow herself to be drawn into a dubious operation or financial pyramid. The logical organization of the mind allows a person to build his own life, career and material well-being.
Do humanists need mathematics?

Certainly! It will certainly help on the path to mastering the humanities. Because there, too, the skills of systems thinking, logic, and the ability to formulate large-scale theories will be required.

There are many excellent lawyers who, in addition to specialized education, also received physics and mathematics. This taught them to come up with non-trivial solutions, build complex lines of defense in court, and carry out systematic work with the legislative framework.

The benefits of math skills in business

Today, many people decide to open their own business. Someone is not satisfied with his current job, and he seeks to change it for something more interesting. Someone immediately decides to find an independent source of income, counting on gaining personal independence and receiving large incomes.

In any case, organizing an individual enterprise will require skills in analysis, forecasting and ongoing calculations. A businessman must master them, since not all powers can be delegated to hired personnel. And even if you assemble a large staff, you will still need the ability to structurally organize their work.

It is impossible to do without mathematical methods of analysis, modeling and forecasting. Without them, it is impossible to achieve success, even when running a small business, not to mention creating a large, reputable company. And the point here is not so much in knowledge of special calculation methods (you can always master them if you wish), but in a certain organization of thinking.

Own business is a strictly ordered system, the construction of which presupposes that its creator has structured thinking skills, the ability to generalize and find relationships. Studying the exact sciences develops all these skills. Even statistics show that the greatest success, as a rule, is achieved by business graduates of mathematical and technical universities.

Mathematical thinking

Among psychologists, the concept of a mathematical mindset is often used as one of the ways to organize human mental activity. Yes, there are people for whom comprehension of arithmetic laws is given with incredible ease. However, this does not mean that the lot of everyone else is to realize their capabilities exclusively in the humanitarian sphere.

Don’t think that you are not naturally gifted with mastering mathematical formulas and solving calculation problems. The human mind is universal. It contains the potential for any intellectual activity. There is no such thing as a complete lack of ability for mathematics. It just takes a little more effort to manifest it than it takes some mathematical genius.
Of course, it cannot be denied that every person has certain innate inclinations in mastering the sciences. In addition, professional specialization requires a large amount of knowledge in some narrow area. For example, it will be difficult to combine a good chemist, physicist, lawyer, historian and literary critic in one person. This is available only to a few.

However, absolutely anyone can master the basic mathematical skills! And this will not interfere in life. On the contrary, new abilities will give a strong impetus to personal development and will serve as the key to achieving success in any area of activity.

Achmizova Samira

If you look around carefully, the role of mathematics in human life becomes obvious. Computers, modern phones and other equipment accompany us every day, and their creation is impossible without the use of the laws and calculations of great science. However, the role of mathematics in the lives of people and society is not limited to such applications. Otherwise, for example, many artists could say with a clear conscience that the time devoted to solving problems and proving theorems in school was wasted. However, this is not the case. Let's try to figure out why mathematics is needed. the role of mathematics in human life

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on the topic: “The role of mathematics in human life.

What is mathematics for?

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6th grade student

MBOU secondary school No. 13

Achmizova S.A.

2018

The role of mathematics in human life.

What is mathematics for?

Base

First, it’s worth understanding what mathematics actually is. Translated from ancient Greek, its very name means “science”, “study”. Mathematics is based on the operations of counting, measuring and describing the shapes of objects. It is the basis on which knowledge about structure, order and relationships rests. They are the essence of science. The properties of real objects are idealized in it and written in a formal language. This is how they are converted into mathematical objects. Some idealized properties become axioms (statements that do not require proof). From these other true properties are then derived. This is how a mathematical model of a really existing object is formed.

Two sections

Mathematics can be divided into two complementary parts. Theoretical science deals with deep analysis of intra-mathematical structures. Applied science provides its models to other disciplines. Physics, chemistry and astronomy, engineering systems, forecasting and logic use the mathematical apparatus constantly. With its help, discoveries are made, patterns are discovered, and events are predicted. In this sense, the importance of mathematics in human life cannot be overestimated.

Basis of professional activity

Without knowledge of basic mathematical laws and the ability to use them, in the modern world it becomes very difficult to learn almost any profession. Not only financiers and accountants deal with numbers and operations with them. Without such knowledge, an astronomer will not be able to determine the distance to the star and the best time to observe it, and a molecular biologist will not be able to understand how to deal with gene mutation. An engineer will not design a working alarm or video surveillance system, and a programmer will not find an approach to the operating system. Many of these and other professions simply do not exist without mathematics. the importance of mathematics in human life

Humanities

However, the role of mathematics in the life of a person, for example, who has devoted himself to painting or literature, is not so obvious. And yet, traces of the queen of sciences are also present in the humanities. It would seem that poetry is pure romance and inspiration; there is no place for analysis and calculation in it. However, it is enough to remember the poetic metres (iambs, trochees, amphibrachs) to understand that mathematics had a hand in this too. Rhythm, verbal or musical, is also described and calculated using the knowledge of this science. mathematics in our lives For a writer or psychologist, such concepts as reliability of information, an isolated case, generalization, and so on are often important.

All of them are either directly mathematical, or are built on the basis of laws developed by the queen of sciences, and exist thanks to her and according to her rules. Psychology was born at the intersection of the humanities and natural sciences. All of its directions, even those that work exclusively with images, rely on observation, data analysis, their generalization and verification. Modeling, forecasting, and statistical methods are used here.

From school

Mathematics is present in our lives not only in the process of mastering a profession and implementing the acquired knowledge. One way or another, we use the queen of sciences at almost every moment of time. That is why mathematics begins to be taught quite early. By solving simple and complex problems, a child does not just learn to add, subtract and multiply. He slowly, from the basics, comprehends the structure of the modern world. And we are not talking about technical progress or the ability to check change in a store. Mathematics shapes certain features of thinking and influences our attitude towards the world. what is mathematics for?

The simplest, the most difficult, the most important

Probably everyone will remember at least one evening while doing homework, when they wanted to desperately howl: “I don’t understand what mathematics is for!”, throw aside the hated complex and tedious problems and run into the yard with friends. At school and even later, at college, the assurances of parents and teachers that “it will come in handy later” seem like annoying nonsense. However, it turns out they are right. mathematics in the life of society It is mathematics, and then physics, that teaches us to find cause-and-effect relationships, lays down the habit of looking for the notorious “where the legs grow from.”

Attention, concentration, willpower - they also train in the process of solving those very hated problems. If we go further, the ability to draw consequences from facts, predict future events, as well as the habit of doing this are also laid during the study of mathematical theories. Modeling, abstraction, deduction and induction - all these are the methods of the queen of sciences and at the same time ways of the brain working with information.

And again psychology

Often it is mathematics that gives a child the revelation that adults are not omnipotent and do not know everything. This happens when mom or dad, when asked to help solve a problem, just shrug their shoulders and declare their inability to do it. And the child is forced to look for the answer himself, make mistakes and look again. It also happens that parents simply refuse to help. “You have to do it yourself,” they say. And they do it right. After many hours of attempts, the child will receive not just completed homework, but the ability to independently find solutions, detect and correct errors. And this also lies the role of mathematics in human life. mathematics in everyday life Of course, independence, the ability to make decisions, be responsible for them, and the absence of fear of mistakes are developed not only in algebra and geometry lessons. But these disciplines play a significant role in the process. Mathematics fosters such qualities as determination and activity. True, a lot depends on the teacher. Incorrect presentation of material, excessive rigor and pressure can, on the contrary, instill fear of difficulties and mistakes (first in the classroom, and then in life), reluctance to express one’s opinion, and passivity.

Mathematics in everyday life

After graduating from university or college, adults do not stop solving mathematical problems every day. How to catch the train? Can a kilogram of meat cook dinner for ten guests? How many calories are in the dish? How long will one light bulb last? These and many other questions are directly related to the Queen of Sciences and cannot be resolved without her. It turns out that mathematics is invisibly present in our lives almost constantly. And most often we don’t even notice it. The role of mathematics in the life of people and society Mathematics in the life of society and the individual affects a huge number of areas.

Some professions are unthinkable without it, many appeared only thanks to the development of its individual areas. Modern technical progress is closely related to the complication and development of the mathematical apparatus. Computers and telephones, airplanes and spacecraft would never have appeared if people had not known the queen of sciences. However, the role of mathematics in human life does not end there. Science helps a child master the world, teaches him to interact with it more effectively, and shapes his thinking and individual character traits. However, mathematics alone would not cope with such tasks. As mentioned above, the presentation of the material and the personality traits of the one who introduces the child to the world play a huge role.

Mathematics in human life

Have you ever heard the following expression: mathematics is a country without borders? This phrase about mathematics has very good reasons. Mathematics occupies a special place in human life. We have become so close to it that we simply don’t notice it.

But our life begins with mathematics. The child has just been born, and the first numbers in his life are already heard: height, weight. The baby is growing up, cannot pronounce the word “mathematics”, but is already doing it, solving small problems of counting toys and cubes. And parents don’t forget about tasks. When preparing food for a child, weighing him, they have to use mathematics. After all, you need to solve a basic problem: how much food you need to prepare for your baby, taking into account his weight.

There are a lot of mathematical problems at school and their complexity increases every year. They don't just teach the child certain actions. Mathematical problems develop thinking, logic, and a set of skills: the ability to group objects, reveal patterns, determine connections between phenomena, and make decisions. Doing mathematics and solving mathematical problems develops a person, makes him more purposeful, active, and independent.

And after school, mathematics will be very useful. While studying at university, at work and at home, you need to constantly solve problems related to mathematics. What is the probability of passing the exam? How much money do you need to earn to buy an apartment? What is the surface area of the walls of your house, and how much brick do you need to buy to insulate your house? How to correctly calculate whether a girl or a boy will be born? And this is where mathematics comes to the rescue. It follows a person everywhere, helps him solve practical problems, and makes his life much more convenient.

What is the purpose of mathematics education?

Preparation for university.
Preparation for a future profession.
Intellectual development.
Formation of worldview.
Orientation in the surrounding world.
Exercise of the brain.

Here are some motivations regarding the importance of mathematics education for the individual.

Mathematics is encountered and used in everyday lifeTherefore, every person needs certain math skills. In life we have to count, for example, money. We constantly use, often without noticing it, knowledge about quantities characterizing lengths, areas, volumes, time intervals, speeds and much more. All this came to us in arithmetic and geometry lessons and was useful for orientation in the world around us.

Mathematical knowledge and skillsare necessary in almost all professions, primarily, of course, in those related to the natural sciences, technology and economics. But there is no doubt that a doctor, linguist, historian needs to use mathematical knowledge and mathematical thinking, and it is difficult to end this list, mathematical education is so important for professional activity in our time. Hence,mathematics and mathematical education are needed to prepare for a future profession. This requires knowledge of algebra, mathematical analysis, probability theory and statistics.

Philosophical comprehension of the world, its general laws and basic scientific concepts is also not possible without mathematics. And that's whymathematics is necessary for the formation of a worldview.

Mathematics should contribute to the development of ethical principles of human society. The study of it is designed to cultivate in a person intellectual honesty, objectivity, the desire to comprehend the truth,it also cultivates the ability for aesthetic perception of the world, the beauty of intellectual achievements.

“Mathematics must be taught later because it puts the mind in order,” M.V. Lomonosov. Not only arms, legs, body require training, but alsothe human brain needs exercise. Solving problems, puzzles, and mathematical puzzles develops logical thinking and reaction speed. It is not without reason that they say that mathematics is mental gymnastics.

Why is mathematics needed?

Like any normal child, even in my school years, I was worried about the question: Why is mathematics needed? Then, I quickly found the answer to it, learning to correctly count change, count how much I had left to save up to the necessary beads and bracelets, at what angle to throw a stone across the water to make a “frog”.

Now, as a university student, I will try once again to ask myself the question about the meaning of mathematics in our lives and understand it more deeply.

To be honest, I thought that mathematics did not play such a great role in people’s lives, but when I started writing an essay and thinking about this topic, it turned out that I was wrong. I had no idea about such a great significance and importance of mathematics in people’s lives.

It’s hard to imagine, but once upon a time people couldn’t count at all!

Evidence strongly suggests that counting arose earlier than the names of numbers. The man used the same type of objects around him: fingers, pebbles, knots, lines drawn on the wall, notches on sticks and trees, piles of stones, etc. When language emerges, words are associated only with those concepts that already exist, that is, they are recognized. The words "one", "two" and possibly "three" appear regardless of the count. Notation (numbering) is a set of techniques for naming and designating numbers. When counting becomes common and commonplace, verbal designations also arise for the most frequently occurring (i.e., small) groups of standard objects.

With the increasing complexity of people's economic activities, it became necessary to count on a wider scale, which required the creation of more complex counting devices. These are various abacus (abacus, soroban, suan-pan, etc.) and later in the Middle Ages mechanical abacus appeared.

Largely thanks to mathematics, civilization has become what it is now: developed, high-tech, educated and wealthy. Mathematical science has enabled the development of civilization in all its aspects.

The meaning of mathematics

The name "mathematics" comes from the Greek word "mathein" - to learn, to know. The ancient Greeks generally believed that the concepts of “mathematics” (mathematike) and “science”, “cognition” (mathema) are synonymous. They were characterized by such an understanding of the universalism of this branch of knowledge, which two thousand years later was expressed by Rene Descartes, who wrote: “The field of mathematics includes sciences in which either order or measure are considered, and it is not at all important whether these are numbers, figures, stars, sounds or something else...; thus, there must be some kind of general science that explains everything related to order and measure, without entering into the study of any particular subjects..."

Another explanation for the origin of the word "mathematics" is associated with the Greek word "mathema" (mathema), which means harvest, harvest. Marking out plots of land (geometry), determining the timing of field work (based on astronomical observations and calculations), preparing the required amount of seed and calculating the harvest required serious mathematical knowledge.

The role of mathematics in science

The role of mathematics in modern science is constantly increasing. This is due to the fact that, firstly, without a mathematical description of a number of phenomena of reality, it is difficult to hope for a deeper understanding and mastery of them, and, secondly, the development of physics, linguistics, technical and some other sciences presupposes the widespread use of mathematical apparatus. Moreover, without the development and use of the latter, it would have been, for example, impossible either to explore space or to create electronic computers that have found application in a wide variety of areas of human activity.

Thanks to mathematical knowledge and skills, we solve not only arithmetic problems. This science allows you to develop mental flexibility, which is necessary to make an objective solution to any problem. This is not only a mathematical problem, but also various life situations that require consideration “from different angles.” To understand and know the essence of a problem, you need to consider it from all sides, which is possible thanks to the imagination. math science language

Mathematics is an exact science that does not tolerate mistakes. It is thanks to this feature that mathematical laws form the basis of all inventions, from primitive ones in the form of levers and pendulums to supercomputers.

Mathematical language

The laws and regularities derived in mathematics are objective and applicable in all other areas of human knowledge. Physics, chemistry, geography, geology and many other areas of scientific knowledge are based on its laws, in which it is simply impossible to do without mathematics. Now we are accustomed to the fact that everything instantly becomes obsolete; for a computer, a year is already a death sentence. Just imagine that everything that was laid down in mathematics two thousand years ago is still relevant, that all those mathematical laws and theorems that were formulated by famous mathematicians of those times are still true. Almost nothing has changed since then.

Mathematics is a country without borders

More than once I have heard the phrase that mathematics is a country without borders. Despite its banality, the phrase about mathematics has very good reasons. Mathematics occupies a special place in human life. We have become so integrated with it that we simply don’t notice it.

But everything begins with mathematics. The child has just been born, and the first numbers in his life are already heard: height, weight.

The baby is growing up, cannot pronounce the word “mathematics”, but is already doing it, solving small problems of counting toys and cubes. And parents don’t forget about mathematics and problems. When preparing food for a child, weighing him, they have to use mathematics. After all, you need to solve basic problems: how much food needs to be prepared for the baby, taking into account his weight.

Builders make the layout of apartments, the optimal layout of apartments, the length and width of the corridor, the sizes of rooms help to find simple functions. You have the area, the main parameters of the house (length and width), the approximate size of the corridor, on the basis of this a system of elementary functions is compiled, in which only the parameters of the rooms that interest you remain unknown. Then this system is reduced to one equation, differentiated, examined for monotonicity, and its extremum points are found. It is the extremum points that are optimal, the theme that is most profitable to use. The values of the unknowns obtained at the extremum points are used by builders.

At the school of mathematical problemsMathematics in antiquity

The ancient Egyptians would never have built their Great Pyramids without the simple laws of mathematics. It seems that it could be easier than drawing a straight line?! But to make the side of the pyramid, you need a straight line several kilometers long! The Egyptians managed to figure out how to solve the problem. Many rules from school textbooks on arithmetic and geometry were known to the ancient Greeks more than two thousand years ago. Other ancient peoples - the Egyptians, Babylonians, Chinese, peoples of India - in the third millennium before our era had information on geometry and arithmetic, which some fifth or sixth grade students lack. After all, wherever you need to count, measure, compare something, you cannot do without mathematics. And the further it went, the more and more accurately it was necessary to count. With each passing decade, mathematics became more and more necessary for people. Now not only mathematicians themselves have to deal with calculations and calculations: engineers, sailors, and builders were faced with calculations at every step.

Who else does math help?

Mathematics also helps astronomers in determining the paths of distant stars. Engineers in the calculation of jet aircraft and ships. Physics reveals the laws of the atomic nucleus. The sailor is shown the path of the ship in the ocean.

Nowadays, more and more computers, complex machine tools, and various automatic machines are appearing, so mathematics is needed not only by engineers and physicists, but also by ordinary craftsmen and factory workers.

And now mathematics has a new powerful assistant, which is called an electronic computer.

With the invention of electronic computers, a new era began in mathematics and many other sciences.

We need to add a thousand large numbers. If you add up the numbers on paper in a column, it will probably take about four hours. An experienced accountant can add up a thousand numbers in about an hour. And an electronic computer will need for this work... a split second. In addition, it will perform the calculation several times to check. Existing high-speed computers work hundreds of thousands of times faster than humans.

Predicting tomorrow's weather required thousands of arithmetic operations. With manual calculation, two specialists would spend five years on these calculations, and the machine would complete the job in an hour.

For example, at many large airports, a computer instead of a human controller controls the takeoff and landing of aircraft. The machine turns out to be a much better dispatcher than a person: it “thinks” faster, never worries, never gets tired, and almost never makes mistakes. It turns out that “with the help” of an electronic computer, mathematics can control airplanes!

Computers control trains, subways, artificial earth satellites, factories, and even translate books from one language to another. Each such machine works according to the laws of mathematics.

Famous sayings about mathematics

*No wonder the brilliant scientist Carl Friedrich Gauss said that mathematics is the queen of sciences!

* “The only reason to study mathematics is that it puts the mind in order” - these are the words of our famous and brilliant M. Lomonosov.

* “Mathematics is mental gymnastics,” said the great commander Suvorov.

* “Science reaches perfection only when it begins to use mathematics,” said the world-famous politician and philosopher Marx.

*The Great Book of Nature is written in mathematical symbols - said G. Galileo.

*“A person who does not know mathematics is not capable of any other sciences,” said R. Bacon