Pacheva Alina

Project Manager:

Filkova Larisa Nikolaevna

Institution:

MKOU "Secondary School No. 27" Nalchik

In this research work in mathematics on the topic "Mathematics in ordinary life" the author studies the branches of human activity and professions where mathematics occurs, proves its necessity, and also finds out whether a person needs mathematics in ordinary, Everyday life?

In the presented research project in mathematics on the topic "Mathematics in ordinary everyday life" a study of the statements of great people about mathematics is carried out, the need for mathematics is proved not only in certain professions, but also in everyday (ordinary) life.

In the research work on mathematics "Mathematics in everyday life", the student plans to acquaint schoolchildren with the results of her research in order to develop interest in this subject, expand knowledge of mathematics and horizons.

Introduction
1. Mathematics in everyday life.
2. Mathematics in professions.
3. Why is mathematics needed in different areas of life?
3.1. Why is math needed?
3.2. Why does a child need math?
3.3. Why do humanities need mathematics?
4. Sayings of great people about mathematics.
Conclusion

Introduction

One day I had a question What is mathematics for?, Why do we learn various equations and theorems? We use mathematics only in the store when buying products. Why do we study mathematics? kindergarten? » And I tried to find out the importance of this subject.

I think my subject research work in Mathematics "Mathematics in everyday life" is relevant .

The purpose of the research work: study where mathematics occurs in life and prove its necessity. Find out if a person needs mathematics in everyday life?

Tasks:

1. To study the types of activities (professions) where a person cannot do without mathematics;
2. Answer the questions: Why is math important in everyday life? and what can mathematics give each individual?;
3. Study the sayings of great people about mathematics.

Hypothesis: mathematics in our life is necessary not only in certain professions, but also in everyday (ordinary) life.

Mathematics in everyday life and work

Mathematics- a set of sciences studying quantities, quantitative relations, as well as spatial forms.

Many famous mathematicians say that the main thing in mathematics is to teach a person to think, sometimes putting before him very difficult tasks. « Mathematics develops logical thinking, the ability to independently solve problems, the ability to quickly grasp the essence and find the most suitable and simple approach to a life task.' adults tell us. Mathematics is closely related to our daily life.

Mathematics is found in our life at almost every step and it is not so gray and boring, but colorful and cheerful...

Thanks to mathematics, we solve many problems in everyday life. Few thought that mathematics surrounds us from the first days of life. Any child, even who did not study arithmetic, came across numbers. He will find out his weight, height in the clinic, he also knows his age. And more than once a day he will face various tasks of counting toys in the room or sweets to treat his friends.

Mathematics and daily routine. For example, our daily routine is a routine, nothing more than determining the time and planning it throughout the day with the help of simple mathematical calculations.

Lessons at school is also the distribution of time between the study different items and rest during breaks. After school, we need to have time to have lunch, go to extra classes, do homework, have dinner, rest and go to bed in order to have a good sleep and start a new day with renewed vigor and in a good mood. And this is how we keep track of time by the clock all day long and learn how to distribute it correctly so as not to be late and not to run earlier than necessary.

At school, we study mathematics from the first grade until graduation, then we are taught mathematics at the university. Every year the course expands to become more in-depth, more and more subjects are related to mathematics.

AT high school we have algebra and geometry in place of arithmetic. Our horizons are expanding. We can understand, see things that previously seemed unclear to us. Mathematical sciences develop our thinking, teach us to think.

With age we solve more and more problems: How many products do you need to buy to last for a week? How much do you need to earn in order to save up for a summer cottage and travel abroad? How much paint do you need to buy to paint the walls in the bedroom?

Without knowledge of mathematics modern life would be impossible. We would not have good houses, because builders must be able to measure, count and construct. Our clothes would be very rough, as they need to be well tailored, and for this, everything must be accurately measured. There would be none railways, no ships, no planes, no big industry.

There would be no radio, television, cinema, telephone and thousands of other things that are part of our civilization. The use of mathematics, measurement " how much?», « how long? are a vital part of the world we live in.

Mathematics has given rise to computing calculating machines. Computer Engineering has gone from simple accounts, arithmometers, slide rulers to microcalculators and computers. Now computers are used in all industries National economy: in statistics, trade, automated management of plants and factories. Machines not only count, they can translate from one language to another, they can compose music, play chess.

Home repairs. If we are going to make repairs at home, then we definitely cannot do without mathematics. We need to do a lot of calculations. The accuracy of which will determine whether we will have even walls and ceilings, as well as whether we have enough wallpaper to paste over the room and tiles to put on the floor in the bathroom.

Thus , I can say that we need mathematics everywhere, and there is no such area of ​​​​life where we could do without it.

Mathematics in professions

There is not a single profession in the world where mathematics is not found. And the opinion of the students that mathematics will not be useful to us is wrong. In any profession, a person needs mathematics. Even a person whose work is not related to mathematics needs it.

After all, you need to know mathematics so that you are not cheated by giving you a salary or pension. Mathematics also teaches to solve any problem with several solutions. Thanks to this, a person develops his extraordinary thinking.

You can bring a lot good examples professions where mathematics is needed:

• Accountant
• Engineer
• Seller, programmer and many others….

Accountant.
In the profession of an accountant, mathematics is simply necessary. An accountant calculates salaries, benefits, vacation pay, taxes, insurance premiums, etc.

Salesman.
In the profession of a seller, mathematics is needed in order to count the money, the products and goods received, the number of remaining products and goods, etc.

Despite the fact that your future profession does not imply a connection with mathematical formulas and calculations, no one knows what you will do in the future. For example, go to become an entrepreneur and start your own business.

Such a change of work will require you to master new skills in organizing and running a business, including accounting, and without mathematical methods of forecasting, modeling, analysis and calculations, there is no way to achieve success.

Why is mathematics needed in different areas of life?

Why is math needed?

What does it give a person, what abilities and skills does it develop?

First of all, this fundamental science develops our mental capacity- analysis, deduction, the ability to predict. Mathematical knowledge improves abstract thinking, increases its speed, teaches to abstract, concentrate and trains memory.

If we specify what mathematics gives us, then the result of acquaintance with it can be represented by the following list of skills:

• communication;
• analysis difficult situations making optimal decisions, regardless of the complexity of the situation;
• search and finding patterns;
• development of logic, reasoning, generalization, competent formulation of thoughts and logical conclusions;
• speed of decision making;
• planning and keeping in mind a complex step-by-step sequence;
• logical construction of complex operations and their storage in memory.

The listed skills are acquired not only as a result of solving problems of various sections of mathematics (algebra, geometry, trigonometry, probability theory, statistics, etc.), but also in the process of using such mathematical and logical methods as puzzles, exact sciences or Mind games, which load your brains and "force" to look for non-standard solutions and analyze.

Why does a child need math?

Mathematics is essential for the development of children. In addition to developing the child's mind, it lays the foundation rational thinking and intellectual development even at the stage of schooling.

Mathematics, forming logic, trains our mind, which allows us to compare various concepts, sensibly analyze them and comprehend. A person with "porridge in the head" is more prone to delusions, both in thoughts and in reasoning. In other words, knowledge of mathematics will not allow you to be deceived, as millions of people who entrusted their deposits to financial pyramids were deceived.

Mathematics is not just formulas and calculations, it is logic and order that follow from their rules and functions! Mathematical knowledge allows a person to reason correctly, form his thoughts, keep complex sequences in his head and build relationships between them.

Why do humanities need mathematics?

Many humanists believe that they do not need mathematics, forgetting that mathematical thinking will help in any profession that is not related to the exact sciences. You don't need to go far, remember the lawyers: they build their defense in court like chess players, coming up with cunning and extraordinary solutions, using the legal framework and a logical order of actions.

It makes no sense to specifically study an in-depth course in mathematics. To obtain the necessary basic knowledge, school and primary university education is sufficient, in which general education subjects are mandatory for everyone, both for techies and for the humanities. The study of multidirectional subjects harmoniously complements human knowledge, which will be useful not only in future profession but also in everyday life.

Sayings of great people about mathematics

• Mathematics is the language in which the book of nature is written. (G. Galileo)
• Mathematics is the queen of sciences, arithmetic is the queen of mathematics. (C.F. Gauss)
• Anyone who has been involved in mathematics since childhood develops attention, trains his brain, his will, cultivates perseverance and perseverance in achieving the goal. (A. Markushevich)
• "Numbers govern the world," said the Pythagoreans. But numbers make it possible for a person to control the world, and the whole course of the development of science and technology of our day convinces us of this. (A. Dorodnitsyn)
• Sooner or later every correct mathematical idea finds application in this or that business. (A.N. Krylov)
• If you want to participate in the big life, fill your head with math while you can. It will then be of great help to you in all your work. (M.I. Kalinin)
• Have you not noticed that a mathematician is skilled in all the sciences in nature? (Plato)
• It would be good if this knowledge were demanded by the state itself and if persons holding the highest public positions were taught to do mathematics and necessary cases contact her. (Plato)
• From the earliest antiquity, the mathematical sciences have attracted special attention; at present, they have received even more interest in terms of their influence on art and industry. (P.L. Chebyshev)
• Mathematics is the best and even the only introduction to the study of nature. (D.I. Pisarev)
• Astronomy (as a science) began to exist since it was combined with mathematics. (A.I. Herzen)
• Flying is math. (V. Chkalov)
• Inspiration is needed in geometry no less than in poetry. (A.S. Pushkin)
• Geometry is full of adventure, because behind every task lies an adventure of thought. To solve a problem is to experience an adventure. (V. Arizvolov)
• Mathematics has its own beauty, as does painting and poetry. (N.E. Zhukovsky)
• Chemistry - right hand physics, mathematics are her eyes. (M.V. Lomonosov)
• Mathematics already then needs to be taught, that it puts the mind in order. (M.V. Lomonosov)
• I love mathematics not only because it has applications in technology, but also because it is beautiful. (R. Peter)
• Everything that was previously in the sciences: hydraulics, aerometry, optics and others is obscure, doubtful and unreliable, mathematics has made clear, true and obvious. (M.V. Lomonosov)
• Aspiring to the closest study of chemistry must be versed in mathematics. (M.V. Lomonosov)
• A physicist without mathematics is blind. (M.V. Lomonosov)
• A mathematician who is not in some way a poet will never be a real mathematician. (K. Weierstrass)
• Mathematics is the language that all exact sciences speak. (N.I. Lobachevsky)
• Only with algebra does rigorous mathematical teaching begin. (N.I. Lobachevsky)
• No matter how well the machine works, it can solve all the tasks required of it, but it will never come up with one. (A. Einstein)
• It is mathematics that gives the most reliable rules: whoever follows them is not dangerous to deceive the senses. (L. Euler)
• Numbers (numbers) do not rule the world, but they show how the world is ruled. (I. Goethe)
• A close, deep study of nature is the source of the most fruitful discoveries of mathematics. "(J. Fourier)
• ... It would have been easier to stop the Sun, it would have been easier to move the Earth than to reduce the sum of the angles in the triangle, reduce the parallels to convergence and move the perpendiculars to the straight line to diverge. (V.F. Kagan)
• Counting and calculations are the basis of order in the head. (Pestalozzi)
• If you want to learn how to swim, then boldly enter the water, and if you want to learn how to solve problems, then solve them. (D. Poya)
• To digest knowledge, one must absorb it with gusto. (A. Franz)
• The subject of mathematics is so serious that no opportunity should be missed to make it more entertaining. (B. Pascal)

Conclusion

To date, we do not know areas of human life where mathematics is not needed. Not a single new discovery can do without it, not a single invention works, not a single enterprise and state functions, therefore, the range of everything where mathematics is needed is quite wide.

When we start studying this discipline at school, we do not know if we will make a discovery in physics, computer science, astronomy or another science. Or maybe we will be an engineer or an architect, an aircraft designer or a pharmacist, i.e. a specialist in the profession where mathematics will be needed for us.

It is possible that we will be a housewife, a makeup artist or a famous fashion designer who needs to make drawings for costume patterns. Or fate will test us in the profession of a programmer, lawyer, captain of an ocean vessel or leader of a geological expedition, since all these are areas where mathematics is simply a must.

While working on the project, we were convinced that everyone should know and study this greatest of all sciences, without which one cannot imagine one's life, since mathematics is a kind of ticket, without which it is impossible to go on a journey. It develops logical thinking, determination, imagination, the ability to find a way out of any situation.

Mathematics makes you think, helps mankind to discover and use the laws of nature, and at all times has been a powerful engine of science and technology.

I was convinced that mathematics is simply necessary in life, everyday life and professions. In this regard, I decided to acquaint as many students as possible with the results of my research in order to develop interest in this subject, expand knowledge of mathematics and broaden their horizons in general.

Hypothesis put forward the fact that mathematics is necessary in our life not only in certain professions, but also in everyday life - was confirmed.

Bibliography

1. Aksenova M.D. - Encyclopedia for children. T. 11. Mathematics / Chief ed. M.D. Aksenova - M. Avanta, 1998.
2. Glazer G.I. "History of Mathematics at School"
3. Sergeev I.S. "Apply Math"
4. Spivak A.V. Math holiday. 4.1 - M .: Bureau Quantum, 2000 (Supplement to the journal "Quantum", No. 2/2000).
5. Shalaeva G.P. Everything about everything. Popular encyclopedia for children. Moscow "Slovo" 1997, 1999.

If you carefully look around, the role of mathematics in human life becomes obvious. Computers, modern telephones and other technology 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 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 true. Let's try to figure out what mathematics is for.

Base

To begin with, it is worth understanding what mathematics is in general. 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. upon which knowledge of structure, order, and relationships is based. They are the essence of science. The properties of real objects in it are idealized and written in a formal language. This is how they are converted into mathematical objects. Some of the idealized properties become axioms (statements that do not require proof). Other true properties are then deduced from them. This is how a real-life object is formed.

Two sections

Mathematics can be divided into two complementary parts. theoretical science engaged in 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 all the time. With its help, discoveries are made, patterns are discovered, events are predicted. In this sense, the importance of mathematics in human life cannot be overestimated.

The basis of professional activity

Without knowledge of the 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. The astronomer will not be able to determine without such knowledge the distance to the star and best time observation of it, and a molecular biologist - to understand how to deal with a 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.

Humanitarian knowledge

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 sheer romance and inspiration, there is no place for analysis and calculation in it. However, it is enough to remember poetic measurements amphibrachs), as the understanding comes that mathematics had a hand in this. Rhythm, verbal or musical, is also described and calculated using the knowledge of this science.

For a writer or psychologist, such concepts as the 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 patterns developed by the queen of sciences, exist thanks to her and according to her rules.

Psychology was born at the intersection of the humanities and natural sciences. All its directions, even those that work exclusively with images, are based on observation, data analysis, their generalization and verification. Modeling, forecasting, and statistical methods are used here.

From school

Mathematics in our life is present not only in the process of mastering the 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 is taught early enough. Solving simple and complex problems, the child does not just learn to add, subtract and multiply. He slowly, from the basics comprehends the structure of the modern world. And this is not about technical progress or the ability to check the change in the store. Mathematics forms some features of thinking and influences the attitude to the world.

The simplest, the most difficult, the most important

Probably everyone will remember at least one evening at homework, when you wanted to desperately howl: “I don’t understand what math is for!”, put aside the hated difficult and tedious tasks and run away to the yard with friends. At school and even later, at the institute, the assurances of parents and teachers “it will come in handy later” seem like annoying nonsense. However, they turn out to be right.

It is mathematics, and then physics, that teaches you to find cause-and-effect relationships, lays 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 tasks. If we go further, then the ability to deduce consequences from facts, predict future events, and also do the same is laid during the study of mathematical theories. Modeling, abstraction, deduction and induction are all sciences and at the same time ways the brain works with information.

And psychology again

Often it is mathematics that gives the child the revelation that adults are not omnipotent and know far from everything. This happens when mom or dad, when asked to help solve a problem, only shrug their hands and announce their inability to do it. And the child is forced to look for the answer himself, make mistakes and look again. Sometimes parents just refuse to help. “You have to do it yourself,” they say. And they do it right. After many hours of trying, the child will receive not only what has been done homework but the ability to independently find solutions, detect and correct errors. And this is also the role of mathematics in human life.

Of course, independence, the ability to make decisions, be responsible for them, the absence of fear of mistakes are developed not only in the lessons of algebra and geometry. But these disciplines play a significant role in the process. Mathematics brings up such qualities as purposefulness and activity. Of course, a lot depends on the teacher. Incorrect presentation of the material, excessive rigor and pressure can, on the contrary, instill fear of difficulties and mistakes (first in the classroom, and then in life), unwillingness to express one's opinion, passivity.

Mathematics in everyday life

Adults after graduating from university or college do not stop solving mathematical problems every day. How to catch the train? Will it be possible to cook dinner for ten guests from a kilogram of meat? How many calories are in a dish? How long will one bulb last? These and many other questions are directly related to the queen of sciences and cannot be solved without her. It turns out that mathematics is invisibly present in our lives almost constantly. And most of the time we don't even notice it.

Mathematics in the life of society and the individual affects great amount areas. Some professions are unthinkable without it, many appeared only thanks to the development of its individual areas. Modern technical progress is closely connected with the complication and development of the mathematical apparatus. Computers and telephones, airplanes and spacecraft would never have appeared if the queen of sciences had not been known to people. However, the role of mathematics in human life is not limited to this. Science helps a child to master the world, teaches him to interact more effectively with it, forms thinking and individual qualities of character. However, mathematics alone would not have coped with such tasks. As mentioned above, the presentation of the material and the personality of the person who introduces the child to the world play a huge role.

Mathematics in human life

Have you ever heard such an expression: mathematics is a country without borders? This phrase about mathematics has a very good reason. Mathematics occupies a special place in human life. We are so close to it that we simply do not notice it.

But our life begins with mathematics. The child has just been born, and the first figures in his life are already being heard: height, weight. The kid grows up, cannot pronounce the word "mathematics", but is already doing it, solving small problems of counting toys, cubes. And parents do not forget about the tasks. When preparing food for a child, weighing him, they have to use mathematics. After all, you need to solve an elementary problem: how much food you need to cook for the baby, given its weight.

At school math problems there are many and their complexity grows every year. They do not just teach the child certain actions. Mathematical tasks develop thinking, logic, a set of skills: the ability to group objects, reveal patterns, determine relationships between phenomena, make decisions. Mathematics, solving mathematical problems develops the personality, makes it more purposeful, active, independent.

And after school, mathematics is very useful. While studying at the university, at work and at home, you need to constantly solve problems related to mathematics. What is the probability successful delivery 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 should you buy to insulate your house? How to calculate correctly so that a girl or a boy is born? And this is where math comes in. It follows a person everywhere, helps him solve practical problems, makes his life much more convenient.

The world and life itself is rapidly changing. It includes new technologies. Only mathematics and problem solving in the traditional sense do not change themselves. Mathematical laws have been verified and systematized, so a person can rely on it at important moments, solve any problem. Math won't let you down.

National action plan for 2012-2016 for the development of functional literacy of schoolchildrenpays special attention to such basic competencies as literacy in reading, mathematics, and science.

What is the purpose of mathematics education?

University preparation.

Preparation for the future profession.

Intellectual development.

Formation of the worldview.

Orientation in the environment.

Physical education of the brain.

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

Mathematics is found and used in everyday life , therefore, certain mathematical skills are needed for every person. We have to count, for example, money in life. We constantly use, often without noticing it, knowledge about the quantities that characterize the extent, 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.

Mathematical knowledge and skills are necessary in almost all professions, first of all, of course, in those related to the natural sciences, technology and economics. But there is no doubt the need to apply 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. 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 patterns 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 ethical principles human hostel. Its study is designed to educate in a person intellectual honesty, objectivity, the desire to comprehend the truth,it also brings up the ability to aesthetic perception of the world, the beauty of intellectual achievements .

“Mathematics already then needs to be taught, that 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, math puzzles develops logical thinking, reaction speed. No wonder they say that mathematics is the gymnastics of the mind.

Mathematics teacher of KSU "Kokpekty secondary school" Germash E.A.

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, 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 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 helps to develop mathematics, and what will you lose if you refuse to master this subject, at least for 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 concrete 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 orbital parameters in advance spacecraft launched from earth to deliver astronauts to 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 develop not only solving problems from different areas 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, studying the exact sciences, solving logic puzzles, and even some are suitable.

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 what other school subject is capable of so raising the mental level of a growing individual 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 pyramid schemes 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 have heard of brilliant lawyers who, in addition to legal education received, in addition, physical and mathematical. 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 initial courses University, I think, everyone should and is capable of.

Do not think that this is not given to you by nature, that your calling is humanitarian sciences and exact subjects you are unable to learn. 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 mathematical ability. 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 certain intellectual skills, structured thinking, the ability to generalize and derive relationships from its creator. 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. Certainly balanced. mental development personality implies the development of not only exact subjects, but also the humanities. 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 own 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 a narrow specialist, an expert in your 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 corresponds to this principle of universality (only an idea, I don’t 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, considering that the growing individual should be given as much as possible from different areas, and when he gets it, let him choose what is closer to him!

We all learned math in school. Moreover, many of those who consider themselves to be "humanists" because of their passion for literature and languages, remember logarithms and quadratic equations like a bad dream. Each of us has repeatedly asked the question “Can this ever be useful to me in life?” and, most likely, did not receive an intelligible answer even from his algebra teacher. Jordan Ellengberg, an American professor of mathematics at the University of Wisconsin-Madison, takes it upon himself to say: “How else can it be”!

Mistakes of planes and soldiers' legs

Ellenberg begins his book with a story about the outstanding mathematician of the 20th century, Abraham Wald, who was forced to emigrate from Austria to the United States in the late 1930s because of the persecution of Jews by the Nazis. During World War II, Wald worked with leading American statisticians on secret military missions for the Statistical Research Group (SRG). The military command turned to the SRG with the task of finding a way to minimize the loss of American bombers.

Damage on aircraft returning from the combat zone was unevenly distributed - most of the holes were on the fuselage, a smaller part - on the engine. The military came to the conclusion that it was necessary to strengthen the most vulnerable parts of the aircraft with armor. The only question was how much armor should be used in the affected areas so as not to overload the aircraft with iron and at the same time effectively strengthen it.

Wald's answer was unexpected. Naturally, he did not dispute that the aircraft needed additional protection. But at the same time, he proposed making fortifications not where there are the most holes, but where there are none - that is, on the engines. There was only one reason why there was less damage in these zones: in the event of a direct hit on the engine, the aircraft simply did not return from combat. The same thing happened with the wounded in the military hospital: the nurses were more likely to see the wounded in the legs, and not in the chest. And it's not that the soldiers did not receive chest wounds, just after them, as a rule, few people survived.

Ellenberg focuses on this story with Wald to make the reader understand what is mathematical way thinking. Being a mathematician is not just about solving numerical problems and deriving algebraic formulas. Being a mathematician means thinking outside the box, formulating the right questions, and most importantly, questioning the assumptions that lead to false conclusions.

A mathematician always asks these questions: “What are your assumptions? Are these assumptions justified? Sometimes this causes irritation. However, this approach can be very productive.

Apply math to sore spots

On the school lessons algebra, few people think about it. We are studying long list rules and formulas, from the entire array of which we then use only the skills of carrying out simple arithmetic operations(in fact, not only that, but many do not even suspect how deeply mathematics is woven into the fabric of our thinking). So, if your understanding of mathematics is limited only to school course- congratulations, you know almost nothing about this subject! There are such fundamental sections of this science as probability theory, mathematical analysis, coding theory, and statistics. (Already scared? I confess, I'm a little too). After all we are talking about such areas of pure mathematics that seem inaccessible to the common man.

Ellenberg is quick to assure us that this abstract, complex language is based on nothing more than common sense, supported by fundamental methods and theorems. And "the true mental work that is required in mathematics is not much different from how we think about solving simple everyday problems." The professor came to this conclusion while working on mathematical research, so far from real life that he does not seek to acquaint us with them. The further this work progressed, the more clearly he understood that mathematical laws go far beyond discussions within the university community.

“Knowledge of mathematics is a kind of x-ray glasses that allow you to see the structure of the world hidden under a disorderly, chaotic surface. Mathematics is the science of not making mistakes, and mathematical forms and methods have been forged over many centuries of hard work and discussion.

Unlike his predecessor Wald, who was not interested in the applied possibilities of mathematics, Ellenberg sets the task of talking about the use of mathematical concepts in politics, medicine, economics, religion, the Internet, and even everyday affairs. Here we are dealing with simple and deep facts that are part of the mathematical universe.

When is the best time to arrive at the airport so as not to waste your time and at the same time not be late? How do you live in a world where Google, Facebook, and even the big retail chains know more about you than your own parents? Should we trust public opinion polls? What about the results of testing new drugs? What can be learned about the existence (or absence) of God using the laws of mathematics? How are statistical surveys created to tell us that in certain geographical areas Is the risk of developing cancer higher than in others? What loopholes exist for candidates in the democratic election process? What, after all, must be done to cheat the system (legally, of course) and win millions of dollars in the lottery? And so on and so forth.

The examples in the book illustrate how believing in thoughtless numbers, unverified facts, and dubious statistics circulated through multiple channels of communication causes people to jump to ridiculous conclusions and make life difficult for themselves. A detailed analysis of each case based on mathematical analysis really helps to take a critical look at the flow of information that daily falls on our heads through the statements of politicians and public figures, online advertising and media.

Math is not just for geniuses

Of particular interest are the author's arguments about rooted in public consciousness notions that all mathematicians are crazy obsessed geniuses who choose scientific escapism as the main idea of ​​life. This image is widely replicated by popular culture, take the story of John Nash's schizophrenia and hallucinations around which the plot of the movie A Beautiful Mind is built, or the whole spectrum of Max Cohen's mental disorders in the movie Pi.

“In real life,” writes Ellenberg, “mathematicians are ordinary people no more insane than everyone else. In fact, we do not often go into seclusion to fight lonely battles in harsh abstract worlds. Mathematics rather strengthens the mind, and does not strain it to the limit.

It is also a mistake to think that mathematics rests only on geniuses alone, and that all the rest, whose achievements seem less outstanding, are on the road to this area. scientific knowledge closed. Meanwhile, this is the opinion of many students who leave universities in the middle of their studies, disappointed not in mathematics itself, but in the fact that they fail to become the best. Ellenberg regrets this, because he believes that mathematics is a collective activity in which thousands of minds around the world take part, and the discoveries of each of them serve a single purpose. Do not underestimate their contribution.

Mark Twain said it very well: “It takes a thousand people to invent the telegraph, or the steam engine, or the phonograph, or the telephone, or anything else as important, and we attribute the invention to the last of them and forget about the rest.”

Make decisions based on a large number possibilities, to use formal logic in evaluating events, not to fall for suggestions that promise us impossible prospects, to remember that the incredible happens when there are many chances - all this means doing mathematics in everyday life. And we have been doing this since childhood - more precisely, those of us who support good relationship with common sense.