The Faculty of Mechanics and Mathematics and the area of my research

The Faculty of Mechanics and Mathematics and the area of my research

Mathematics has always been the basis of natural science and, together with mechanics, it is the basis of all engineering sciences and the main means to investigate laws of the Universe.

When MSU was founded there was no department of Mathematics. The lectures were read but considered Mathematics to be a secondary subject. The faculty of Physics and Mathematics began exist only in 1804. After the revolution in 1917 there were great problems with learning process at this faculty and in 1933 was founded department of Mechanics and Mathematics. The last change in its structure was in 1970, when the Department of Computational Mathematics and Cybernetics broke off. 

Nowadays, the Division of Mechanics includes 9 branches and the Division of Mathematics consists of 17 departments, for example, Department of Mathematical Analysis, Department of Higher Algebra, Department of Higher Geometry and Topology, and many others. 

Now, I’d like to tell some words about the area of my research. At the end of the last century it was developed the branch of geometry which deals with the fi nite sets of points in the plane.

In 1970s, the planar convex hull algorithm was generalized; it found the shape of a finite point set. This algorithm was based on the pivoting the line segment and sometimes this approach caused the mistakes. However, the difference between the logic structure of algorithm and the numerical evaluation of its geometric primitives makes difficult to turn the algorithm into correct software. Any mistake causes geometrical constructions which do not exist. Thus there are a lot of cases, for example, three collinear points, and all of these cases must be examined.

The main important structures in this branch of geometry are the Voronoi diagram and the Delaunay triangulation, named after two Russian mathematicians. A great number of algorithms of their constructions are known today, but it’s very important and difficult problem to find faster and more efficient method. These two structures are very useful and have a high significance value. In climatology, Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In epidemiology, they can be used to correlate sources of infections in epidemics. One of the early applications of Voronoi diagrams was implemented by John Snow to study the 1854 Broad Street cholera outbreak in England.

A great result in this sphere has been already achieved, but still there are directions that remain largely unexplored. Finally, there are ideas of creating shape spaces from alpha complexes which have yet unrealized potential. Today the range of application and development of this branch is very wide: pattern recognition, digital shape sampling and processing, structural molecular biology. It is applied in ecology, materials science, chemistry and even in mathematical statistic.

 

The art in man’s life

When we talk about art what we imagine? Probably we remember such names as Picasso, Dali, Chopin or Tchaikovsky. And if we think about technology we imagine maybe a smartphone or a computer. Throughout history, technology has provided artists with new tools for expression. Nowadays, these two disciplines are interlinked more than ever, and technology becomes a fundamental force in the development and evolution of art. Naturally entirely new art forms are evolving as well. More and more artists are pushing the boundaries of art, looking outside of what's perceived as " traditional" to incorporate other aspects into their work. Art is becoming less static, taking up many new different shapes. Artist Ollie Palmer has created a machine to control the way synthetic pheromone directs ants - hoping this way to stage an 'ant ballet'.

Digital technology and modern techniques have had the strongest impact on the art of painting and drawing. In the past, painting and drawing depended on the artist’s skills in using his traditional tools - the brush, the pencil or pastels. The artist, through conventional and calculated steps, was in control of the density of color, different hues, the realism or abstraction of his work of art. Artists today operate with clicks of the mouse, video tools and digital colors. Contemporary art has been greatly influenced by the astonishing progress in the introduction of new, more attractive and convenient materials that artists could work with. Artist could focus more on contents of theirs works, creativity and developing delightful ideas. In other words, artists today have an enormous variety of techniques. Possessing this vast quantity of tools and potential must be accompanied by a comprehensive and in-depth knowledge of every detail of these tools and their capabilities, so as to enable the artist incarnate all his fantasies via the designated tool, using the best and the shortest way which is possible. Therefore artists need to improve their skills and understand these techniques well in order to use all opportunities they offer.

But on the other hand there are many people who think another way. One young artist from Japanize writes, that she is still learning the aspects of Digital painting and she thinks, painting digitally makes any Art work easy, efficient, fast and convenient, due to Undo / Redo commands and effects which you cannot use in traditional painting. In addition, you can paint digitally almost everywhere. But as I think digital painting is not easy as it seems, it is not just pressing any button or using a command. A digital artist must have deep knowledge in art in order to create painting comparable to traditional art.

Apparently digital technologies are changing the art very much. Firstly throughout history and until recently, the public was merely a passive observer. Today, in our modern world, everyone can create something. Digital painting tutorials are all out on the internet. You can find them easily and start your new hobby, digital painting. They are presented through a video where each step is demonstrated. All you have to do is to carefully watch the video and remember the steps and strategies that are showed by the expert. A lot of people don’t understand that it is not enough to make a really art. However, because it is now easier to create, we see a lot of strange things being created and exposed. A huge problem is that, as a result of so many new tools and techniques, we may lose our sense and ability to evaluate what is great art. But today, technology, and especially computer technology, develops and there will always be those who will experiment.

 

Finance and economics

Nowadays practically everyone adult has a credit card. They appeared recently and became very popular. I’d like to tell about the history of the system of credit card. Many people think of credit cards as a modern day convenience, but the history of the earliest credit cards actually dates back to the beginning of 20^th century.

As far back as the late 1800s, consumers and merchants exchanged goods through the concept of credit. Plastic payments as we know them today became a way of life in about half a century. Credit cards were not always been made of plastic. There have been credit tokens made from metal coins, metal plates, paper, and now mostly plastic cards.

At the beginning of 20^th century, oil companies and department stories issued their own cards entitled " Credit Cards and Payment Efficiency." Such cards were accepted only at the business that issued the card and in limited locations. While modern credit cards are mainly used for convenience, these predecessor cards were developed as a means of creating customer loyalty and improving customer service.

 The first bank card, named " Charg-It, " was introduced in 1946 by John Biggins, a banker in Brooklyn. When a customer used it for a purchase, the bill was forwarded to Biggins' bank. The bank reimbursed the merchant and obtained payment from the customer.  But there were some catches: Purchases could only be made locally, and Charg-It cardholders had to have an account at Biggins' bank. In 1951, the first bank credit card appeared in New York's Franklin National Bank for loan customers. It also could be used only by the bank's account holders.

 The Diners Club Card was the next step in credit cards. According to a representative from Diners Club, the story began in 1949 when a man had a business dinner in New York. When the bill arrived, Frank realized he'd forgotten his wallet. He managed to find his way out of the pickle, but he decided there should be an alternative to cash. Thus the Diners Club credit card was invented to pay restaurant bills. A customer could eat without cash at any restaurant that would accept Diners' Club credit cards. The Diners Club card was at first technically a charge card rather than a credit card since the customer had to repay the entire amount when billed by Diners Club.

Credit cards were first promoted to traveling salesmen for use on the road. By the early 1960s, more companies offered credit cards, advertising them as a time-saving device rather than a form of credit.

Speaking about the future, while the plastic card has been the standard for a half century, recent developments show alternative forms of payment which become more popular, from online services such as PayPal to credit card key fobs to chips that can be implanted into cell phones or other devices. But from my point of view, credit cards aren’t going anywhere any time soon, also cash would be still used for many years.

 

Man in the modern world

In the last century there was a time of unprecedented technical and scientific achievements. We can't imagine our life today without telephone, television, cars or computers. Nowadays modern industry is fulfilled with the help of robots which replaced man in some hard or dangerous labor and run by computers. Machines provide people most of necessities. In the 20th century, many infectious diseases have been conquered through vaccines and antibiotics. The advance of medical knowledge enables people to perform the most difficult operations with the help of modern equipment and to keep people alive with the help of implanted organs. It is necessary to notice that as a result of the advance of medical service average life expectancy in Europe has increased from 50 years to about 75 years.

Nevertheless in spite of the all advantage of the modern world there are a lot of problems today: terrorism, overpopulation, poverty, water scarcity. But I’d like to tell about the problem of consumerism in the 21^st century. Economists tell us that natural resources are scarce but that human wishes are unlimited. What are the main humans’ needs? Food, health care, education, the opportunity to express themselves, and leisure. At the same time mass marketing and advertising makes people believe that they can't brush their teeth without the help of an electronic gadget. In other words people sometimes buy different things, which they don’t need.

Consumerism is an integral part of the 21st century lifestyle. Every person today is a consumer. Everyone buys anything practically every day. Shopping gives people a sense of choice and power which is often absent from the rest of their life. Certainly, consumerism has some advantages. For example, with the power of new technology, the consumer has the power to influence on the companies by choosing the products of high quality or by protecting his consumer’s rights.

But on the other hand consumerism in its most basic form is the creation of a system in which each of us do not need to go out and kill his food, make his clothing or build his house. In the modern world we could go to a store or to a company and buy what is needed. New products make more and more tasks ever easier, minimizing the amount of intelligence or even physical activity we must expend to get something. We have become quite lazy since our ability to obtain what we need has been easily, and we make an effort to obtain what we want. We need a little money to get food and clothes, and then we want to buy the latest gadget or toy to produce a sense of happiness. Many of us take up uninteresting jobs in order to make more money to buy more wanted items.  As a result of consumer society people often couldn’t do anything with their own hands. We are accustomed to buy anything we need, and the major part of society doesn’t create or produce anything. So we become more and more depended and disabled to deal with difficult situations.

 

Eminent men of science

There are a lot of men in the natural sciences, but I’d like to tell about the greatest women, who dedicated herself to the Mathematics.

Sofia Kovalevskaya was the middle child of Vasily Korvin-Krukovsky, an artillery general, and Yelizaveta Shubert, both well-educated members of the Russian nobility. Sofia was educated by tutors and governesses. She was attracted to mathematics at a very young age. Her uncle Pyotr Krukovsky, who had a great respect for mathematics, spoke about the subject.

 When Sofia was 11 years old, the walls of her nursery were papered with pages of Ostrogradski's lecture notes on differential and integral analysis. It was Sofia's introduction to calculus. Sofia 's father decided to put a stop to her mathematics lessons but she borrowed a copy of Bourdeu's Algebra which she read at night when the rest of the household was asleep.

 A year later a neighbour, Professor Tyrtov, presented her family with a physics textbook which he had written, and Sofia attempted to read it. She did not understand the trigonometric formulae and attempted to explain them herself. Tyrtov realised that in her working with the concept of sine, she had used the same method by which it had developed historically. Tyrtov argued with Sofia's father that she should be encouraged to study mathematics further but he permitted Sofia to take private lessons several years later.

 Sofia was forced to marry so that she could go abroad to enter higher education. Her father would not allow her to leave home to study at a university, and women in Russia could not live apart from their families without the written permission of their father or husband. At the age of eighteen, she entered a nominal marriage with Vladimir Kovalevski, a young palaeontologist.

In 1869 Sofia travelled to Heidelberg to study mathematics and the natural sciences, only to discover that women could not join to the university. Eventually she persuaded the university authorities to allow her to attend lectures unofficially. Sofia studied there successfully for three semesters and, according to the memoirs of a fellow student, she immediately attracted the attention of her teachers with her uncommon mathematical ability.

 In 1871 Kovalevskaya moved to Berlin to study with Weierstrass. Despite his the efforts the senate refused to permit her to attend courses at the university. This actually helped her since over the next four years Weierstrass tutored her privately.

 In 1874 Kovalevskaya was granted her doctorate from Gö ttingen University. Despite this doctorate and letters of strong recommendation from Weierstrass, Kovalevskaya was unable to obtain an academic position. This was for a combination of reasons, but her sex was a major handicap.

 In 1878, Kovalevskaya gave birth to a daughter, but from 1880 increasingly returned to her study of mathematics. In the spring of 1883, Vladimir her husband committed suicide. After the initial shock, Kovalevskaya immersed herself in mathematical work in an attempt to rid herself of feelings of guilt. Mittag-Leffler managed to overcome opposition to Kovalevskaya in Stockholm, and obtained for her a position as private docent.

 She taught courses on the latest topics in analysis and became an editor of the new journal Acta Mathematica. She took part in the organisation of international conferences. Her status brought her attention from society, and she began again to write reminiscences and dramas that she had enjoyed doing when young. In 1889, on the initiative of Chebyshev, Kovalevskaya was elected a corresponding member of the Imperial Academy of Sciences.

In early 1891, at the height of her mathematical powers and reputation, Kovalevskaya died of influenza complicated by pneumonia.

 

Global English

 

There are over 70 English-speaking countries in the world. They are: Great Britain, the United States of America, Canada, Australia, New Zealand and also some small states, which are situated on the islands in the Pacific Ocean.

The history of these countries is closely connected with the history of Great Britain as a great sea-power. In ancient times, England had the most powerful fleet in the world, which was the best in all the seas and oceans. The English ships sailed across the seas and oceans in all the directions and the English sailors made sea-voyages to different regions of the world. It’s not surprising, that the majority of great discovers and explorers were among the English people who were eager to bring glory to their native country and they took part in the exploring expeditions around the world and to different far-away regions. The aims of their expeditions were to discover new lands and to explore unknown continents and islands. As a result England conquered a lot of new territories. After that thousands of the people left their Motherland – England, reached the shores of new lands which had been just discovered, settle down on those territories and stayed there for ever.

Nowadays, the English-speaking countries are situated in different parts of the world. They differ in their geographical position, their climate, their nature and the way of life, which their people lead. Every country has its own national history, traditional, holidays and customs. But all of them have one thing in common. All of them speak a common language, the language of people who many centuries ago came from England to make their home in new countries.

Therefore English could be called a world language. It is a universal language of progressive science and technology, trade and cultural relations, commerce and business. It is also the major language of diplomacy. Hundreds and hundreds of books, magazines and newspapers are printed in English and read all over the world. Half of the world’s scientific literature is written in English. More than 350 million people speak on this language. Geographically it is the most widespread language on earth, second only to Chinese in the number of people who speak it. English can be at least understood almost everywhere among scholars and educated people, as it is the world media language, and the language of cinema, TV, pop music and the computer world

English is also one of the most studied languages across the world, in many countries it is learned as a second language from primary school. As per the statistics, it said that the English language is one of the easiest languages to learn, if we compare it with languages like Chinese, German, French and even Spanish. It is such an important language worldwide, that 80% of the information that we find in the internet is in English.

 

The Faculty of Mechanics and Mathematics and the area of my research

Mathematics has always been the basis of natural science and, together with mechanics, it is the basis of all engineering sciences and the main means to investigate laws of the Universe.

When MSU was founded there was no department of Mathematics. The lectures were read but considered Mathematics to be a secondary subject. The faculty of Physics and Mathematics began exist only in 1804. After the revolution in 1917 there were great problems with learning process at this faculty and in 1933 was founded department of Mechanics and Mathematics. The last change in its structure was in 1970, when the Department of Computational Mathematics and Cybernetics broke off. 

Nowadays, the Division of Mechanics includes 9 branches and the Division of Mathematics consists of 17 departments, for example, Department of Mathematical Analysis, Department of Higher Algebra, Department of Higher Geometry and Topology, and many others. 

Now, I’d like to tell some words about the area of my research. At the end of the last century it was developed the branch of geometry which deals with the fi nite sets of points in the plane.

In 1970s, the planar convex hull algorithm was generalized; it found the shape of a finite point set. This algorithm was based on the pivoting the line segment and sometimes this approach caused the mistakes. However, the difference between the logic structure of algorithm and the numerical evaluation of its geometric primitives makes difficult to turn the algorithm into correct software. Any mistake causes geometrical constructions which do not exist. Thus there are a lot of cases, for example, three collinear points, and all of these cases must be examined.

The main important structures in this branch of geometry are the Voronoi diagram and the Delaunay triangulation, named after two Russian mathematicians. A great number of algorithms of their constructions are known today, but it’s very important and difficult problem to find faster and more efficient method. These two structures are very useful and have a high significance value. In climatology, Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In epidemiology, they can be used to correlate sources of infections in epidemics. One of the early applications of Voronoi diagrams was implemented by John Snow to study the 1854 Broad Street cholera outbreak in England.

A great result in this sphere has been already achieved, but still there are directions that remain largely unexplored. Finally, there are ideas of creating shape spaces from alpha complexes which have yet unrealized potential. Today the range of application and development of this branch is very wide: pattern recognition, digital shape sampling and processing, structural molecular biology. It is applied in ecology, materials science, chemistry and even in mathematical statistic.

 

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