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Учебное пособие по чтению математических

текстов на английском языке

Нижний Новгород 2011

Reading: Учебное пособие по чтению математических текстов на английском

языке. - Нижний Новгород: НГПУ, 2011. - 65с.

Учебное пособие предназначено для студентов математических факультетов неязыковых педвузов, изучающих английский язык. Пособие состоит из трёх разделов, включающих оригинальные тексты, лексические, грамматические и речевые упражнения в пределах определенной авторами тематики, а также приложения.

Составители: Ю. М. Борщевская, канд.пед.наук, ст. преподаватель каф. ин. яз. НГПУ Ю. В. Клопова, ст. преподаватель каф. ин. яз. НГПУ

Рецензенты: Е. Ю. Илалтдинова, канд.пед.наук, доцент каф. ин. яз. НГПУ Е. Р. Пермякова, канд.пед.наук, доцент каф. филологии и журналистики НФ УРАО

Ответственный редактор: А. А. Шавенков, канд.психол.наук, доцент каф. ин. яз. НГПУ

Предисловие

Предлагаемое учебное пособие предназначено для студентов математических

факультетов дневного отделения неязыковых педагогических вузов. Пособие

включает оригинальные тексты о выдающихся математиках, тексты по

информатике и математике.

Данное пособие имеет целью развивать и совершенствовать навыки чтения и

понимания оригинальной литературы на английском языке, а также литературы

по своей специальности.

В пособии представлены упражнения на контроль понимания содержания

текста, грамматические упражнения, коммуникативные задания, позволяющие

развивать такие виды речевой деятельности как слушание, говорение, чтение и

перевод.

Пособие рекомендуется для использования магистрантами и студентами

математических факультетов при обучении иностранному языку.

Contents

Famous mathematicians……………………………………………………………….5

David the teenage tycoon………………………………………………………………..5

Grace Hopper……………………………………………………………………………6

Benjamin Banneker……………………………………………………………………...9

Louis Posa, by Paul Erdos……………………………………………………………...11

The Moore method……………………………………………………………………..13

Saunderson, a blind mathematician…………………………………………………….15

Fabre, spiders, and geometry…………………………………………………………...18

Sonya Kovalevskaya……………………………………………………………………20

Computer studies……………………………………………………………………...24

What is a computer……………………………………………………………………..24

What is hardware……………………………………………………………………….25

Windows ……………………………………………………………….………………29

Computer operations. Types of data……………………………………………………29

Types of software………………………………………………………………………32

Operating systems………………………………………………………………………36

Introduction to the WWW and the Internet…………………………………………….40

Analytical geometry…………………………………………………………………...44

Cartesian coordinates………………………………………………………………...…44

Polar coordinates……………………………………………………………………….47

Locus of a variable point……………………………………………………………….51

***……………………………………………………………………………………...54

The folium of Descartes………………………………………………………………..59

Appendix……………………………………………………………………………….63

References……………………………………………………………………………...65

FAMOUS MATEMATICIANS

DAVID THE TEENAGE TYCOON

Teenager David Bolton has just put 9,000 pounds in the bank-after only six months of

part-time work аs a computer consultant. The electronics expert from Croydon, South

London, is fast establishing a reputation as one of the country's top troubleshooters - the

person to call if no one else can cope.

For David, 15, his first steps to fame and fortune began when he was only nine, when

his parents bought him a computer, a ZХ-90. 'I soon learned to program it. I needed

something bigger, so I had to save for ages to buy an Amstrad.'

It was only about a year ago, however, that he decided to get serious about computing.

He went to night school to learn how to write business programs, and did a

correspondence course with an American college.

He got in touch with a computer seller, Eltec, who were so impressed that they gave

him computers and software worth more than £3,000. In return, he has to send them a

monthly report saying what he has done and what his plans are. He helps companies by

suggesting which computers they should buy, and by writing individual programs for

them.

He can work more quickly than many older professionals. In one case, he went to a

company where a professional programmer worked for six months and couldn't find the

problem. David finished the job in five days.

It is because of work of this standard that in the short period he has been in business

David has made about £9,000. With it he has bought more equipment. How did he do it?

You have to be ambitious, and you have to really want to get to the top. Believe in

yourself, and tell yourself that you're the best´.

I. ANSWER THE QUESTIONS:

1. What did it mean for Bolton 'to get serious about computing'?

2. What helped him to find a good job?

3. Why was he welcomed by Eltec?

4. What do you need, in David's opinion, to get to the top?

5. Do you want to be the best? Why?

II. DEFINE TO WHAT PART OF SPEECH THE FOLLOWING WORDS BELONG

TO, TRANSLATE THEM:

teenager

troubleshooter

learner

programmer

reporter

III. TRANSLATE THE FOLLOWING SENTENCES, USING THE TEXT:

1. Дэвид работал в банке консультантом неполный рабочий день.

2. Свои первые шаги к славе он сделал, когда ему было девять лет.

3. Год назад Дэвид решил всерьез заняться компьютером.

4. Он связался с представителями фирмы, торгующей компьютерами.

IV. ARE THESE SENTENCES TRUE OR FALSE?

1. David Bolton is one of the country’s top troubleshooters.

2. His parents bought him a ZХ-90 and then an Amstrad.

3. When David decided to get serious about computing, he finished night school and

a full time course with an American college.

4. Now he works for Eltec and other companies helping them to choose computers

and writing programs for them.

5. The money David has earned he has invested in new equipment.

V. FILL IN THE BLANKS WITH SUITABLE WORDS:

1. David Bolton was (…) one of the best computer consultants.

2. After buying ZX-90 David (…) about computing.

3. Trying to find a job the electronics expert from Croydon (…) with Eltec.

4. Bolton could (...) with problems other professionals had failed to solve.

5. If you want (...) you should believe in yourselves.

GRACE HOPPER

'Retired Rear Admiral Grace M. Hopper, an internationally renowned computer

programming pioneer, died on January I, 1992. She was 85 years old. Her career in the

US Navy spanned 43 years, from World War П to her retirement in 1986.

After graduating with a Ph.D. in mathematics from Yale in 1934 she taught for

nearly a decade at Vassar, then entered the Naval Reserve in 1943. She was assigned to

the Bureau of Ordnance Computation Project at Harvard University, where she worked

with the computer pioneer Howard Aiken.

In 1949 she joined the Eckert-Mauchly Computer Corporation. The company, whose

founders had developed the ENIAC, one of the world's first digital computers, was at

that time building the first commercial computer, the UNIVAC I. Grace Hopper played

an active role in the design and development of COBOL, the Common Business

Oriented Language, for usе on the UNIVAC. COBOL is still widely used today for

business applications.

After retiring from the Naval Reserve in 1966, Grace Hopper was recalled a year

later to work on standardizing the Navy's computer languages. She finally retired in

1986 at the grand old age of 80. She had been promoted to the rank of Rear Admiral by

presidential appointment in 1983.

It was Grace Hopper who coined the term "bug" for anything that causes trouble in a

computer. The first computer bug wаs actually a moth, discovered one night in 1945 in

a Harvard computer. This is how Grace Hopper tells the story.

"Things were going badly. There was something wrong in one of the circuits.

Finally, someone located the trouble spot, and, using ordinary tweezers, removed the

problem, a two-inch moth. Frоm then on, when аnуthing went wrong with a computer,

we said it had bugs in it".


1. Why was Grace Hopper hired by the Naval Reserve?

2. What services has she to the country?

3. How was her work recognized?

4. Do you want to work for the state? Why?

5. What kind of reward would you like to get for your work?


TO, TRANSLATE THEM:

development

retirement

assignment

temperament

appointment

achievement

establishment


1. Грейс Хоппер была прославленным на весь мир компьютерным

программистом.

2. Она принимала активное участие в создании и развитии компьютерного

языка КОБОЛ.

3. КОБОЛ до сих пор используется в деловых прикладных программах.

4. Именно Грейс Хоппер придумала термин “вирус” для всего, что вызывает

сбои в работе компьютера.


1. Grace Hopper worked for US Navy for half of her life.

2. She wanted to work at the Bureau of Ordnance Computation Project at Harvard

University, where Howard Aiken worked, but failed to get a vacancy.

3. From 1949 she worked with Eckert-Mauchly Computer Corporation until her

retirement in 1966.

4. Grace was promoted to the rank of Rear Admiral three years later.

5. The term "bug" belongs to Grace Hopper.


1. Grace Hopper was a (...) in computing.

2. Eckert-Mauchly (...) the ENIAC.

3. The term (…) was (...) by Grace Hopper.

4. She was (...) to the rank of Rear Admiral.

5. The "bug" is everything that (...) trouble in a computer.

BENJAMIN BANNEKER

"There is so much to admire in the life of Benjamin Banneker (1731-1806). Не was

the first American Negro mathematician; he published a very meritorious almanac from

1791 to 1806, making his own astronomical calculations; using a borrowed watch as a

model, he constructed entirely from hard wood a clock that served as a reliable

timepiece for over twenty years; he won the enthusiastic praise of Thomas Jefferson,

who was then the Secretary of State; he served as a surveyor on the Commission

appointed to determine the boundaries of the District of Columbia; he was known far

and wide for his ability in solving difficult arithmetical problems and mathematical

puzzles quickly and accurately. These achievements аre all the mоre remarkable in that

he had almost no formal schooling and was therefore largely self-taught, studying his

mathematics and astronomy from borrowed books while he worked for a living as a

farmer.

But laudable as all the accomplishments of Benjamin Banneker mentioned above

are, there is a further item that perhaps draws stronger applause. In his almanac of 1793,

he included a proposal for the establishment of the office of Secretary of Peace in the

President's Cabinet, and laid out аn idealistic pacifist plan tо insure national peace.

Every country in the world has the equivalent of a Secretary of War. Had Benjamin

Banneker's proposal been sufficiently heeded, the United States of America might have

been the first country to have a Secretary of Реacе! The possibility of realizing this

honor still exists and the time for it is overripe".


1. What was there to admire about Benjamin Banneker?

2. In what period of American history did he live?

3. Was it easy for him to become a mathematician?

4. Did he have any formal schooling?

5. How did he thrust his way in science?

6. What did it depend on: personal qualities, political situation, reliable backing,

local authorities?

7. Why did he propose to establish the office of Secretary of Peace in the President's

Cabinet?

8. How do you understand the expression "to have а social conscience"?

9. What is more important: to be a professional or to have a social соnscienсе?

10.How do they correspond to each other?


TO, TRANSLATE THEM:

astronomical remarkable

arithmetical reliable

mathematical laudable


1. В жизни Бенжамина Беннекера есть многое, чем можно восхищаться.

2. Он делал свои собственные астрономические вычисления.

3. Беннекер, используя заимствованные часы в качестве модели, собрал

полностью из дерева часы, которые более 20 лет показывали точное время.

4. Он был широко известен из-за своей способности быстро и точно решать

арифметические задачи и математические головоломки.


1. Thomas Jefferson paid much attention to Benjamin Banneker's inventions.

2. Banneker was able to solve quickly any arithmetical problem.

3. He never worked devoting all his time to studying.

4. The idea of establishing the post of Secretary of Peace belongs to him.

5. If Banneker's suggestion had been given consideration the USA would have been

the 1st country with a Secretary of Реacе.


1. A (…) almanac was published by Benjamin Banneker from 1791 to 1806.

2. Benjamin Banneker constructed a (...) clock entirely from hard wood.

3. He was appointed to determine (...) of the District of Columbia.

4. Though Benjamin Banneker had (...) and was (…) he made a great progress in

sciences.

5. The time for the establishment of the office of Secretary of Peace in the

President's Cabinet is (…).

LOUIS POSA, BY PAUL ERDOS

'I will talk about Posa who is now 22 years old and the author of about 8 papers. I

met him before he was 12 years old. When I returned from the United States in the

summer of 1959 I was told about a little boy whose mother was a mathematician and

who knew quite a bit about high school mathematics. I was very interested and the next

day I had lunch with him. While Posa was eating his soup I asked him the following

question: Prove that if you have n+1 positive integers less than or equal to 2n, some pair

of them are relatively prime. [That is, have no common factor, other than one.] It is

quite easy to see that the claim is not true of just n such numbers because no two of the

n even numbers up to 2n are relatively prime. Actually I discovered this simple result

some years ago but it took me about ten minutes to find the really simple proof. Posa sat

there eating his soup, and then after a half a minute or so he said, "If you have n+1

positive integers less than or equal to 2n, some two of them will have to be consecutive

and thus relatively prime." Needless to say, I was very much impressed, and I venture to

class this on the same level as Gauss' summation of the positive integers up to 100 when

he was just 7 years old.'

Paul Erdos


1. How did Paul Erdos learn about Louis Posa?

2. Why do you think he knew quite a bit about high school mathematics?

3. What kind of problem did Paul Erdos offered to Louse Posa?

4. How did the author venture to estimate Posa's gift for mathematics?

5. What do you think influenced Posa's gift for mathematics?

6. Did his mother feel responsibility for developing her son’s talent? Why?

7. Do your parents worry about you, your future, your self-determination?

8. What do they do to help you?

9. Are you always ready to accept their ideas about you?

10.How can you explain the misunderstanding between the youth and older

generations?

11.What can be done to eliminate this problem?


TO, TRANSLATE THEM:

mathematician positive

musician relative

politician consecutive

geometrician destructive


1. Полу Эрдосу рассказали о маленьком мальчике, который знал достаточно

много о высшей математике.

2. Докажите, что если вы имеете сумму n+1 положительных целых чисел,

которые меньше или равны 2n , то какая-либо пара из этих чисел есть

соответственно простое число.

3. Чтобы найти это простое решение Полу потребовалось около 10 минут.


1. Being a child of a mathematician Posa knew quite a lot about high school

mathematics.

2. He proved to be a very intelligent boy.

3. Paul Erdos thought Posa to be as talented as Gauss.


1. When Posa was l2 years old he knew (...) about high school mathematics.

2. The multiplicand and multiplier are called (…).

3. Paul Erdos (…) to compare Posa's achievements on the same level as Gauss'

ability to add numbers in childhood.

4. Paul Erdos (…) by Posa' s gift.

5. There are some types of (…) in mathematics.

THE MOORE METHOD

R. L. Moore (1881-1974) was а Тexan topologist and a big man in every way. He

was famous for inventing the Moore method of teaching mathematics.

At the first meeting of the сlass Moore would define the basic terms and either

challenge the class to discover the relations among them, or, depending on the subject,

the level , and the students, explicitly state a theorem, or two, or three. Class dismissed.

Next meeting: "Mr.Smith, please prove Theorem 1. Oh, you can’t? Very well, Mr.Jones,

you? No? Mr.Robinson? No? Well, let’s skip Theorem 1 and come back to it later. How

about Theorem 2, Mr.Smith?" Someone almost always could do something. If not, class

dismissed. It didn’t take the class long to discover that Moore really meant it, and

presently the students would be proving theorems and watching the proofs of others

with the eyes of eagles. One of the rules was that you mustn’t let anything wrong get

past you - if the one who is presenting a proof makes a mistake, it’s your duty to call

attention to it, to supply a correction if you can, or, at the very least, to demand one.

The procedure quickly led to an ordering of the students by quality. Once that was

established, Moore would call on the weakest student first. That had two effects: it

stopped the course from turning into an uninterrupted series of lectures by the best

student, and made for a fierce competitive attitude in the class – nobody wanted to stay

at the bottom. Moore encouraged competition. Do not read, do not collaborate - think,

work by yourself, beat the other guy. Often a student who hadn't yet found the proof of

Theorem 2 would leave the room while someone else was presenting the proof of it - each

student wanted to be able to give Moore his private solution, found without any help.

Once, the story goes, a student was passing an empty classroom, and, through the open

door, happened to catch sight of a figure drawn on a blackboard. The figure gave him the

idea for a proof that had eluded him till then. Instead of being happy, the student became

upset and angry, and disqualified himself from presenting the proof. That would have been

cheating - he had outside help!


1. Why was Moore respected by his students?

2. What kind of rules did he introduce in his work?

3. What did Moore encourage? Why?

4. Is the competitive attitude useful for you?

5. Do you want to be ordered?

6. What way of working is the best: to collaborate or to work by oneself?

7. What personal features are needed for individual work?

8. What personal features are needed for work in groups?

9. Which of them coincide?

10.Which of them are the most valuable for you?


TO, TRANSLATE THEM:

meritorious

famous

marvelous

conscientious

curious

various

ingenious


1. Мор стал известен благодаря своему изобретению метода преподавания

математики.

2. При первой встрече с классом Мор объяснял основные понятия и либо

побуждал класс выявить связь между ними, либо, в зависимости от

материала, уровня сложности и способностей студентов, выводил теорему.

3. Одним из главных правил являлось то, что ты не должен был пропустить

неточность.

4. У метода Мора имелось два эффекта: метод не давал курсу превратиться в

непрерываемые лекции самого лучшего студента и создавал в классе

конкурентные отношения.


1. More never challenged the class.

2. His students competed against each other proving theorems.

3. Calling on the weakest student first Moore encouraged competition.

4. Students who were unable to prove a theorem watched someone else presenting

the proof of it.

5. Once one of his students became angry because another student had stolen papers

with his private solution of the proof of a theorem.


1. Most of Moor's (…) were (…).

2. Moore had strong (…).

3. He was respected by his students for his (…).

4. Moore (…) competitive (…) in the class.

SAUNDERSON, A BLIND MATHEMATICIAN

Saunderson (1683-1739) was blinded by smallpox in his twelfth year. Nevertheless,

amazing to relate, he was appointed in 1711 to Newton's chair at Cambridge, becoming

the fourth Lucasian Professor of Mathematics.

He was the author of a very perfect book of its kind, the Elements of Algebra, in

which the only clue to his blindness is the occasional eccentricity of his demonstrations,

which would perhaps not have been thought up by a sighted person. To him belongs the

division of the cube into six equal pyramids having their vertices at the centre of the

cube and the six faces as their bases; this is used for an elegant proof that a pyramid is

one-third of a prism having the same base and height.

Saunderson taught mathematics at the University of Cambridge with astonishing

success. He gave lessons in optics, and on the nature of light and colours; he explained

the theory of vision; he considered the effects of lenses, the rainbow and many other

matters relating to sight and the eye. These facts lose much of their strangeness if you

consider that there are three things which must be distinguished in any question that

combines geometrical and physical considerations: the phenomena to be explained; the

axioms of the geometry; and the calculation which follows from the axiom. Now, it is

obvious that however acute the blind man may be, the phenomena of light and colour

are completely unknown to him. He will understand the axioms, because he refers them

to palpable object, but he will not understand why geometry should prefer them to other

axioms, for to do so he would have to compare the axioms with the phenomena directly,

which for him is an impossibility. Тhе blind man thus takes the axioms аs they are given

to him; he interprets a ray of light as a thin elastic thread, or as a succession of tiny

bodies that strike the eyes with incredible force - and he calculates accordingly. The

boundary between physics and mathematics has been crossed, and the problem becomes

purely formal.

Saunderson invented the 'pin-board'. It consisted of many sets of nine holes, each

arranged in three rows of three, into which small pegs fitted. When he used this aid for

arithmetical calculation, at which he became extraordinarily proficient, each hole stood

for a digit. When used as a geometrical aid, he joined thе pegs with thread to form the

figures. A similar, albeit simpler, device is nowadays used by school-children as an aid

to geometry.


1. What was remarkable about Saunderson?

2. Why many wondrous things told about him are considered as reliable?

3. Was his blindness notable to others?

4. What kind of mathematical problems did he solve?

5. Why could he give lessons in optics, explain the theory of vision, in spite of being

blind?

6. Was it easy for him to achieve such results being a disabled person?

7. How can a disabled person apply his gift nowadays?

8. What do they need for it?

9. What can we do to help people like these?


TO, TRANSLATE THEM:

blindness mathematics

strangeness physics

eagerness optics

tenderness

bitterness

completeness

happiness


1. Николас Сондерсон ослеп в результате перенесенной в 12 лет оспы.

2. Сондерсону принадлежит деление куба на 6 равных пирамид с вершинами

сходящимися в центре куба и с шестью плоскостями в качестве их

основания.

3. Он давал уроки оптики, уроки о природе света и цвета, он объяснил теорию

зрения, он рассматривал эффекты линз, радугу и другие явления, связанные

со зрением.

4. Слепой человек воспринимает аксиомы так, как они ему даются, луч света

он представляет как тонкую эластичную нить или как ряд крошечных

частиц, бьющих в глаз с невероятной силой – и соответствующим образом

он делает вычисления.


1. Saunderson was blind since he was born.

2. He suggested to divide a cube into six equal pyramids to prove that a pyramid is

one-third of a prism with the same base and height.

3. Saunderson managed to explain many things sighted people couldn’t explain.

4. Though Saunderson was blind he taught optics successfully.

5. Saunderson invented the 'pin-board', a device which helps students to understand

high mathematics.


1. Saunderson achieved an (…) teaching maths.

2. A blind man understands axioms because he refers them to (…) objects.

3. Saunderson became (…) mathematics.

FABRE, SPIDERS, AND GEOMETRY

Jean Henri Fabre (1813-1915) was а brilliant entomologist who demonstrated that

insects behaved by instinct and not by reasoning comparable to more evolved species.

Curiously, although Darwin admired his work and cited him in The Origin of Species,

Fabre never accepted Darwin's theory of evolution.

Fabre referred to himself as "a surveyor of spider's webs" and in a geometrical

appendix to his The Life of the Spider he combined all his marvelous talents of

observation and analysis :

"Let us direct our attention to the nets of the Epeirae ... We shall fast observe that the

radii are equally spaced; the angles formed by each consecutive part are of perceptibly

equal value; and this in spite of their number, which in the case of Silky Epeira exceeds

two score. We know not by what strange means the spider attains her ends and divides

the area wherein the web is to be warped into a large number of еqual sectors, a number

which is almost invariable in the work of each species...

We shall also notice that, in each sector, the various chords, the elements of the

spiral winding, are parallel to one another and gradually draw closer together as they

near the center. With the two radiating lines that frame them form obtuse angles on оnе

side and acute angels on the other; and these angles remain constant in the same sector,

because the chords are parallel.

There is more than this: these same angles, the obtuse as the acute, do not alter in

value, from one sector to another, at any rate so far as the conscientious eye can judge.

Taken as a whole, therefore, the rope-latticed edifice consists of a series of crossbars

intersecting several radiating lines obliquely at angles of equal value. By this characteristic we recognize the "logarithmic spiral". Geometricians give this

name to the curve which intersects obliquely, at angles of unvarying value, all the

straight lines оr "radii vectors" radiating from a center called the "pole". The Epeira's

construction, therefore, is a series of chords joining the intersections of a logarithmic

spiral with a series of radii. It would become merged in this spiral if the number of radii

were infinite, for this would reduce the length of the rectilinear elements indefinitely

and change this polygonal line into a curve … Тhe Epeira winds nearer and nearer

around her pole so far as her equipment, which like our own, is defective, will allow

her. One would believe her to be thoroughly versed in the laws of the spiral."


1. While observing insects to what conclusion did Fabre come?

2. What was Fabre’s and Darwin’s attitude towards each other’s research work?

3. Do human beings have instincts? What are they?

4. In which situations do we behave by instinct and in which by reasoning?

5. Does our society make us suppress our instincts?


TO, TRANSLATE THEM:

curiously

equally

consecutively

perceptibly

gradually

constantly

obliquely

indefinitely

thoroughly


1. Фабре называл себя “исследователем паутин”, а в геометрическом

приложении к его изданию Жизнь паука он объединил свои удивительные

таланты вести наблюдения и делать выводы.

2. Углы, образованные каждой последующей частью, воспринимаются как

равные.

3. Мы так же должны отметить, что в каждом секторе различные хорды,

элементы спиралей параллельны друг другу и постепенно они становятся

ближе, чем ближе к центру.

4. Геометры называют термином логарифмическая спираль кривую,

пересекающую под углами с неизменными величинами все прямые линии

или “радиусные векторы”, расходящиеся из центра, называемого

“полюсом”.


1. Fabre studied spider’s webs.

2. The number of sections wherein the web depends on the species.

3. In each sector there are obtuse and acute angels whose value is constant.

4. Geometricians called the curve which intersects radii vectors at angels constant in

value the "logarithmic spiral".

5. It is believed that Epeira knows a lot about the laws of the spiral.


1. Fabre referred to himself as (…).

2. Looking at to the nets of the Epeirae we observe that the radii (…); the angles

(…) in spite of their number.

3. In each sector the chords are (…) as they near the center.

4. The angles formed by the two radiating lines and the chords do not (…) from one

sector to another.

5. "Logarithmic spiral" is the curve (…).

SONYA KOVALEVSKAYA ( 1850- 1891)

One day Professor Weierstrass was rather surprised to see a young lady present

herself before him, asking to be admitted as his pupil in mathematics. The Berlin

University was, and still is, closed to women, but Sonya's ardent desire to be taught by

the man who was generally acknowledged to be the father of modern mathematical

analysis, made her apply to him for private lessons.

Professor Weierstrass felt a certain distrust in seeing this unknown female

applicant; however , he promised to try her, and gave her some of the problems which

he had set apart for the more advanced pupils in the seminагу for mathematics. He felt

convinced that she would not be able to solve them, and forgot all about her, the more

so as her outward appearance on the first visit had left no impression at all upon his

mind. She never dressed well, and on this occasion she wore a hat which hid her face

completely, and made her look very old, so that Professor Weierstrass as he told me

himself, after having seen her for the first time, had neither the slightest idea of her age,

nor of her unusually expressive eyes, which used to attract everybody at first sight. A

week later she called again, and said that she had solved all the problems. He did not

believe her, but asked her to sit down beside him, after which he began to examine her

solutions one by one. To his great surprise everything was not only correct, but very

acute and ingenious. Now in her eagerness she took off her hat and uncovered her short

curly hair; she blushed at his praises, and the elderly professor felt something like

fatherly tenderness towards this young woman, who possessed the divination of genius

to a degree he had seldom found, even in his more advanced male pupils. And from that

moment the great mathematician became her friend for life, the most faithful and

helpful friend she could wish. In his family she was received as a daughter and sister. It

was her great object to find the logical connection between all manifestations of life, as

for instance, between the laws of thought and the outward phenomena. She could not

satisfy herself with seeing in part, and understanding in part; it was her delight to dream

of a more perfect form of life, where, according to the apostle, "we shall see no longer

in part, but face to face". To see the unity in the variety was the aim and end of all her

philosophy and her poetry.

Has she reached this end now? Our thought cannot fathom this possibility, but our

heart beats with a trembling hope which breaks the point of death's bitterness.

Besides, she had always wished to die young. Though hers seemed an inexhaustible

well of life, ready for every new impression, open to every joy, great or small, in the

innermost recess of her heart there was a thirst, which this life could never satisfy. As

her mind craved absolute truth, absolute light, so her heart craved absolute love – a

completeness which human life does not yield, and which her own character in

particular rendered impossible. It was this discord that consumed her. If we start from

her own belief in a fundamental connection between all phenomena of life, we see that

she was bound to die, not because some strong and destructive microbes had settled in

her lungs, or because the chances of her life had not brought her the happiness she

desired, but because the necessary organic connection between her inward and outward

life was missing; because there was no harmony between her thought and her feeling,

her temperament and her character'.

Anna Carlota Leffler


1. Why did Sonya Kovalevskaya desire to study mathematics?

2. What did she crave?

3. Comment the statement: outward life is a result of innerward one and reflects

innermost needs of a man.

4. What do you think about destiny and karma?


TO, TRANSLATE THEM:

family delightful

unity trustful

variety faithful

philosophy helpful

poetry

possibility

harmony


1. Пылкое желание Сони обучаться у человека, признанного

основоположником математического анализа, заставило ее обратиться к

нему с просьбой о частных уроках.

2. Профессор Виерштрасс пообещал проверить ее знания и дал несколько

заданий, которые он отложил для своих сильнейших учеников.

3. К его великому удивлению все задания были решены не только правильно,

но и очень аккуратно и изобретательно.

4. Увидеть единство в многообразии было целью и концом ее поэзии и

философии.


1. Sonya Kovalevskaya couldn’t be admitted to the Berlin University.

2. Professor Weierstrass gave Sonya problems too difficult to solve to get rid of her.

3. Sonya was so young and had so expressive eyes that Professor Weierstrass felt

fatherly tenderness towards her and took her as his pupil in spite of her average

abilities.

4. She studied connection between the laws of thought and the outward phenomena

because she dreamt of a better form of life.

5. She wished to die young because she had a serious lungs disease.


1. Once Sonya Kovalevskaya (…) before Professor Weierstrass.

2. She had аn (...) desire to study mathematics.

3. Professor Weierstrass felt (...) towards Sonya.

4. We can not (…) the possibility of the perfect form of life.

5. In the (…) of her heart she (…) the absolute love.

COMPUTER STUDIES

WHAT IS A COMPUTER ?

Computer is a device for processing information. Computer has no

intelligence by itself and is called hardware. A computer system is a

combination of four elements:

• Hardware

• Software

• Procedures

• Data/information

Software are the programs that tell the hardware how to perform a task.

Without software instructions, the hardware doesn't know what to do.

The basic job of the computer is the processing of information.

Computers take information in the form of instructions called programs and

symbols called data. After that they perform various mathematical and log-

ical operations, and then give the results (information). Computer is used

to convert data into information. Computer is also used to store

information in the digital form.


1. What does the term «computer» describe?

2. Is computer intelligent?

3. What are four components of computer system?

4. What is software?

5. What's the difference between the hardware and software?

6. In what way terms «data» and «information» differ?

7. How does computer convert data into information?


TO, TRANSLATE THEM:

processing

programming

performing

converting

storing

III. ARE THESE SENTENCES TRUE OR FALSE?

1. Computer is made of electronic components so it is referred to as electronic

device.

2. Computer has no intelligence until software is loaded.

3. There are four elements of computer system: hardware, software,

diskettes and data.

4. Without software instructions hardware doesn't

know what to do.

5. The software is the most important component because it is made by

people.

6. The user inputs data into computer to get information as an output.

IV. COMPLETE THE SENTENCES:

1. Information in the form of instruction is called a ...

2. The basic job of the computer is the ...

V. WHICH OF THE FOLLOWING WORDS HAVE EQUIVALENS WITH THE

SAME ROOTS IN RUSSIAN?

computer, diskette, metal, processor, scanner, information, data, microphone,

printer, modem, Internet.

WHAT IS HARDWARE?

Webster's dictionary gives us the following definition of the hardware —

the devices composing a computer system.

Computer hardware can be divided into four categories:

1) input hardware

2) processing hardware

3) storage hardware

4) output hardware.

Input hardware

Input hardware collects data and converts them into a form suitable for

computer processing. The most common input device is a keyboard. It looks very

much like a typewriter. The mouse is a hand-held device connected to the computer

by a small cable. As the mouse is rolled across the desktop, the cursor moves across

the screen. When the cursor reaches the desired location, the user usually pushes a

button on the mouse once or twice to give a command to the computer.

Another type of input hardware is optic-electronic scanner. Microphone and

video camera can be also used to input data into the computer.

Processing hardware

Processing hardware directs the execution of software instructions in the

computer. The most common components of processing hardware are the central

processing unit and main memory.

The central processing unit (CPU) is the brain of the computer. It reads and

interprets software instructions and coordinates the processing.

Memory is the component of the computer in which information is stored. There

are two types of computer memory: RAM and ROM.

RAM (random access memory) is the memory, used for creating, loading and

running programs

ROM (read only memory) is computer memory used to hold programmed

instructions to the system.

The more memory you have in your computer, the more operations you can

perform.

Storage hardware

The purpose of storage hardware is to store computer instructions and data and

retrieve when needed for processing. Storage hardware stores data as electromag-

netic signals. The most common ways of storing data are Hard disk, CD, DVD, CD-

ROM and a USB flash drive.

Hard disk is a rigid disk coated with magnetic material, for storing programs and

relatively large amounts of data.

CD (compact disc), DVD (digital video disc), CD-ROM (compact disc read only

memory) are a compact discs on which a large amount of digitized data can be

stored. They are very popular now because of the growing speed which their drives can

provide nowadays.

Output hardware

The purpose of output hardware is to provide the user with the means to view

information produced by the computer system. Information is in either hardcopy

or softcopy form. Hardcopy output can be held in your hand, such as paper with

text (words or numbers) or graphics printed on it. Softcopy output is displayed on

a monitor.

Monitor is a display screen for viewing computer data, television programs,

etc. Printer is a computer output device that produces a paper copy of data or

graphics.

Modem is an example of communication hardware — an electronic device that makes

possible the transmission of data to or from computer via telephone or other

communication lines.

Hardware comes in many configurations, depending on what you are going to do

on your computer.


1. What is the Webster's dictionary definition of the hardware?

2. What groups of hardware exist?

3. What is input hardware? What are the examples of input hardware?

4. What is the mouse designed for?

5. What is processing hardware? What are the basic types of memory used in a

PC?

6. What is a storage hardware? What is CD-ROM used for? Can a user record his or

her data on a CD? What kind of storage hardware can contain more

information: CD-ROM, RAM or ROM?

7. What is modem used for? Can a PC user communicate with other people

without a modem?


TO, TRANSLATE THEM:

typewriter

computer

cursor

user

scanner

printer


1. The purpose of the input hardware is to collect data and convert them into a

form suitable for computer processing.

2. Scanner is used to input graphics only.

3. CPU reads and interprets software and prints the results on paper.

4. User is unable to change the contents of ROM.

5. Printer is a processing hardware because it shows the information.

6. Modem is an electronic device that makes possible the transmission of data

from one computer to another via telephone or other communication lines.

7. The purpose of storage hardware is to store computer instructions and data.

IV. GIVE DEFINITIONS, USING THE TEXT:

1. CPU

2. ROM

3. CD-ROM

4. Printer

5. Modem

6. Hard disk

7. Keyboard

V. WHICH OF THE FOLLOWING ITEMS ARE HARDWARE:

program, mouse, CPU, printer, modem, instruction, cursor or the pointer,

keyboard, symbol

WINDOWS

Windows is an operational system based on the expanding windows principle

which uses icons to graphically represent files. It's very easy to use Internet if you

have Windows on your computer.

Windows makes the way you and your computer interact with Internet more

easy. Most everyday tasks are easier to do than before. For example, the second

mouse button has become a powerful weapon. Recycle Bin makes it easier to

recover accidentally deleted files. Your computer probably will crash less with

Windows. Microsoft says that it is moving forward to the time when we will all

think more about our data and less about the programs used to create them.

Window plug-and-play capability makes it easy to upgrade your computer

hardware. A new Windows shortcuts capability makes it easy to reach frequently

used files.

COMPUTER OPERATIONS

TYPES OF DATA

Much of the processing computers can be divided into two general types of

operation. Arithmetic operations are computations with numbers such as addition,

subtraction, and other mathematical procedures. Early computers performed mostly

arithmetic operations, which gave the false impression that only engineers and

scientists could benefit from computers. Of equal importance is the computer’s

ability to compare two values to determine if one is larger than, smaller than, or

equal to the other. This is called a logical operation. The comparison may take place

between numbers, letters, sounds, or even drawings. The processing of the computer

is based on the computer's ability to perform logical and arithmetic operations.

Instructions must be given to the computer to tell it how to process the data it

receives and the format needed for output and storage. The ability to follow the

program sets computers apart from most tools. However, new tools ranging from

typewriters to microwave ovens have embedded computers, or built-in computers.

An embedded computer can accept data to use several options in its program, but

the program itself cannot be changed. This makes these devices flexible and

convenient but not the embedded computer itself.

Types of data

With the advent of new computer applications and hardware, the

definition of data has expanded to include many types.

Numeric data consists of numbers and decimal points, as well as the

plus (+) and minus (-) signs. Both arithmetic operations and logical

operations are performed on numeric data. This means that numbers can

be used for calculations as well as sorted and compared to each other.

Text, or textual data, can contain any combination of letters, numbers and

special characters. Sometimes textual data is known as alphanumeric data.

Various forms of data that we can hear and see makes up audio-visual data.

The computer can produce sounds, music and even human voice. It can also

accept audio-information as an input. Data can also take form of drawings

and video sequences.

Physical data is captured from the environment. For example, light,

temperature and pressure are all types of physical data. In many large

buildings, computer systems process several kinds of physical data to

regulate operations. Computers can set off security alarms, control

temperature and humidity, or turn lights on and off, all in response to

physical data. These applications increase people's safety and save the time

and money.


1. In what two major parts could be computer operations divided?

2. What are arithmetic operations?

3. What are logical operations?

4. Can computer compare two graphical objects?

5. What makes computer so different from other tools?

6. What is embedded computer? What modern devices have embedded

computers?

7. How many types of data are there?

8. What is physical data?


TO, TRANSLATE THEM:

logical

mathematical

physical

special

audio-visual


1. Arithmetic operations are operations with numbers — subtraction and

division.

2. Early computers gave false impression about their capabilities.

3. Logical operations are computer's ability to compare two values.

4. The major difference between the computer and tools lies in the flexibility

of the program.

5. Embedded computers are found only in typewriters and ovens.

6. Microwave oven's program is flexible and could be changed because of the

embedded computer.

7. Numeric data consist of numbers, decimal points and the (+) and (-) signs.

8. Computer can accept human speech as an audio-visual input data.

IV. FILL IN THE BLANKS WITH SUITABLE WORDS:

1. (...) are computations with numbers such as addition, subtraction, and other

mathematical procedures.

2. The computers ability to compare two values to determine if one is larger

than, smaller than, or equal to the other is called a (...).

3. New tools ranging from typewriters to microwave ovens have embedded

computers, or (...) computers.

4. An (...) can accept data to use several options in its program, but the

program itself cannot be changed.

5. (...) can be used for calculations as well as sorted and compared to each other.

6. (...) can contain any combination of letters, numbers and special characters.

7. Various forms of data that we can hear and see makes up (...) which is

captured from the environment.

V. GIVE DEFINITIONS, USING THE TEXT:

1. Software

2. Arithmetic operation

3. Logical operation

4. Numeric data

5. Textual data

6. Physical data

7. Audio-visual data

TYPES OF SOFTWARE

A computer to complete a job requires more than just the actual equipment or

hardware we see and touch. It requires Software — programs for directing the

operation of a computer or electronic data.

Software is the final computer system component. These computer

programs instruct the hardware how to conduct processing. The computer

is merely a general-purpose machine which requires specific software to

perform a given task. Computers can input, calculate, compare, and output

data as information. Software determines the order in which these

operations are performed.

Programs usually fall in one of two categories: system software and

applications software.

System software controls standard internal computer activities. An

operating system, for example, is a collection of system programs that aid

in the operation of a computer regardless of the application software

being used. When a computer is first turned on, one of the systems

programs is booted or loaded into the computers memory. This software

contains information about memory capacity, the model of the processor,

the disk drives to be used, and more. Once the system software is loaded,

the applications software can start to work.

System programs are designed for the specific pieces of hardware. These

programs are called drivers and coordinate peripheral hardware and

computer activities. User needs to install a specific driver in order to

activate his or her peripheral device. For example, if you intend to buy a

printer or a scanner you need to worry in advance about the driver program

which, though, commonly go along with your device. By installing the driver

you «teach» your mainboard to «understand» the newly attached part.

Applications software satisfies your specific need. The developers of

applications software rely mostly on marketing research strategies trying

to do their best to attract more users (buyers) to their software. As the pro-

ductivity of the hardware has increased greatly in recent years, the

programmers nowadays tend to include all kinds of gimmicks in one

program to make software interface look more attractive to the user. This

class of programs is the most numerous and perspective from the marketing

point of view.

Data communication within and between computers systems is handled

by system software.

Communications software transfers data from one computer system

to another. These programs usually provide users with data security and

error checking along with physically transferring data between the two

computer's memories. During the past five years the developing

electronic network communication has stimulated more and more

companies to produce various communication software, such as Web-

Browsers for Internet.


1. What is a software?

2. In what two basic groups software (programs) could be divided?

3. What is system software for?

4. What is an operating system - system or applications software?

5. What is a «driver»?

6. What is applications software?

7. What is applications software for?

8. What is the tendency in applications software market in recent years?

9. What is the application of the communication software?


TO, TRANSLATE THEM:

given

used

turned on

loaded

installed

written


1. Программное обеспечение определяет порядок выполнения

операций.

2. Прикладные программы выполняют поставленную вами

конкретную задачу (удовлетворяют вашу потребность).

3. Этот класс программ самый многочисленный и перспективный с

точки зрения маркетинга.

4. Системные программы предназначены для конкретных устройств

компьютерной системы.

5. Устанавливая драйвер, вы «учите» систему «понимать» вновь

присоединенное устройство.

6. Когда компьютер впервые включается, одна из

системных программ должна быть загружена в его память.

7. Развитие систем электронной коммуникации за последние пять лет

стимулировало производствo соответствующих программных

продуктов возрастающим числом компаний-разработчиков.


1. Computer programs only instruct the hardware how to handle data

storage.

2. System software controls internal computer activities.

3. System software is very dependable on the type of application software being

used.

4. The information about memory capacity, the model of the processor and disk

drives is unavailable for system software.

5. The driver is a special device usually used by car drivers for Floppy-disk

driving.

6. It is very reasonable to ask for a driver when you buy a new piece of

hardware.

7. Software developers tend to make their products very small and with poor

interface to save computer resources.

8. Communication software is of great need now because of the new

advances in communication technologies.

9. Applications software is merely a general-purpose instrument.

10. Web-browsers is the class of software for electronic communication

through the network.

V. GIVE DEFINITIONS, USING A DICTIONARY:

1. Software

2. Driver

3. Application software

4. Operating system

5. Communication software

6. Computer

7. Peripheral device

8. Operating system

VI. WHICH OF THE FOLLOWING ITEMS ARE SOFTWARE:

1. Program

2. Mouse

3. CPU

4. Word processor

5. Modem

6. Web-browser

7. Operating system

8. Scanner

9. Developer

10. Equipment

OPERATING SYSTEMS

When computers were first introduced in the 1940's and 50's, every program

written had to provide instructions that told the computer how to use devices such

as the printer, how to store information on a disk, as well as how to perform

several other tasks not necessarily related to the program. The additional program

instructions for working with hardware devices were very complex, and time-

consuming. Programmers soon realized it would be smarter to develop one

program that could control the computer's hardware, which others programs could

have used when they needed it. With that, the first operating system was born.

Today, operating systems control and manage the use of hardware devices such as

the printer or mouse. They also provide disk management by letting you store infor-

mation in files. The operating system also lets you run programs such as the basic

word processor. Lastly, the operating system provides several of its own commands

that help you to use the computer.

DOS is the most commonly used PC operating system. DOS is an abbreviation for

disk operating system. DOS was developed by a company named Microsoft. MS-DOS

is an abbreviation for «Microsoft DOS». When IBM first released the IBM PC in

1981, IBM licensed DOS from Microsoft for use on the PC and called it PC-DOS.

From the users perspective, PC-DOS and MS-DOS are the same, each providing the

same capabilities and commands.

The version of DOS release in 1981 was 1.0. Over the past decade, DOS has

undergone several changes. Each time the DOS developers release a new version,

they increase the version number.

Windows NT (new technology) is an operating system developed by Microsoft. NT

is an enhanced version of the popular Microsoft Windows 3.0, 3.1 programs. NT re-

quires a 386 or greater and 8 Mb of RAM. For the best NT performance, you have to

use a 486 with about 16 Mb or higher. Unlike the Windows, which runs on top of

DOS, Windows NT is an operating system itself. However, NT is DOS compatible.

The advantage of using NT over Windows is that NT makes better use of the PC's

memory management capabilities.

OS/2 is a PC operating system created by IBM. Like NT, OS/2 is DOS

compatible and provides a graphical user interface that lets you run programs with

a click of a mouse. Also like NT, OS/2 performs best when you are using a powerful

system.

Many IBM-based PCs are shipped with OS/2 preinstalled.

UNIX is a multi-user operating system that allows multiple users to access the

system. Traditionally, UNIX was run on a larger mini computers to which users ac-

cessed the systems using terminals and not PCs. UNIX allowed each user to

simultaneously run the programs they desired. Unlike NT and OS/2, UNIX is not DOS

compatible. Most users would not purchase UNIX for their own use.

Windows 95 & 98 are the most popular user-oriented operating systems with a

friendly interface and multitasking capabilities. The usage of Windows 95 and its

enhanced version Windows 98 is so simple that even little kids learn how to use it

very quickly. Windows 95 and 98 are DOS compatible, so all programs written for

DOS may work under the new operating system. Windows 95 requires 486 with

16 megabytes of RAM or Pentium 75-90 with 40 megabytes of free hard disk

space.


1. What problems faced programmers in the 1940's and 1950's?

2. Why were first programs «complex» and «time-consuming»?

3. What are the basic functions of operating system?

4. What does DOS abbreviation means?

5. What company developed the first version of DOS operating system? For what

purpose? Was the new operational system successful?

6. What is the difference between the PC-DOS and MS-DOS?

7. What does the abbreviation NT stand for? Is it DOS-compatible? What

are the basic requirements for NT?

8. Who is the developer of OS/2?

9. What makes UNIX so different from the other operational systems?

10.What are the remarkable features of Windows 95?


TO, TRANSLATE THEM:

requirement

instrument

management

development

enhancement


1. Современные операционные системы контролируют использование

системного оборудования, например, принтера и мыши.

2. С точки зрения пользователя, операционные системы PC-DOS и MS-DOS

идентичны, с равными возможностями и набором системных команд.

3. OS/2 — DOS совместимая операционная система, позволяющая

запускать программы при помощи графического интерфейса

пользователя.

4. Дополнительные программы для работы с устройствами системного

оборудования были очень сложны и поглощали много времени.

5. Операционная система также позволяет запускать программы, такие

как простейший текстовый редактор.

6. DOS — наиболее распространенная операционная система для

персонального компьютера.


1. When computers were first introduced in 40's and 50's programmers had to

write programs to instruct CD-ROMs, laser printers and scanners.

2. The operational system control and manage the use of the hardware and the

memory usage.

3. There are no commands available in operating systems, only word

processors.

4. Microsoft developed MS-DOS to compete with IBM's PC-DOS.

5. NT requires computers with 486 CPU and 16 M random access memory.

6. OS/2 is DOS compatible because it was developed by Microsoft.

7. Traditionally, UNIX was run by many users simultaneously.

8. Windows 95 and Windows 98 are DOS compatible and have very «friendly»

and convenient interface.


1. Like NT, (...) is DOS compatible and provides a graphical user interface that lets

you run programs with a click of a mouse.

2. (...) is the most commonly used PC operating system.

3. (...) is a multi-user operating system that allows multiple users to access the

system.

4. (...) is an operating system developed by Microsoft, an enhanced version of

the popular Microsoft Windows programs.

5. The usage of (...) is so simple that even little kids learn how to use it very

quickly.

INTRODUCTION TO THE WWW AND THE INTERNET

Millions of people around the world use the Internet to search for and retrieve

information on all sorts of topics in a wide variety of areas including the arts,

business, government, humanities, news, politics and recreation. People

communicate through electronic mail (e-mail), discussion groups, chat channels and

other means of informational exchange. They share information and make

commercial and business transactions. All this activity is possible because tens of

thousands of networks are connected to the Internet and exchange information in

the same basic ways.

The World Wide Web (WWW) is a part of the Internet. But it's not a collection

of networks. Rather, it is information that is connected or linked together like a

web. You access this information through one interface or tool called a Web

browser. The number of resources and services that are part of the World Wide Web is

growing extremely fast. In 1996 there were more than 20 million users of the

WWW, and more than half the information that is transferred across the Internet is

accessed through the WWW. By using a computer terminal (hardware) connected to

a network that is a part of the Internet, and by using a program (software) to browse

or retrieve information that is a part of the World Wide Web, the people connected to

the Internet and World Wide Web through the local providers have access to a

variety of information. Each browser provides a graphical interface. You move

from place to place, from site to site on the Web by using a mouse to click on a

portion of text, icon or region of a map. These items are called hyperlinks or links.

Each link you select represents a document, an image, a video clip or an audio file

somewhere on the Internet. The user doesn't need to know where it is, the browser

follows the link.

All sorts of things are available on the WWW. One can use Internet for

recreational purposes. Many TV and radio stations broadcast live on the WWW.

Essentially, if something can be put into digital format and stored in a computer,

then it's available on the WWW. You can even visit museums, gardens, cities

throughout the world, learn foreign languages and meet new friends. And of

course you can play computer games through WWW, competing with partners

from other countries and continents.

Just a little bit of exploring the World Wide Web will show you what a much of

use and fun it is.


1. What is Internet used for?

2. Why so many activities such as e-mail and business transactions are possible

through the Internet?

3. What is World Wide Web?

4. What is a Web browser?

5. What does user need to have an access to the WWW?

6. What are hyperlinks?

7. What resources are available on the WWW?

8. What are the basic recreational applications of WWW?


TO, TRANSLATE THEM:

variety usage

humanity storage

activity exchange


1. Объем ресурсов и услуг, которые являются частью WWW растет

чрезвычайно быстро.

2. Каждая ссылка, выбранная вами, представляет документ, графическое

изображение, видео-клип или аудио-файл где- то в Интернете.

3. Интернет может быть также использован для развлечения.

4. Вы получаете доступ к ресурсам интернета через интерфейс или

инструмент, который называется веб-браузер.

5. Вся эта деятельность возможна благодаря десяткам тысяч

компьютерных сетей, подключенных к интернету и обменивающихся

информацией в одном режиме.

6. Пользователи общаются через электронную почту, дискуссионные

группы, чэт-каналы (многоканальный разговор в реальном времени) и

другие средства информационного обмена.


1. There are still not so many users of the Internet.

2. There is information on all sorts of topics on the internet, including

education and weather forecast.

3. People can communicate through e-mail and chat programs only.

4. Internet is a tens of thousands of networks which exchange the information

in the same basic way.

5. You can access information available on the World Wide Web through the

Web browser.

6. You need a computer (hardware) and a special program (software) to be a

WWW user.

7. You move from site to site by clicking on a portion of text only.

8. Every time the user wants to move somewhere on the web he/she needs to

step by step enter links and addresses.

9. Films and pictures are not available on the Internet.

10. Radio and TV-broadcasting is a future of Internet. It's not available

yet.


1. You access the information through one interface or tool called a (...).

2. People connected to the WWW through the local ( ...) have access to a

variety of information.

3. The user doesn't need to know where the site is, the (...) follows the (...).

4. In 1996 there were more than 20 million users of the (...).

5. Each (...) provides a graphical interface.

6. Local (...) charge money for their services to access ( ...) resources.

VI. GIVE DEFINITIONS, USING A DICTIONARY:

1. Internet

2. World Wide Web

3. Web browser

4. Internet provider

5. Hyperlinks

ANALYTICAL GEOMETRY

CARTESIAN COORDINATES

Cartesian uniquely

coordinate n. conversely

coordinate v. arbitrarily

referred mutually

similarly rectangular

parallelepiped oblique

diagonal

In a plane the position of a point is defined by two coordinates, X and Y, referred to

two straight lines OX, OY, the coordinate-axes.

To fix the position of a point in space we take three planes. These have a point O in

common and intersect in pairs in three lines X'OX, Y'OY, Z'OZ. O is called the origin,

the three lines the coordinate - axes, and the three planes the coordinate-planes.

Let P be any point. Through P draw PL parallel to XOX' cutting the plane YOZ in

L, and similarly PM and PN parallel to the other axes. Let the plane MPN cut OX in L',

and similarly obtain M' and N'. We obtain then a parallelepiped whose faces are parallel

to the coordinate-planes, and edges parallel to the coordinate-axes, and OP is a diagonal.

We then define the coordinates of the point P as the three lengths OL'=X, OM'=Y,

ON'=Z

To every point P there corresponds uniquely a set of three numbers (X, Y, Z) and

conversely to every set of three numbers, positive or negative, there corresponds a

unique point.

CONVENTION OF SIGHS

Let the positive directions along the axes of X and Y be defined arbitrarily, say OX and

OY; then in the plane XOY we may pass from OX to OY by a rotation through an angle

XOY less than two right angles. Viewed from one side of the plane this rotation is

clockwise, and from the other side it appears counter-clockwise. We define that side of

the plane from which the rotation appears to be counter-clockwise as the positive side of

the plane. Then the positive direction of the axis of Z is defined to be that which lies on

the positive side of the plane XOY. This relation then holds for each of the axes, viz., the

positive direction of the axis of Y is on the positive side of the plane ZOX. This is called

a right-handed system of Cartesian coordinates.

When the planes are mutually at right angles we call it a rectangular system, otherwise

it is oblique.


1. What are the coordinate-axes of the Cartesian system of coordinates?

2. How many coordinates are necessary to define a point in a plane?

3. How many coordinates are necessary to define a point in a space?

4. What point is called the origin?

5. What side of the plane is regarded positive?

6. What system of coordinates is called rectangular?

7. What system of coordinates is called oblique?


TO, TRANSLATE THEM:

convention arbitrarily

definition commonly

direction definitely

intersection conversely

position mutually

relation similarly

rotation uniquely

III. TRANSLATE THE FOLLOWING SENTENCES:

1. The straight lines in the same plane either intersect or are parallel.

2. The position of a point P in a line may be defined to fixed points A and B instead

of with respect to a single origin O.

3. The angle is measured from OX to OP with the usual sign convention of

trigonometry, similar convention is made for the angle, measured from OX to OP'.

4. In the general Cartesian system the planes are not necessarily at right angles. The

system will be defined by the angles between the coordinate axes, viz. YOZ= λ,

ZOX= μ , XOY= ν .

5. After the rotation of the axis OX counter-clockwise through angle 90° it will

coincide with the axis OY.

6. There is an advantage for certain problems in using oblique axes (XOY ≠ ½π)

and many formulae are as easily obtained for oblique as for rectangular axes, but

rectangular axes are often used in applications to coordinate geometry.

7. Euclid posed the question: to find a rectangle such that, when a square is cut from

it the remaining smaller rectangle has the same shape as the original.

8. The rectangular axes are generally much more convenient in practice than are

oblique (nonrectangular).


1. To define the position of a point in a plane we take two (...) lines OX and OY.

2. When the coordinate planes are mutually at right angles we

have (...) system.

3. The point of intersection of coordinate-axes is called (...).

4. The faces of a cube are at (…. ….).

5. Points in (…) can be represented by pairs of numbers.

6. The (...) which represent a point are called the coordinates

of that point.

7. The sum of two algebraic numbers is an algebraic number, and

the same (...) for the other operations of arithmetic.

V. COMPLETE THE SENTENCES:

1. The position of a point is defined by two coordinates ...

2. The position of a point is defined by three coordinates ...

3. We take two axis to define ...

4. We take three planes to define ...

5. To every point in a plane there corresponds ...

6. To every point in space there corresponds ...

7. When the coordinate planes are at right angles, we have ...

8. When the coordinate planes are not at right angles, we

have …

VI. FIND IN THE TEXT THE WORDS HAVING THE SAME ROOTS WITH THE

FOLLOWING RUSSIAN ONES:

координата, позиция, линия, параллелограм, фиксировать, диагональ, параллельный, параллелепипед, позитивный,

система, негативный.

VII. DEFINE THE POSITION OF A POINT

1. in a plane

2. in space

USING CARTESIAN COORDINATES.

POLAR COORDINATES

Euclidean initial

pair argument

determines major

assigning measured

coordinatization liberty

coordinatized convenient

It is evident from your observation that every point in the Euclidean plane has an

infinity of coordinate representations, but that each pair of coordinates of the form (± r,

θ±2nπ) determines one and only one point. The method of assigning to each point P of

the Euclidean plane a distance r and an angle θ is known more formally as a polar

coordinatization of the plane. The coordinates (r,θ) are called polar coordinates, and the

coordinatized plane is called the polar plane. The initial ray is called the polar axis, the

radius r (the segment OP) is called the radius vector, and the origin is called the pole.

Finally, the angle θ will be referred to as the argument of the point P. You can become

more familiar with this new coordinate system by comparing it with a rectangular

coordinate system. One of the major differences between them is the method by which a

point P is located in the two systems. Recall that, by convention, the first coordinate in

the ordered pair (X, Y) refers to the horizontal displacement of the point P from the

origin, and the second coordinate gives the vertical displacement from the origin. If,

however, polar coordinates are used, then the first coordinate of the pair (r,θ) determines

the distance to the point P, measured along the radius vector. If r is negative, then

measured backward along the extended vector. The angle θ, generally measured in ra-

dians, is the angle between the polar axis and the radius vector. When θ is positive, the

angle is generated in a counter-clockwise direction, and in a clockwise direction when θ

is negative. Also observe that when you construct a rectangular coordinate system you

are at liberty to choose any convenient scales for both the horizontal and vertical

distances. This is not the case when polar coordinates are used. You do not have a choice

for the θ-scale, as there are exactly 2π radians in a complete rotation of the radius vector.

Thus, no arbitrary unit angle exists for O'. You do, however, have freedom in choosing

any convenient scale when you measure distance along the radius vector.


1. What method is called a polar coordinatization of the plane?

2. What coordinates are called polar?

3. What do we call the initial ray?

4. How can you become more familiar with the new coordinate system?

5. What is the major difference between the two coordinate systems?

6. What does the first coordinate in Cartesian system refer to?

7. What does the first coordinate in polar system determine?

8. How is the angle θ measured?

9. Why has every point in a rectangular coordinate system an infinity of

representations and only one in a polar system?


TO, TRANSLATE THEM:

coordinatize displacement

symbolize argument

characterize assignment

familiarize measurement

factorize requirement

generalize movement

summarize statement

emphasize achievement

rationalize development

accomplishment


1. The equation Rx+my+nz+pw=0 represents the condition that the

point lies on the plane.

2. Points whose coordinates satisfy an equation y=f(x) can be

plotted by assigning value to x and calculating the corresponding value of y.

3. An arbitrary point of the curve y=x³ has only one degree of

freedom: it requires only one coordinate to determine the position of a point on the

curve.

4. Cartesian coordinates are particularly convenient for the investigation of problems in

metrical geometry, i.e., problems in which distances are involved.

5. The degree as a unit for measuring angles may be defined as the value of the angle

formed by dividing a right angle into 90 equal parts.

6. While a decimal representation is most convenient for practical purposes, the well-

known ratio 22/7 shows that rational approximations have their uses.

7. With a given arbitrary segment AB as a unit, one could measure any segment CD

which was an exact multiple of the unit.

8. Every problem on changing from rectangular to polar form is a problem on the

solution of a right triangle with two legs given.

9. It is sometimes necessary to locate the maximum or minimum of

a function f(x).

10. It is customary to use the same scale on both axes and we will do so unless we state

otherwise.

11.There exists a number of system of coordinates, but the most convenient is a

Cartesian one.

12.The major difference between rectangular and oblique systems of coordinates lies

in the fact that in a rectangular system the angle between coordinate planes is right.

13.In algebra we deal with numbers and also with line segments and geometrical

formations in general.

14.When we compared segments we saw that they are equal.

15.Since three mutually perpendicular planes meet in three mutually perpendicular

lines, we may also consider the Cartesian coordinates of a particle as a

displacement in the direction of these lines needed to move the particle from the

point of intersection of the three lines to its actual position.


1. A point in space (... ...) by three data, its three coordinates.

2. When we (...) distances, we are at liberty to choose units of measurement.

3. The way of (...) ordered pairs of real numbers to points in the plane is the basis of

analytic geometry.

4. If you are (...) with the rectangular system you know that the coordinate planes

intersect at right angles.

5. Usually the most (...) points to draw the graph of a straight line are those where

the line crosses the two axes.

6. The map of a country may be drawn on a (...) of 50 miles to an inch, or on any

other convenient (...).

7. A cylinder can be considered as a cone whose vertex is a point at (…).

V. COMPLETE THE SENTENCES:

1. Every point in the Euclidean plane … .

2. Each pair of coordinates determines … .

3. The coordinates (r,θ) are called … .

4. The initial ray is called ... .

5. The angle θ will be referred to as ... .

6. We can become more familiar with a polar coordinate system

by comparing it ... .

7. The first coordinate in the ordered pair (X,Y) refers to … .

8. The first coordinate of the pair (r,θ) determines ... .

9. If r is negative … .

10.The angle θ is ... .

11.When θ is positive … .

VI. SPEAK ON:

1. Polar coordinates.

2. The major difference between polar and Cartesian coordinates.

LOCUS OF A VARIABLE POINT

locus ordinate

aggregate satisfy

particular endeavour

relevant accurately

abscissa squared

associated emphasized

Consider a point P (x, y). If x and y are unspecified, P can be

anywhere in the plane defined by the axes of coordinates. But, if some

geometrical condition is imposed-for example, the distance of P from the

origin is constant the positions of P are restricted and the aggregate

of such positions, conforming to the given condition, is called the

locus of P. In a particular problem the relevant condition leads to a

relation involving the abscissa x, and the ordinate y, of any point P on

the locus, and this relation is the equation of the locus. In many

instances the locus is a single curve (a straight line is included in the

category of "curves"); it may, however, consist of two or more distinct curves, and all, or

part, of the locus may even be a single point.

In analytical geometry we are concerned with two distinct problems. In the first, a

condition is given, and it is our task to derive the equation of the locus or curve each

point of which is to be in accordance with the given condition; and no point which is not

in accordance with the given condition has coordinates which can satisfy the equation. In

the second, the equation of the curve is given (or has been found) and it is then our

endeavour to interpret this equation by investigating the properties of the curve and, if

need be, to make a sketch of the curve or even to plot it accurately on squared-paper. It

is, of course, evident that we may have the composite problem involving (1) the

derivation of the equation of the locus resulting from a given condition and (II) the

discussion of the properties of the associated curve.

One important principle requires to be emphasized. When we have derived, or if we

are given, the equation of the curve, this equation in x and y is then the analytical

condition that a point P (x,y) should lie on the curve. In particular, if a point A(x1,y1)

lies on the curve, then the values of x1 and y1 satisfy the equation of the curve; for

example, it is easily seen that the point (2, 12) lies on the curve y = 3x² for, when x = 2

then 3x² =12, and hence y =12. Further, if A (x1,y1) does not lie on the curve then the

values of x1, and y1 do not satisfy the equation.


1. Where can the position of a point P be found if x and y are unspecified?

2. When are the positions of P restricted?

3. What is the locus of P?

4. What relation is called the equation of the locus?

5. Is a straight line included in the category of curves?

6. What two distinct problems are we concerned with in analytical geometry?

7. If the equation of the curve is given what is our task?

8. What parts does a composite problem consist of?

9. What principle should be emphasized?


TO, TRANSLATE THEM:

clarify algebraic

identify analytic

justify asymptotic

satisfy geometric

simplify elliptic

specify hyperbolic


1. When the properties of a single parabola are to be investigated, it is best to use the

equations y² = kx or y² = 4ax, or the parametric equation equivalent to them.

2. The relation which holds between the coordinates x,y of the

arbitrary point P on the locus must hold no matter which point of the locus is

chosen as P.

3. Most of us have a good intuitive understanding of the concept of area as a measure

of size or extent, derived from the physical plane.

4. The problem of proving that a particular number is transcendental is difficult one.

5. If we are concerned with triangles we shall show that a triangle can be dissected

into three pieces that form a rectangle.

6. The distance between parallel tangents to a circle is constant but it is not the only

curve with this property.

7. Among all curves of given circumference the circle has the greatest area.

8. In space of three dimensions there are two fundamentally different kinds of loci, of

which the simplest examples are the plane and the straight line.

9. We shall now consider a method of determining the n constants of integration

from the initial conditions of the system.

10.A straight line is specified uniquely if we are given one point on it and the angle

which the line makes with OX.

11.It should be emphasized, that a function is never determined before its domain is

specified.

12. If two lines have a common point, the coordinates of this point satisfy the

equation of' the line and are found by solving these equations.

13. In particular if the coordinates can be separately expressed as rational algebraic

functions of one parameter the curve is called a rational algebraic curve.

14.Sometimes the solution is valid under the limited conditions imposed by our

assumptions.

15.The use of vector algebra is not restricted to the study of fluid mechanics.

16.The study of vector quantities leads into what is known as vector analysis.


1. An algebraic (...) is cut by an arbitrary plane in a finite number of points, this

number is called the order of the (...).

2. An important part of analytical geometry is the discussion

of the (...) of special curves.

3. Polar equations are rarely used in the general theory of algebraic (...), but an

algebraic equation can always be expressed in polar form and this form is useful

for (…) problems.

4. The function Ø (t) can assume only integral values and therefore cannot pass

continuously from the (...) O to the (...) n.

5. Sometimes it is almost impossible to describe physical phenomena with absolute

mathematical (...).

6. A point can be (...) as an intersection of two or more lines.

V. DEFINE THE FORM AND THE FUNCTION OF THE WORDS ENDING IN ING

IN THE TEXT.

***

loci minor

circle coincide

parabola eccentricity

ellipses conjugate

hyperbola obtainable

degenerate

CONICS

The loci: circles, parabolas, ellipses and hyperbolas, with axes parallel to the

coordinate axes, have Cartesian equations in x and y of second degree. In each case the

resulting equation was a special case of the general second-degree equation, and in all

cases we noted that no term in xy appeared. Now we are going to learn about the graphs

obtainable from the general equation and show that, with the exception of certain

degenerate cases, the resulting curve is one of the four conics.

As was mentioned before, the curve that results when a plane intersects a cone is

called a conic section. There are, however, situations in which the plane and the cone

may intersect in a single point (plane passing through the vertex of the cone), a line,

two intersecting lines, or no intersection at all between plane and cone.

THE ELLIPSE

An ellipse is defined as the set of points the sum of whose distances from two fixed

points is constant. The two fixed points denoted by F and F' are called the foci. The

distance F'F is denoted by 2c and the constant sum by 2a. A simple equation of an

ellipse is obtained by placing the foci at (-c,o) and (c,o).

An arbitrary point is denoted by P (x,y), then the equation of the ellipse is

+ =1

The points V' (-a,o) and V (a,o) are called the vertices; the line segment V'V- the

major axis, and the line segment from (o,-b) to (o,b)-the minor-axis. The origin is called

the centre C of the ellipse.

If we permitted F' and F to coincide, C would be zero and the ellipse would be a

circle radius 2a/2=a. Thus a circle is sometimes regarded as an ellipse of eccentricity

zero.

THE PARABOLA

A parabola is the locus of a point whose distance from a line varies as the square

of its distance from a perpendicular line. If the lines are taken as axes of coordinates, the

equation of the parabola is x² = ky or

y² = kx.

All parabolas are similar, for if the value of K in y² = kx is changed to λK, this is

equivalent to the substitution of λx for x and λy for y. It only changes the scale of the

graph.

The parabola y² =kx is symmetrical about the line y = 0, which is called the axis of

the parabola.

THE HYPERBOLA

A hyperbola is the locus of a point that remains in the plane and moves so that the

difference of the distances from two fixed points is constant. The two fixed points,

denoted by F and F' are called the foci.

The origin is called the centre of the hyperbola, the points V and V' the vertices, the

line segment V'V the transverse axis, and the line segment from (o,-b) to (o,b) the

conjugate axis. The equation is

– =1


1. What is the degree of Cartesian equations of the following loci: circles, parabolas,

ellipses, and hyperbolas?

2. Does the term in xy appear in the equations of conics?

3. What curve results when a plane intersects a cone?

4. When does the plane intersect the cone in a single point?

5. How can we define an ellipse?

6. How are the foci in the ellipse denoted?

7. What points of the ellipse are called the vertices?

8. In what case does the ellipse become a circle?

9. What are the properties of a parabola as a locus?

10.How can you prove that all parabolas are similar?

11.What are the properties of a point of a hyperbola?

12.What axes of the hyperbola do you know?


TO, TRANSLATE THEM:

comparable arbitrary

measurable customary

movable necessary

notable ordinary

observable primary

variable stationary


1. It is found that the only non-degenerate curves of order 2 are the ellipse,

parabola, and hyperbola; the circle is regarded as a special case of the ellipse.

2. Square is a rectangle whose sides are all equal.

3. A cone is a surface generated by a line which passes through a fixed point, the

vertex, and through the points of a fixed curve.

4. A cross section of a prism is a section that is perpendicular to the edges of the

prism.

5. A curve of order 2 is called a conic section or conic because these curves were

first obtained as plane sections of circular cones.

6. If a point moves only on a line or curve it has one degree

of freedom.

7. Any meridian plane cuts the surface in conic congruent to the

generating conic, and any plane perpendicular to this axis of revolution cuts it in a

circle.

8. The graph of an equation in two variables x and y is simply the set of all points

(x,y) in the plane whose coordinates satisfy the given equation.

9. We can regard the irrational number as the limit of a sequence of rationale,

chosen so that their squares are closer and closer to 2.

10.The graphs show clearly how the values of the function increase as x varies.

11.The Euclidean and hyperbolic geometries, which differ widely in the large,

coincide so closely for relatively small figures that they are experimentally

equivalent.

12.Conics are of three main types and we shall regard their equations which

particularly simple on account of the special choice of axes.

13.A fundamental mathematical concept is that of one-one, or (1,1) correspondence

between two sets of objects.

14.The ordinary curves which occur in elementally geometry such as straight lines,

circles and conies, have much more "regularity" than is implied by mere

continuity.

15.We will assume that the pole coincides with the origin and the polar axis coincides

with the origin and the positive X-axis.

16.The applications of conies to space mechanics are often simplified when a polar

equation of a conic is employed.

17.The projection of a circle is an ellipse, and any two perpendicular diameters of the

circle project into conjugate diameters of the ellipse.


1. A (...) is the intersection of a sphere and a plane.

2. A surface may be (...) by the motion of a line or a plane.

3. There is much in common in the generation of a cylinder and a (...).

4. The curve represented by the general algebraic equation of (...) n is called a curve

of order n.

5. If we (...) the base by b and the altitude by a, the area of rectangle will be

determined by the formula A=ab.

6. The equation of the second order represents (…) (...) – that is, curves formed by

the intersection of a plane with right circular (...).

7. The line x = 0 does not meet the hyperbola, it is called the (...) axis.

8. The graph of an equation of the second (...) in x,y is a conic section that is the

section of a (...).

9. The development of physical intuition is (...) as one of the important functions of

engineering analysis.

V. COMPLETE THE SENTENCES ACCORDING TO THE PATTERN:

When a plane intersecting a cone is perpendicular to its axis … (we have a circle in the

section).

1. When a plane intersecting a cone is not perpendicular to its axis …

2. When a plane intersecting a cone is parallel to a generating line ...

3. When a plane intersecting a cone is parallel to its axis …

4. When a plane intersects a cone ...

5. When F' and F coincide ...

VI. DEFINE THE FORM AND THE FUNCTION OF THE WORDS ENDING IN –ED,

TRANSLATE THE SENTENCES:

1. The curve represented by the general algebraic equation of degree n is called a

curve of order n.

2. The tangents are usually found by the method of repeated roots.

3. We rarely used polar equations in the general theory of algebraic curves, but we

applied them for particular problems.

4. Created by the human mind to count the objects in various assemblages numbers

have no reference to the individual characteristics of the objects counted.

5. Although the method of undetermined coefficients cannot always be used, it is

usually the simplest.

VII. SPEAK OH THE PROPERTIES OF:

1. the ellipse

2. the parabola

3. the hyperbola

THE FOLIUM OF DESCARTES

folium asimptote

straight neither

touches substitute

homogeneous

Descartes, the discover of coordinate geometry, studied the curve of

Figure 1. Its equation is x³+y³ = 3axy (1) and we see that neither x nor y

can be expressed explicitly in terms of the other.

The general equation of a straight line is Ax + By + C =0, and if we substitute for y

in (1) we get a cubic equation in x indicating that there are 3 points of intersection.

However, if the line touches the curve, or goes through its double point, 2 of the roots

will coincide. Still more special is an inflectional tangent which both touches and crosses

a curve, in this case 3 roots coincide at the point of contact. We see later that the Folium

has such a tangent. We may lose 2 roots if our line, besides going through a double

point, touches the curve there. It is general result that, for a curve through the origin, the

tangent(s) there come from the homogeneous group of terms of lowest degree in its

equation. Here this group consists of the right- hand side of (1). So the axes x=0, y=0

touch the curve at the origin.

Some lines lose points of intersection with a curve in quite a different way. Thus

the line x + y + c = 0 when combined with (1), leads to a quadratic. The vanishing of the

cubic term indicates that, as c varies, these lines all go through a point at infinity on the

curve. One of them, with c=a, when combined with (1) leads to the result a³ =0,

indicating that all 3 roots are at infinity.

This line, shown dotted in Figure 1, is an asymptote: it touches the curve at infinity.

It is in fact a rather special asymptote, for the curve has an inflection at the infinite point

of contact. This accounts for the loss of 3 roots rather than 2, and for the fact that the

curve comes in from infinity on the same side of the line at either end.


1. Who discovered the curve of Figure 5?

2. What will we get if we substitute for y in (1)?

3. When will two of the roots coincide?

4. In what case do 3 roots coincide at the point of contact?

5. At what point do the axes x=0, y=0 touch the curve?

6. What does the vanishing of the cubic term indicate?

7. What do we call the dotted line shown in Figure 5?

8. Where does the asymptote touch the curve?


TO, TRANSLATE THEM:

central eccentricity

exceptional familiarity

general infinity

horizontal perpendicularity

transversal polarity

vertical similarity


1. Frequently, special problems involve simple equations because

some of the terms of the general energy equation vanish.

2. When mathematician presents the results of his analysis, he

should state the underlying assumptions clearly and explicitly.

3. Using physical laws we write equations expressing those relations which must

hold for our particular problem.

4. It is evident that the notation y = f(x) is most appropriate in the case in which y is

defined by an explicit formula in x.

5. It is natural to ask whether every continuous curve has a definite tangent at every

point.

6. An algebraic equation of the n-th degree has n roots.

7. Physically, a point may be represented by a dot made on paper by a pencil.

8. A number a² is read "a square", the figure 2 indicates that a must be taken twice

as a factor.

9. The root sign, or the radical sign indicates that a root of a number is sought.

10.All terms of a dimensionally homogeneous equation have the same dimensions.

11.Points of inflection are determined by using the second derivative instead of the

first.

12.The plus or minus sign is to be chosen in each of the above equations according as

the circles are to be externally or internally tangent.

13.It will be found that in general a cubic curve with no double point does not possess

rational parametric equation.

VI. COMPLETE THE SENTENCES:

1. Descartes discovered ...

2. He studied …

3. Neither x nor y ...

4. We get a cubic equation if ...

5. Two of the roots will coincide if …

6. Three roots coincide when ...

7. Some lines lose ...

8. The vanishing of the cubic term …

V. TRANSLATE THE SENTENCES PAYING ATTENTION TO THE PASSIVE:

1. A vector whose end points coincide is denoted by the symbol O.

2. Any function that can be represented by a finite number of the

five basic algebraic operations is called an algebraic function.

3. The arguments, the justification of which will be dealt with

later on, are essential for our purpose.

4. Such forms as a parallelogram, a rectangle, a square, a trapezoid have already

been discussed - they are very important, as any figure bounded by straight lines

may be thought of as composed of rectangles and triangles.

5. The body is projected away from a point P with a known velocity and is acted

upon by a force which is proportional to the distance x of the body from P and

directed toward P.

6. The learner is led to some of the principal elementary ideas of group theory and

is given an opportunity of becoming familiar with them by using them in the

analysis of several notions which are important in the later development.

7. The process of successively getting rid of unknowns (elimination), which can be

applied to simultaneous linear equations, is usually taught in elementary algebra

just for the case of ordinary numbers (rational or real) as coefficients. Figure 1

APPENDIXGreek letters

Αα

Ββ

Γγ

Δδ

Εε

Ζζ

Ηη

Θθ

Ιι

Κκ

Λλ

Μμ

Alpha

Beta

Gamma

Delta

Epsilon

Zeta

Eta

Theta

Iota

Kappa

Lambda

Mu

Νν

Ξξ

Οο

Ππ

Ρρ

Σσ

Ττ

Υυ

Φφ

Χχ

Ψψ

Ωω

Nu

Xi

Omicron

Pi

Rho

Sigma

Tau

Upsilon

Phi

Chi

Psi

Omega

Mathematical formulae

= equal

≠ not equal

≈ approximately equal to

< less than

> greater than

+ plus

– minus

× is multiplied by

÷ divided by

⅔ two thirds

4 ½ four and a half

0.6 point six

2.01 two point zero one

9,510 nine thousand five hundred and ten

0.007 point zero zero seven

= the ratio of twenty to five is equal to the ratio of sixteen to four

ai a [ei] prime

aii a second prime

9³ nine cubed or nine to the third power

b–10 b to the minus tenth(power)

= 33 ⅓ four C [si:] plus W third plus M first a prime plus R a th [eiθ] is

equal to thirty three one third

the square root of four

the cube root of a

the fifth root of a square

the square root of R square plus x square

A to the m divided by nth power is equal to the nth root of a to the mth power

square root of F second plus A divided by x to the dth power

REFERENCES

1. Варнаков С.В. Учебно-методическая разработка по английскому языку для студентов

технического профиля. НГТУ, 2002.

2. Костерик Г.А. Тексты и упражнения для студентов математиков. г.Горький, 1976.

3. Агабенян И.П. Английский язык. Ростов-на-Дону, 2002.

4. Английский язык для аспирантов: Методические разработки к курсу английского

языка. Н. Новгород, 2006.

Рецензия

на учебно-методическое пособие по чтению математических текстов на

английском языке “Reading” Борщевской Ю.М. и Клоповой Ю.В.

Рецензируемое пособие предназначено для студентов математических

факультетов неязыковых вузов, изучающих английский язык и отвечает

требованиям Государственного образовательного Стандарта по высшему

профессиональному образованию.

Предлагаемый курс предназначен для самостоятельной и аудиторной

работы студентов по развитию навыков чтения и понимания оригинальной

литературы на английском языке, а также литературы по своей специальности.

Данное пособие состоит из трёх разделов, включающих оригинальные

тексты, лексические, грамматические и коммуникативные упражнения.

Пособие написано на должном теоретическом и методическом уровне и

может быть рекомендовано к опубликованию и использованию.

Доцент каф. ин. яз. ППФ,

канд. пед. наук Илалтдинова Е.Ю.

Рецензияна учебно-методическое пособие по чтению математических текстов на

английском языке “Reading”.

Авторы: Борщевская Ю.М. и Клопова Ю.В.

Рецензируемое пособие предназначено для развития таких видов речевой

деятельности как слушание, говорение, чтение и перевод при обучении

английскому языку студентов математических факультетов неязыковых

педагогических вузов и отвечает требованиям Государственного

образовательного Стандарта по высшему профессиональному образованию.

Предлагаемое учебно-методическое пособие рекомендуется для

самостоятельной и аудиторной работы студентов по развитию и

совершенствованию навыков чтения и понимания оригинальной литературы на

английском языке, а также литературы по своей специальности.

Учебно-методическое пособие состоит из трех разделов, включает

оригинальные тексты о выдающихся математиках, тексты по информатике и

математике. Авторы предлагают упражнения на контроль понимания содержания

текста, грамматические упражнения, коммуникативные задания, позволяющие

развивать необходимые навыки.

Данное учебно-методическое пособие может быть использовано как

студентами, так и магистрантами в неязыковых педагогических вузах.

Рецензируемая работа написана на должном теоретическом и

методическом уровне, содержит аутентичные материалы, является актуальной и

рекомендуется к опубликованию.

Рецензия

на учебно-методические материалы по английскому языку для студентов-

заочников высших учебных заведений Борщевской Ю.М.

Рецензируемое пособие предназначено для студентов заочного отделения

неязыковых вузов, изучающих английский язык и отвечает требованиям

Государственного образовательного Стандарта по высшему профессиональному

образованию.

Предлагаемый курс предназначен для самостоятельной и аудиторной работы

студентов по развитию навыков чтения и понимания оригинальных текстов на

английском языке, навыков монологической речи. В пособие также включены

грамматические упражнения и контрольные задания.

Данное пособие состоит из пяти разделов.

Пособие написано на должном теоретическом и методическом уровне и может быть рекомендовано к опубликованию и использованию.

Доцент каф. ин. яз. ППФ, кандидат пед. наук

Илалтдинова Е.Ю.

Рецензия

на учебно-методические материалы по английскому языку для студентов-

заочников высших учебных заведений.

Автор: Борщевская Ю.М.

Рецензируемое пособие предназначено для развития таких видов речевой

деятельности как говорение, чтение и перевод при обучении английскому языку

студентов заочного отделения неязыковых педагогических вузов и отвечает

требованиям Государственного образовательного Стандарта по высшему

профессиональному образованию.

Предлагаемое учебно-методическое пособие рекомендуется для

самостоятельной и аудиторной работы студентов по развитию и

совершенствованию навыков чтения и понимания оригинальных текстов на

английском языке, навыков монологической речи с опорой на тематические

тексты.

Учебно-методическое пособие состоит из пяти разделов, включает задания на

грамматику, контрольно-тренировочные задания, тексты для их выполнения, а

также базовые тематические тексты, сопровождаемые вопросами, для подготовки

устных монологических высказываний.

Рецензируемая работа написана на должном теоретическом и методическом

уровне, содержит аутентичные материалы, является актуальной и рекомендуется

к опубликованию.

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