Пособие по английскому языку "English Course for Mathematician". Семестр 1

UNIT 1

Pronouns

Ex. 1. Analyze the following sentences and translate them into Russian.

1. They live together with their parents. 2. Oxford is famous for its University. 3. I didn’t have an umbrella, so Ann gave me hers. 4. Are those people friends of yours? 5. Michael had an argument with a neighbour of his. 6. We went on holiday with some friends of ours. 7. I am meeting a friend of mine this evening. 8. He wants to see us at his place. 9. I can’t find my keys. Where are they? 10. We want the photographs. Can you give them to us?

Ex. 2. Put in my/our/your/his/her/their/its/mine/yours/ours.

Pronoun “it”

Ex. 3. a) We use a personal pronoun “it” as a subject or an object

1. Where is your pen? – It is in the bag. 2. Your translation is good. I like it. 3. This is our classroom. It is large. 4. Where is my ticket? I can’t find it. 5. Your new car is nice. Is it expensive? 6. I want that book. Please give it to me.

b) We use “it” as a subject with expressions that refer to time, weather, day temperature or distance.

1. It is ten miles to the nearest petrol station. 2. It is Monday again. 3. It is thirty degrees. 4. It is half past ten. 5. It is a nice day today. 6. It was very windy yesterday. 7. It was my birthday yesterday. 8. How far is it to the nearest restaurant?

c) Preparatory “it”.

1. It is nice to talk to you. 2. It was good of you to phone me. 3. It is impossible to understand her. 4. It wasn’t easy to find your house. 5. It is difficult to get up early in the morning. 6. It was a pleasure to listen to her.

the verb “to be”

Analyze the interrogative and negative forms.

Ex. 4. Make the following sentences interrogative and negative.

a) 1. Twenty miles is a long way to walk. 2. My native city is very large. 3. The pair of black trousers is cheap.4. Phonetics is a branch of linguistics. 5. The family are fond of their house. 6. The students’ books are on their desks. 7. The capital of my homeland is Minsk. 8. We are at the English lesson now. 9. The man in this photograph is my brother. 10. My father is interested in politics.

b) 1. The boy was at home three days ago. 2. My lessons were over at 2 yesterday. 3. She was ready for the seminar last week. 4. Their plans for the holiday were clear. 5. The girl’s family was very large. 6. The film at the Odeon was long and dull. 7. We were at the university yesterday. 8. Kate and Olga were pupils last year. 9. A nice play was on at the theatre last week. 10. My favourite subject at school was mathematics.

c) This book will be interesting. 2. I shall be late for the lesson tomorrow. 3. The house will be ready soon. 4. The text of the next lesson will be short. 5. Mike will be a student next year. 6. My sister will be a post-graduate in two years. 7. She will be present at the meeting on Monday. 8. It will be a nice block of flats here. 9. The students will be free in some minutes. 10. I shall be ready for the next seminar.

Ex. 5. a) Say the following sentences in the past.

1. The facts from the newspaper article are old. 2. The boy’s family is at home. 3. The students from group 2 are in the next room. 4. He is ready to read this text. 5. Their plans are simple and short. 6. The weather is good at this time of the year. 7. Bob and James are foreign students. 8. A city is a place with big industry and busy streets. 9. The article in the newspaper is interesting. 10. Sport is an essential part of Mike’s life.

1. Our street is very green in spring. 2. Children are already in bed at 9 o’clock. 3. Saturday morning is a very busy time for shopping. 4. It is not hot in winter. 5. The chief method of teaching is the lecture method. 6. Travelling by sea is very interesting. 7. The leaves are not green in autumn. 8. Our trip to Moscow is very tiring. 9. The workers are at the meeting at this time of the day. 10. At the end of the lecture she is very tired.

The Construction there is … , there are …

Read the sentences and compare the information given.

Ex. 6. Analyze the following sentences and translate them into Russian.

a) 1. There are some big trees in the garden. 2. There is a seminar on philosophy today. 3. There are comfortable apartments in this block of flats. 4. There are a lot of accidents on this road. 5. There is something in my eye. 6. There are 11 players in a football team. 7. There is a book and two pens on the desk.

b) 1. There were a lot of children in the yard an hour ago. 2. There was an important meeting of students with the Dean last week. 3. I know there were some letters for me yesterday. 4. When I got home, I was hungry but there wasn’t anything to eat. 5. There was a swimming pool at our hotel last summer.

c) 1. There will be one more department at the University next year. 2. When you arrive tomorrow, there will be somebody at the station to meet you. 3. I don’t think there will be any problems at the exam. 4. There will be dictionaries on every table. 5. There will be no underground service between Vostok and Kupalovskaya stations tomorrow.

Ex. 7. Make the sentences interrogative and negative. Follow the models.

a) Are there any new messages for me today?

Yes, there are. / No, there aren’t.

There are no (not any) new messages for you today.

How many new messages are there for me today?

1. There are twelve students in my group. 2. There are twenty six letters in the English alphabet. 3. There is only one chair in this room. 4. There are thirty days in September. 5. There is one button on my jacket.

b) Was there little time for this work?

Yes, there was. / No, there wasn’t.

There wasn’t much time for this work.

How much time was there for this work?

1. There was little water in the bottle. 2. There was only one circus in the city 50 years ago. 3. There were a lot of lights in my Christmas-tree last year. 4. There was a shop at the end of the street. 5. There were seven flowers in the vase. 6. There were three pictures on the wall near the door. 7. There was little food in the fridge.

c) Will there be a new tube station in our street?

Yes, there will. / No, there won’t.

There won’t (will not) be a new tube station in our street.

What will there be in your street?

1. There will be a meeting in the hall. 2. There will be a bridge across the river. 3. There will be one more flight to London next month. 4. There will be four seatbelts in my car. 5. There will be a traffic jam in your area.

Pre-reading activity

Read and learn the basic vocabulary terms.

Memorise the following word combinations

Reading Activity

About My Family and Myself

I believe that everything has its beginning in the family. Family is very important for every person, because it gives you a sense of stability and tradition, a feeling of having support and understanding. It seems a bit sad that families are getting so small these days. A family with three or four children is not a common thing. More often you will find many families where there is just Mummy, Dad, one kid and may be a dog. I don't know what it feels like being an only child in the family. There are three children in our family. So by modern standards we are considered to be a fairly large family.

I think I'd better start my story with my dad. His name is Ivan Petrovich. He is in his late forties, but he looks powerful and impressive. He is tall with dark hair and brown eyes and is of a strong built. My father is a research worker by profession. But about 10 years ago he had to look for a better paid job to support us. He went in for trade. At present he is trying his luck in several trade aspects. My father is determined, strong-willed, energetic. He looks very businesslike and at the same time he tries not to lose the sense of humour. And though he is very busy, he always devotes his free time to the children, mainly to my younger brother and sister because he takes me for a grown-up person, he trusts me and relies on me. He is even sure that I can be his partner in business translating some business papers and documents for him. Generally speaking my father and me are very similar in character though in appearance I take after my mother.

My mother's name is Larisa Ivanovna. She has turned 40 this year. But if you look at her you won't give her a year older than 30. My mother is a programmer by profession. Though there were no grandparents around to help my mother when we were small, she practically never gave up working. She is very interested in her work, she is a good professional and she enjoys respect from her colleagues. Mum's life is not easy, of course, because she has to keep the house in addition to her work. My mother is a quiet and charming person. She is very kind and she does a good job of being a mother. She is concerned about her appearance, tries to be in good shape, elegant and dressed according to the latest vogue, that's why she looks so good for her age.

My younger brother Sasha is only 7 years old. He studies at school. He does well at school, which makes all of us happy. He is a diligent, kind and intelligent boy. He is tall for his age, sporty and we hope he'll make a good basketball player one day.

As for my younger sister Kate, she is only 4 years of age. She is a very pretty, lively, cheerful and energetic little thing. She is very restless and it's hard for her to stay in one and the same place for more than a minute, so when the two of them are playing they make a hell of the house.

Now a few words about me. My name is Denis. I am seventeen. This year I entered the Belarusian State University. At present I am a first-year student at the Mechanics and Mathematics Faculty. I have always liked mathematics. My friends say that I am sociable, honest, helpful and cheerful, but my parents think that sometimes I am stubborn and hard to deal with. My favourite occupation is playing the guitar, reading. I am fond of sport as well.

Of course I have many remote relations: two grandmothers and a grandfather, aunts, uncles and cousins. But only my grandfather and grandmother on the mother's side live in Minsk. Though my grandma is already an elderly woman, she often visits us, helps my mother to look after the children and always brings something delicious to eat. We all enjoy her visits.

There is no «fathers-and-sons» problem in our family. We all are getting along all right and I think we are a united family. That's all I can say about my family.

Additional Vocabulary

Ex. 8. Look through the vocabulary below that may be useful when speaking about your family.

Looks and Appearance

Features of Character

Interests and Ambitions

Family Members and Relations in the Family

Post-reading Activity

Ex. 9. Answer the following questions.

1. How old are you? 2. Where are you from? 3. Where and when were you born? 4. What are your good habits? 5. Who do you most take after? 6. Do you easily make friends? 7. Are you on friendly terms with all your group mates? 8. What talents do you think you have? 9. Is it necessary to have a hobby? Why? 10. What is the right age for young people to get married? 11. Are you for small or large families? 12. What do you do if your parents are not right (in your opinion)? 13. What do your parents make you do that you don't like doing? 14. What is your parents' attitude to your friends? 15. Why does the fathers-and-sons problem always exist? 16. What is your idea of a good husband (wife)? 17. What does family happiness depend on?

Ex. 10. Arrange the following words in pairs of antonyms and translate them.

Ex. 11. Study the list of professions in the box and guess the profession of each person.

Ex. 12. Translate into English making use of the words from the box.

1. У ее брата очень широкие плечи. 2. Она симпатичная, а вот сестра ее некрасивая.3. Сегодня она чувствует себя нехорошо и кожа у нее бледная.4. Невысокого роста и толстые дети часто бывают стеснительными. 5. Моей подруге нравятся молодые люди с бородой и карими глазами.6. У близнецов моей сестры кудрявые волосы. 7. Какие девушки нравятся твоему двоюродному брату? – Рыженькие. 8. Все люди хотят быть стройными. 9. У моего племянника курносый нос и полноватые щечки, он похож на отца. 10. Мой друг добрый и честный, но очень уж ленивый.

Ex. 13. Put in it or there

1. … rains a lot in winter. 2. … was a strong wind yesterday. 3. Is … a bookshop near here? 4. … was a nice day yesterday. 5. We can't go skiing. … isn't any snow. 6. … is hot in this room. Open a window. 7. I was afraid because … was very dark. 8. … was a storm last night. Did you hear it? 9. …is a long way from here to the nearest shop. 10. … wan’t anything on television last night. 11. How far is … from Milan to Rome?

Ex. 14. Put in him/her/yours etc.

1. Where's Ann? Have you seen … ? 2. Where are my keys? Where did I put … ? 3. That is not my bag, … is black. 4. This letter is for Bill. Can you give it to … ? 5. We wrote to John but he didn't answer … letter. 6. “I can't find my pen. Can I use … ?” “Yes, of course.” 7. We're going to the cinema. Why don't you come with … ? 8. Can we use your washing machine? … is broken. 9. Did your sister pass … exams? 10. Tom invited some friends of … to the restaurant. 11. Some people talk about … jobs all the time. 12. Last night I went out for a meal with a friend of … . 13. We had dinner with a neighbour of … .

Ex. 15. Fill in the blanks with the necessary form of the verb to be.

1. I … at home now. My room … small. 2. He … at the University yesterday. 3. We … in the man’s house last week. 4. Our work … over tomorrow. 5. The girls … in the next room now. 6. Next year she … a teacher of English. 7. The children … at home at this time of the day. 8. My friend … in bed tomorrow because he is ill. 9. My brother … at school at 2 o’clock yesterday. 10. This time last year Jack … in Paris. 11. Today the weather … nice, but yesterday it … very cold. 12. It … a public holiday yesterday. 13. When I was a child, I … afraid of dogs.

Ex. 16. Ask special questions.

1. Her desk is in the room (what, where). 2. These houses are old (what). 3. We are in the classroom (who, where). 4. They will be ready soon (who, when). 5. She was a post-graduate last year (who, when). 6. The work will be over tomorrow (what, when). 7. They were ready to begin the work (who, what). 8. I was at the University last week (where, when). 9. The next text is in the note-book (what, where). 10. They will be students next year (when). 11. This ancient monastery is a museum now (what).

Ex. 17. Translate into English.

1. Завтра будет урок английского языка. 2. Эта книга моя или твоя? 3. Сегодня солнечно, но не тепло. 4. Это не мой пиджак, мой черный. 5. Десять минут назад дети были в саду. 6. Было приятно послушать ее рассказ. 7. В этом тексте для меня нет новых слов. 8. Двух студентов не было на уроке английского языка в прошлую пятницу. 9. Сейчас это их проблема, а не наша. 10. До ближайшего почтового отделения 500 метров. 11. Будет интересно увидеть ее в этом новом фильме. 12. Сколько страниц в этой книге?

Ex. 18. Writing. Using the words given in the list for the text do the following assignments.

UNIT 2

The verb “to have”

In questions and negative sentences the following forms are used.

The verb to HAVE is also used for many actions and experiences.

Ex. 1. Make the sentences interrogative and negative.

8. The boy had his father’s blue eyes.

Ex. 2. Say the following sentences in the past.

1. They have a few lectures this week. 2. He has much work to do this summer. 3. You have an interesting seminar today. 4. He has good ideas how to spend the weekend. 5. My parents have a nice little dog. 6. My friend has a reasonable answer. 7. They have lots of visitors in the Art museum. 8. Pete has many bookshelves in his room. 9. Olga has got a black leather bag. 10. Our students haven’t got much free time in winter.

Ex. 3. Say the following sentences in the future.

1. On Sunday my brother has breakfast at 9. 2. We have special seminars on Wednesday and Friday. 3. He has got a lot of publications. 4. Students have examinations in winter and in summer. 5. She has 3 hours at her disposal. 6. Our city has many green parks. 7. They haven’t got any money to pay their bills. 8. Our paper usually has much information about science. 9. First-year students have English classes two times a week. 10. My friend’s father has got a fine collection of pictures.

Present, Past, Future Simple

Present Simple

The Present Simple tense denotes:

Ex. 4 . Make the following sentences interrogative and negative.

1. We do a lot of things in our free time. 2. The shops open at 9 o’clock and close at 5.30. 3. It costs a lot of money to stay in luxury hotels. 4. The Moon goes round the Earth. 5. They usually sit for hours without saying a word. 6. She keeps her room tidy as a rule. 7. Mother makes strawberry jam every year. 8. People traditionally prepare coloured eggs at Easter. 9. A new school opens next week. 10. My father shaves every other day. 11. Once a week Dave stays in the office till six o’clock. 12. The water in this lake freezes in winter.

Ex. 5. Write sentences using these words. Put the verb in the right form (arrive or arrives etc.).

Past Simple

The Past Simple tense describes:

Ex. 6. Make the following sentences interrogative and negative.

Ex. 7. Write sentences about the past (yesterday / last week etc.).

Future Simple

The Future Simple tense denotes:

Facts to be remembered

Ex. 8. Make the following sentences interrogative and negative.

Types of Questions

General

Special (except the subject)

Special (to the subject)

Pre-Reading Activity

Guess the meaning of the following words.

Mathematician [,mxTImq`tIS(q)n], founder [`faundq], progress [`prqugres]

information [Infq`meIS(q)n], privilege [`prIvIlIG], union [`jHnIqn], especially [I`speS(q)lI], comfortable [`kAmf(q)tqbl].

Read and learn the basic vocabulary terms.

Memorise the following word combinations.

Reading Activity

A Letter to a Friend

Dear Linda,

I’m very sorry for the delay in answering your recent letter. I was so awfully busy. In the spring I passed my A-Level examinations and tests at school and managed to get good results. Now I am a first-year student at the Mechanics and Mathematics Department at the Belarusian State University. It certainly is a great privilege to belong to the faculty among whose founders were outstanding mathematicians.

I have so much to tell you about my life in Minsk. I live in the students’ hall of residence and share the room with two other girls. One of them is from Gomel, the other girl is from Brest. As a matter of fact they are not only my room-mates but also my good friends. We have a nice and comfortable room, it faces South.

And now I would like to describe the routine I more or less follow everyday. During the week I usually wake up at 6.30 a.m. I sometimes lie in bed for five minutes but then I have to get up. I have a shower, clean my teeth and at 7 a.m. I’m ready for breakfast. In the morning I don’t bother to cook very much, so I have a light breakfast. We usually have lectures and seminars in the morning and sometimes in the afternoon. On some days lessons flash by very quickly, but sometimes they drag more slowly, especially when we write tests or have some colloquium. In general I enjoy my university hours because they are instructive and interesting. After classes we have dinner at the students’ dining room and sometimes go to the reading-room, where the computer-based information is available six days a week.

Oh, I haven’t told you yet that I learned how to use a computer and bought one for myself. But one thing worries me greatly. Once people managed to write and think using their brains, but now people can’t do anything without these machines. On the one hand, I am for progress. It is impossible to imagine our life without computers nowadays. But on the other hand, I’m against everything depending on pressing a button.

If I don’t go to the library, I get back to the hall of residence and try to have a nap, especially if I had a late night. Then I am busy doing my homework. It usually takes me two or three hours.

I don’t only attend lectures and read books here. I have the chance of developing myself as a person. Students organize clubs and societies covering various areas such as sport, drama, music, dances, etc. Every university has a students’ union which organizes recreational facilities and entertainments. As you remember, I used to play tennis, but I don’t anymore. Here I joined the Athletics Club. We compete in area, regional and national competitions. So on weekdays I am up to my neck in work and often very tired by the end of the day. Most evenings I go to bed at about 11.30 p. m. and fall asleep very quickly.

The weekends are different. On Sunday I have a lie-in. In the evening I often go out. There is so much to see and so many places to go to in Minsk. Why don’t you come for two or three days? I’d love to see you.

My best regards to your parents.

Yours, Kati

Post-Reading Activity

Ex. 9. Answer the following questions.

1. Do you take a cold or a hot shower in the morning? 2. What time do you leave home to get to university? 3. Have you ever been late for classes? 4. How many classes do you have every day? 5. Eating is such a waste of time and effort, isn’t it? It would be better if we could simply take pills. 6. What is your idea of a good rest after classes? 7. How long does it take you to prepare your homework? 8. What sports are you good at? 9. Do you take part in any organized sporting activities? 10. Do you prefer to stay in or go out in the evening? 11. What is your favourite pastime? 12. Do you make any plans for the weekend? 13. Do you like to spend your free time with your friends or on your own? 14. How often do you go to the cinema (to the theatre)? 15. Why do some people prefer to watch films at the cinema instead of relaxing in front of their TV sets? 16. Are theatres as popular now as they used to be? 17. What is the best time for you to go to bed?

Ex. 10. Find the Russian equivalents for the following English word combinations.

Ex. 11. Read what Sharon says about a typical working day:

I usually get up at 7 o'clock and have a big breakfast. I walk to work, which takes me about half an hour. I start work at 8.45. I never have lunch. I finish work at 5 o'clock. I'm always tired when I get home. I usually cook a meal in the evening. I don't usually go out. I go to bed at about 11 o'clock. I always sleep well.

Yesterday was a typical working day for Sharon. Write what she did or didn't do yesterday.

Ex. 12. Complete the sentences. Use I’ll (I will) + one of these verbs:

Ex. 13. Write sentences beginning I think... or I don't think... .

Ex. 14. Ask special questions.

1. They had an important paper in the desk. (what, where) 2. Five girls from our group live in the hall of residence. (how many) 3. Paul and Jim played tennis yesterday. (when) 4. This student has got three lectures today. (how many) 5. His friends work hard all day. (whose) 6. Professor Smirnov will hold a seminar tomorrow. (what, when) 7. These men have a logical plan. (who) 8. It took me two hours to do my homework yesterday. (how long) 9. We will probably go to Scotland for our holiday. (where) 10. We usually have our meals in the kitchen. (where) 11. I like a big breakfast in the morning. (who, when) 12. Sally goes to the theatre once a month. (how often) 13. My cousin won one million rubles in the lottery. (how much)

Ex. 15. Translate into Russian.

1. I overslept this morning because I had a late night yesterday. 2. Helen will stay in this evening. 3. Did you go out last Sunday? 4. At the end of each term students are always up to their neck in work. 5. Jennifer and her room-mate get on well because they respect each other. 6. Jack left his house a bit late in the morning, missed the bus and was late for classes. 7. We have a long lunch break but I never go to the University canteen. 8. At times there are other things to do like going shopping, doing sports and so on. 9. Later in the evening Kate does a bit of painting which is a sort of a hobby for her. 10. I used to go fishing when at school, but now I haven’t got any time to do that.

Ex. 16. Translate into English.

1. Летом я принимаю душ по утрам, а зимой я часто принимаю ванну. 2. В Минске есть много мест отдыха и развлечений. 3. Твоя квартира выходит окнами на юг или на север? 4. Я занимаюсь английским в выходные дни, так как я по горло загружен работой в течение недели. 5. К сожалению, у меня очень мало времени на отдых. 6. Моя подруга никогда не опаздывает на первую лекцию. 7. В наше время не так уж легко поступить в университет. 8. Если вечером я ложусь поздно спать, то на следующий день я стараюсь поспать немного днём. 9. Здесь у меня есть возможность играть в теннис два раза в неделю. 10. Как правило, рабочая неделя пролетает очень быстро. 11. Катя живёт в студенческом общежитии №7, и с ней в комнате живут ещё две девушки.

Ex. 17. Writing.

UNIT 3

Continuous tenses

Present Continuous Tense

Ex. 1. Compare and analyze the usage of Present Simple Tense and Present Continuous Tense.

1. I usually watch TV in the evenings. I am watching TV now. 2. Are you looking for a key now? You always look very smart. 3. Why are you not wearing your new dress now? She usually wears fashionable clothes. 4. Today it is raining heavily outside. It rains heavily in autumn in this part of the country. 5. He walks very slowly as a rule but now he is walking fast. 6. I usually don’t rest after university, but today I’m very tired and I am having a rest. 7. I think I will be on holiday next month. I am going on holiday next month. 8. We live in Washington, though we are staying in London at the moment. 9. I play tennis every week. Where are the children? – They are playing tennis on the court now. 10. The foreign scientists are flying back to Europe tomorrow. Some passenger planes fly faster than sound.

Past Continuous Tense

Ex. 2. Compare and analyze the usage of the Past Simple Tense and the Past Continuous Tense.

1. I dropped my bag when I was running for a bus. 2. I played computer games yesterday. I was playing computer games at 3 o’clock yesterday. I was playing computer games the whole evening yesterday. 3. When I came into the kitchen, mother was cooking. 4. Did you do your homework yesterday? – I was doing my homework from 6 till 9 o’clock yesterday. 5. She always looked very smart. When I met her in Rome, she was wearing a long beautiful dress. 6. Father came home at 5 o’clock yesterday. Then he was reading a newspaper while mother was watching TV.

Future Continuous Tense

Ex. 3. Compare and analyze the usage of the Future Simple Tense and the Future Continuous Tense.

1. Tomorrow I will begin decorating my flat as soon as I come home from the market. I’ll be decorating it from 2 till 6 o’clock. 2. I think I’ll use a bike to get to school tomorrow. Will you be using your bike this evening? 3. Richard will be cleaning the house while Sue is cooking dinner. 4. This time tomorrow evening my friends will be flying over France. They’ll probably go to the UK too. 5. I think I’ll take an umbrella because it is still raining. They say it will be raining the whole week-end.

Ex. 4. Make the following sentences interrogative and negative.

This time next month I will be sitting on the beach. 2. Mr. Molden was driving a car at the time of the accident. 3. Peter will be working the whole evening tomorrow. 4. The little boy was swimming in the sea the whole morning. 5. Yesterday the teams were playing football from 2 till 5 o’clock. 6. It is getting cooler and cooler day by day. 7. Mr. Pitt is talking on the phone at the moment. 8. The Browns are moving house next week. 9. In two years’ time he will be living in the country.

Pronouns some, any, no

Ex. 5. Analyze the following sentences and translate them into Russian.

1. Are there any English books in the library? 2. I can’t find any mistakes in your dictation. 3. I’d like to have some more jam. 4. Can you give me some more information? 5. There is some sugar in the cake but there is no salt. 6. What book shall I take? – Any you like. 7. Take some juice, please. It’s very tasty. 8. Would you like some time to finish your work? 9. I know some funny jokes. 10. No students are happy to have extra seminars. 11. I can do it without anybody’s help. 12. Once I ate some ten ice-creams a day. 13. I want to know if you have done anything good in your life. 14. Can I have some of these books?

Ex. 6. Chose the right word.

Ex. 7. Answer the following questions using the pattern below.

- Have you got any sisters?

- Yes, I have some.

- No, I have no sisters.

- No, I haven’t any sisters.

1. Do you want something to eat? 2. Have you got any news? 3. Do you know anybody in the village? 4. Have you invited anybody to the party? 5. Do you understand anything? 6. Was there anything interesting at the exhibition? 7. Do you have any energy left? 8. Have you seen John anywhere? 9. Is there any coffee in the coffee-pot?

Pre-Reading Activity

Guess the meaning of the following words.

system n. ['sIstqm], symbol n. [sImbl], positive adj. ['pOzItIv], diagram n. ['daIqgrxm], complex adj. ['kOmpleks], rational adj. ['rxSqnl], fundamental adj. [ֽfAndq'mentl], fact n. [fxkt], express v. [Iks'pres], negative adj. ['negqtiv], start n. [sta:t], position n. [pq'zISn], direction n. [dI'rekSn], occupy v. [`OkjupaI], zero n. [`ziqrou], different adj. ['dIfrent], basic adj. [`beIsIk].

Read and learn the basic vocabulary terms.

number (n) [`nAmbq]- число, количество, номер

date back to (v) [`deIt] – датироваться, относиться к определенному времени

antiquity (n) [xn`tIkwItI]- древность, античность

integer (n) [`IntIGq]- целое число

aid (n) [`eId] - помощь

complete (v) [kqm`plJt] - завершать, делать полным

fraction (n) [`frxkSn] - дробь

imaginary (adj) [I`mxGInqrI] - мнимый

count (v) [`kaunt] - считать

real (adj.) [rIql] - действительный

unity (n) [`jHnItI] - единица, единство

establish (v) [Is`txblIS] - устанавливать

ratio (n) [`reISIOu] - отношение, пропорция

negative (adj) [`negqtIv] - отрицательный

division (n) [dI`vIZn] - деление

either (conj.) [`aIDq] - любой, каждый

allow (v) [q`lau] - позволять, допускать

divisor (n) [dI`vaIzq] - делитель

quotient (n) [`kwOuSnt] - частное, отношение

include (v) [In`klHd] - заключать, содержать в себе

special (adj.) [`speSql] - особый, специальный

compose (v) [kqm`pouz] - составлять

Memorize the following word combinations

Reading Activity

Numbers

The beginning of our number system dates back to antiquity where symbols, which we call positive integers, were used as an aid in counting, and only in the nineteenth century the system, which we know today, was completed. As an aid in studying this number system, let’s use the diagram.

The first numbers we use are the positive integers, and the fundamental fact that there is a first integer, unity, but not a last is soon established. Later positive fractions, or numbers, which can be expressed as the ratio of two of these integers, are used and understood. Then it is seen that these integers and fractions can be negative as well as positive. The division point between the positive and negative numbers which is the position from which we start to count in either direction, is occupied by the number zero. This number is different from all others in that we are not allowed to use it as a divisor.

The positive integers are often written without the plus sign, thus we may write 789 instead of + 789. Since zero is neither positive nor negative, it has no sign.

If we take a straight line and label a point on the line 0 and another point +1, we impose a scale on the line in terms of which we can mark off the line with the positive numbers to the right of 0 and the negative numbers to the left.

To each point on the line we assign a number whose length is the distance of the point from zero and whose sign + or - is determined whether the point is to the left or right of zero. The numbers in this uncountable set are known as the real numbers. The integers correspond to a small subset of the reals.

The positive and negative integers and fractions, together with zero, are called rational numbers.

Besides rational numbers we find irrationals, which are defined as numbers that cannot be expressed as the quotient of two integers. The √2; -√3 and π are examples of such numbers.

The two classes of numbers, rational and irrational, form the real number system, which we shall use in the first part of our course. Later we shall study such numbers as √-2, -√-1, etc., which are called imaginaries; and finally it will be seen that the basic system of all numbers is the complex, in which the reals and imaginaries are included as special cases. 2+ √-3 is such a number and we see, that it is composed of a real and an imaginary parts.

To denote the part of a complex number, we use the notation R (a + bi) = a for the imaginary part.

Arithmetic is performed on complex numbers in the same way as on real numbers, except that i2 is replaced by - 1 whenever it occurs.

Post-Reading Activity

Ex. 8. Answer the following questions.

1. What were positive integers used for? 2. When was the number system completed? 3. Are the first numbers which we use the positive integers or the negative ones? 4. Is unity a first or a last integer? 5. By what is the division point between positive and negative numbers occupied? 6. What are rational numbers? 7. Can irrational numbers be expressed as quotients of two or three integers? 8. What numbers are called imaginaries? 9. What do we assign to each point on the line? 10. What do we use to denote the real part of a complex number?

Ex. 9. Find the Russian equivalents for the following English word combinations.

1. in either direction; 2. imaginaries; 3. is composed of; 4. real and imaginary parts; 5. a quotient of two integers; 6. the number system; 7. to denote the real part; 8. is replaced by; 9. the basic system; 10. in terms of; 11. to correspond to a subset.

a. основная система; b. система чисел; c. действительные и мнимые части; d. в любом направлении; e. заменяется; f. обозначать действительную часть; g. состоит из; h. мнимые числа; i. частное двух чисел; j. через, посредством; k. соответствовать подмножеству

Ex. 10. Give the proper English equivalents for the Russian expressions.

1. … is occupied by the number zero. 2. The irrationals can not be expressed as …. 3. Positive fractions or numbers can be expressed as…of two of these integers. 4. We are not allowed to use the number zero as… 5. The beginning of our number system dates back to… 6. The real number system is formed of… 7. Numbers √-2, -√-1 are called… 8. The expression 2+√-3 is composed of… 9. To denote the real part of a complex number we use…

Ex. 11. Open the brackets putting the verbs in the correct form.

1. Why you (look at) me like that? 2. We (read) a book while he (cook) lunch at that time yesterday. 3. This time next month I (to cross) the Pacific Ocean. 4. I (wait) for you when you come out. 5. He (sit) in a café when I saw him. 6. I (go) to the cinema tonight. 7. Look! She (wear) the same dress as me. 8. Yesterday at 8 o’clock we (watch) the football match. 9. He (drive) his car himself today. 10. Great news! Jack (come) in a week.

Ex. 12. Fill in the blanks with the pronouns from the box.

1. Is there … juice left in the fridge? 2. Could I have … coffee? 3. Has … called me? 4. Is there … I can do for you? 5. She said … very interesting. 6. Don’t go … tonight. 7. When I came home there was … there. 8. Does … know … funny jokes? 9. Would you like ... more tea? 10. Did you notice … strange about him? 11. There is … time left at all. 12. We can rarely meet … as brave as he is.

Ex. 13. Ask special questions.

1. The students are applying irrationals in the given mathematical problems. (Who?) 2. The teacher is explaining how to mark off the line with numbers. (What?) 3. There are some positive numbers in the expression. (What?) 4. He was trying to find the common ratio of the three fractions from 3 until 5 o’clock. (How much time?) 5. We will be using this notation to introduce imaginaries next term. (When?) 6. The students are doing the research now. (Who?) 7. At 4 o’clock yesterday Professor Clarkson was delivering a lecture. (When?) 8. This time next month we will be having a winter session. (What?) 9. They are solving some mathematical problems at the moment. (Who?) 10. We are going on a summer holiday in a couple of days. (When?)

Ex. 14. Translate from English into Russian.

1. We will be considering complex numbers next term. 2. They are trying to find the quotient of these two numbers. 3. This time last week we were having a holiday. 4. We are substituting unknowns for irrationals to get a right result. 5. The researchers were using this equipment all month long. 6. Are there any irrational numbers in this system? 7. The students were finishing the test on mathematics when the bell rang. 8. The delegation of scientists is coming to Minsk in a week. 9. This time next term the students of MMF will be celebrating the birthday of the faculty. 10. I don’t see any other ways to arrange this matter. 11. I can do it without anybody’s help. 12. You can take any of these books.

Ex. 15. Translate from Russian into English.

1. Студенты выполняют контрольную работу сейчас. 2. Группа аспирантов отправляется в Германию в декабре. 3. Мы будем использовать комплексные числа в следующем семестре. 4. В это время через неделю мы будем сдавать экзамены. 5. Мы решали эту задачу целый урок вчера. 6. Мы стараемся найти частное этих целых чисел. 7. Что ты делаешь завтра после занятий? 8. В это время вчера мы обедали в столовой. 9. Что ты делал, когда я позвонил тебе? 10. Некоторые из этих числовых систем сложны. 11. Студенты выбирают мнимые и иррациональные числа из данных выше.

UNIT 4

CAN

Ex. 1. Analyze the following sentences and translate them into Russian.

1. She could do sums in her head when she was 6 years old. 2. Peter was able to carry out the experiment successfully, but Nick couldn’t finish it without any help. 3. I can speak three languages but I can’t spell in any of them. 4. Will you be able to notice the difference between these two proofs? 5. Can I discuss the subject with my group-mates? 6. Could you tell me the way to the University? 7. You can’t use these dangerous materials in your research. 8. When she sings you can hear her all over the house. 9. Can I do anything for you? 10. You can get this book at the library. 11. Anybody can make mistakes. 12. Can (could) you show me these data? – I’m afraid I can’t. 13. You can speak to Jane now. 14. Could you spell your name for me?

MAY

Ex. 2. Analyze the following sentences and translate them into Russian.

1. The students may not use the calculator at the exam. 2. Professor, may I take the exam next week? 3. Were students allowed to visit the laboratory? 4. The answer may give the key to the whole problem. 5. Will he be allowed to take part in the conference? 6. The teacher may ask you to stay after the lessons and copy the text. 7. You are not allowed to use the machine without permission. 8. You may do the rest of the work tomorrow. 9. May I smoke here? – No, you mustn’t. 10. May I take this map? – No, you may not. 11. May he wait for us in the hall? – Yes, he may.

MUST

Ex. 3. Analyze the following sentences and translate them into Russian.

1. As a postgraduate student you must obtain some new scientific results. 2. Must we send them the results of our work immediately? – Yes, do please. 3. You must pay more attention to details. 4. The door to the laboratory must not be left open. 5. The meeting is at 10 o’clock sharp and you mustn’t be late. 6. He must be at the library now. 7. You must let him know about it. 8. You must be tired after your hard work. 9. Must I type the document? – No, you needn’t. 10. People must not cross the border without passports. 11. Everyone must go to school. 12. Must we measure the perimeter? – Yes, you must. 13. Must I really help him with the translation?

TO HAVE TO

Ex. 4. Analyze the following sentences and translate them into Russian.

1. Do I have to present another schedule? 2. I had to explain the rule twice to make it perfectly clear. 3. They didn’t have to change the date of the conference. 4. You‘ve got to study the relation between these two discoveries. 5. Does she have to wear glasses? – Yes, she does. 6. They will have to arrange everything for the meeting. 7. Did you have to walk all the distance to the station yesterday? 8. Do we have to define prime numbers? – No, you needn’t. 9. Have I got to make another drawing? – Yes, you have.

TO BE TO

Ex. 5. Analyze the following sentences and translate them into Russian.

1. The students are not to take the books out of the reading-room. 2. Were they to meet at four o’clock at the University? 3. You are to write an abstract of your thesis. 4. Am I to follow you? 5. We are to have six lessons of English this week. 6. You are to give the books back to the library at the end of the year. 7. The concert was to take place yesterday. 8. Who is to meet Jack? 9. She was to finish school last year. 10. The lessons are to begin at eight o’clock. 11. Is she to make a speech? – Yes, she is.

NEED

Ex. 6. Analyze the following sentences and translate them into Russian.

1. Need we continue working by this plan? 2. You needn’t do all this in written form, you know. 3. He didn’t need to read his paper at the seminar. 4. Do you need to write sentences about numbers in all branches of mathematics? 5. Need you worry about the man who always deceives you? 6. They needn’t hurry now. They will have to wait for another train. 7. Need I come myself? – Yes, you must. 8. Need we perform any other construction? – No, you needn’t.

SHOULD, OUGHT TO

Ex. 7. Analyze the following sentences and translate them into Russian.

1. You shouldn’t miss lectures and seminars if you want to pass the exams. 2. If you want to know mathematics you should work hard at it. 3. Doctor, what should I do? 4. You ought to go further with this investigation. 5. Ought you to tell everybody what has happened? 6. You ought not to participate in their useless argument. 7. You should switch off your mobile in class. 8. They ought to ban smoking in public places.

Pre-Reading Activity

Guess the meaning of the following words.

Decimal [`desIm(q)l] adj, combination [,kOmbI`neISqn] n, positive [`pozItIv] adj, negative [`negqtIv] adj, symbol [`sImbql] n, plus [plAs] n, minus [`maInqs] n, indicate [`IndIkeIt] v, sum [sAm] n, product [`prodqct] n, numeration [,nju:mq`reISqn] n, base [beIs] n, arithmetic [q`rITmqtIk] n, system [`sIstIm] n, represent [,reprI`zent] v

Read and learn the basic vocabulary terms.

number (n) [`nAmbq] число, количество; v перечислять

numeral (n) [`nju:mqrql] цифра, символ, число

digit (n) [`dIGIt] цифра

value (n) [`vxlju:] величина, значение; (v) ценить

derive (v) [dI`raIv] происходить, получать

introduce (v) [,Intrq`djHs] вводить, представлять, знакомить

denote (v) [dI`nqut] обозначать, отмечать, означать

determine (v) [dI`tE:mIn] определять, устанавливать

invent (v) [In`vent] изобретать, создавать, придумывать, открыть

enable (v) [I`neIb(q)l] давать возможность, делать возможным

appear (v) [q`pIq] появляться

sign (n) [saIn] n знак, v подписывать

addition (n) [q`dIS(q)n] сложение

add (v) [xd] складывать

addend (n) [x`dend] слагаемое

subtraction (n) [sqb`trxkS(q)n] вычитание

subtract (v) [sqb`trxkt] вычитать

minuend (n) [`mInjuqnd] уменьшаемое

subtrahend (n) [`sAbtrqhend]вычитаемое

difference (n) [`dIfqrqns] разность

inverse (adj) [In`vE:s] обратный, противоположный

multiplication (n) [,mAltIplI`keIS(q)n] умножение

multiply (v) [`maltIplaI] умножать

multiplicand (n) [,mAltIplI`kxnd] множимое

multiplier (n) [`mAltIplaIq] множитель

factor (n) [`fxktq] сомножитель; v разложить на множители

division (n) [dI`vIZqn]деление

divide (v) [dI`vaId] делить

dividend (n) [`dIvIdent] делимое

divisor (n) [dI`vaIzq] делитель

quotient (n) [`kwquSqnt] частное

meaningless (adj) [`mJnINlIs] бессмысленный

Memorize the following word combinations

Reading Activity

Four Basic Operations of Arithmetic

Many thousands of years ago this was a world without numbers. Today, using the same numbers in many different ways, man can build bridges, skyscrapers, fly off the Earth like a bird, even measure the distance to the Moon. So you see, mathematics and numbers, are very important to life nowadays.

Until XVI century people in Europe used Roman numerals. The Roman system of numbers is based upon the letters I, V, X, L, C, D, and M. These letters were mixed together to form many different combinations. The arithmetic symbols now in use were derived from the Arabs and the Hindus, the latter of whom introduced the symbol 0.The invention of this symbol for zero was very important, because it enabled the nine Hindu symbols 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent any number, no matter how great. The work of a zero is to keep the other nine symbols in their proper place. The Hindu-Arabic numeration system is a decimal system: that is, it is based on tens. In this system the value a digit represents is determined by the place it has in the number; if a digit is moved to the left one place, the value it represents becomes ten times as great.

The invention of our present notation for the decimal number system made possible simple and systematic operations with numbers. Arithmetic is the elementary branch of mathematics dealing with the properties of numbers and their operations. We work with only positive numbers in arithmetic. Negative numbers appear in algebra. An operation is a way of thinking of two numbers and getting one number. The fundamental operations of arithmetic are addition, subtraction, multiplication, division.

There are special signs to indicate operations with numbers. They are plus (+), minus (-), multiplication (x) and division (:) signs.

The process of finding a simple expression for the sum of two or more numbers is known as addition. In the arithmetic sentence 3+5=8 three and five are addends and eight is the sum.

In the operation of subtraction the number to be made smaller is called the minuend. The subtrahend is the number to be subtracted. The result of the process is the difference. A sentence like 6-4=2 represents an operation of subtraction. Here the difference is the number that when added to the subtrahend gives the minuend. Thus, subtraction is the inverse operation of addition since 2+4=6 and 6-4=2.

In multiplication the number being multiplied is the multiplicand. The number by which we are multiplying the multiplicand is the multiplier. When two or more numbers are multiplied, each of them is called a factor. The number resulting from the multiplication is known as the product. You must remember that the product of any number multiplied by zero is zero. The product of any number multiplied by one is the same number.

In division the number to be divided is called the dividend. The divisor is the number by which the dividend is to be divided. When we are dividing the dividend by the divisor we get the quotient. You may check division by using multiplication since 4:2=2 and 2x2=4.Therefore, division and multiplication are inverse operations. The remainder is what is left over after the dividend has been divided into equal parts. If there is a remainder, it may be written over the divisor and expressed as a fraction in the quotient. There are some important facts that must be remembered about division. The quotient is 0 (zero) whenever the dividend is 0 and the divisor is not 0. That is, 0:n=0 for all values of n except n=0. Division by 0 is meaningless for all values of n.

Post-Reading Activity

Ex. 8. Answer the following questions.

1. What numerals were used in Europe until XVI century? 2. Who introduced the symbol 0? 3. Is the Hindu-Arabic system a decimal system or a binary one? 4. What does the value which a digit represents depend on? 5. What are the signs most used in arithmetic? 6. What are the fundamental operations of arithmetic? 7. Are division and multiplication inverse operations? 8. Are subtraction and multiplication inverse operations? 9. What must you remember about multiplication? 10. What important facts about division must be remembered?

Ex. 9. Find the Russian equivalents for the following English word combinations.

1. to use the same numbers; 2. to represent numbers; 3. present notation; 4. numeration system; 5. decimal system; 6. to be based on tens; 7. inverse operation; 8. capital letters; 9. arithmetic sentence; 10. to measure the distance

a. основываться на десятках; b. обратная операция; c. заглавные буквы; d. измерять расстояние; e. десятичная система; f. представить числа; g. использовать одни и те же числа; h.система счисления; i. арифметическое выражение; j. современная система записи

Ex. 10. Mark the following as True or False.

1. People used numbers thousands of years ago. 2. The decimal number system was invented by the Romans. 3. The Roman system of numbers is based upon the letters A, B, C, D, E, F and G. 4. The symbol 0 was introduced by the Arabs. 5. The work of a zero is to keep the other nine symbols in their proper place. 6. Our decimal number system is positional. 7. We go from right to left in forming larger and larger units of ten, hundred, thousand and so on. 8. We work both with positive and negative numbers in arithmetic. 9. The product of any number multiplied by one is the same number. 10. The quotient is 0 whenever the divisor is 0.

Ex. 11. Fill in the blanks with necessary words and word combinations from the box.

1. We get … as a result of addition. 2. The numbers to be added are called …. 3. You may check … by multiplication. 4. Will there be … if you divide 25 by 7? 5. If you are … two numbers, you must remember that division by 0 is meaningless. 6. To find the minuend … and the subtrahend must be known. 7. Addition and … are inverse operations. 8. The multiplicand and multiplier are the names for the … . 9. The result of division is known as …. 10. The difference is the number that when added to the … gives the minuend. 11. The plus sign between two numbers means that these numbers are … . 12. A dot placed between two numbers is used as … . 13. A symbol used to represent a number is called … .

Ex. 12. Make the sentences negative and interrogative.

1. We can add numbers in any order. 2. You should discuss the rules of multiplication at the next lesson. 3. Mathematicians were able to discover another fundamental law of nature. 4. The result must be checked immediately. 5. You have to decide on the subject of your thesis. 6. They may misunderstand the theoretical character of the problem. 7. We were allowed to work on our experiment out of class. 8. They will be able to use some symbols instead of words. 9. We need to use special methods to obtain necessary results. 10. You ought to study carefully the definitions given above.

Ex. 13. Ask special questions.

1. Scientists should develop this important branch of mathematics. (What) 2. In antiquity people could count using positive integers. (When) 3. We are not allowed to use zero as a divisor. (Who) 4. Natural numbers may be divided into two classes: even and odd. (How many) 5. She was able to obtain the solution by multiplying two numbers. (How) 6. He had to speak English at the international conference. (Where) 7. I must discuss the details of my dissertation with the science adviser. (Who(m)) 8. You need to follow your teacher’s instructions during the test. (Whose) 9. You ought to do your best and fulfil the task. (What) 10. First you are to perform the operation of division and then multiply the quotients. (Which)

Ex. 14. Choose the phrase closest in meaning to the given statement.

1. Dan can’t be a teacher.

a) I’m sure Dan isn’t a teacher.

b) I think Dan isn’t a teacher.

2. Need I take the tablets every day?

a) Is it a good idea to take the tablets every day?

b) Is it necessary to take the tablets every day?

3. If it is hot tomorrow, we may go to the beach.

a) We will definitely go to the beach tomorrow.

b) It is possible that we will go to the beach tomorrow.

4. You mustn’t steal.

a) It is against the law to steal.

b) It isn’t necessary to steal.

5. Alison has to work on Saturday. Her boss told her so.

a) Alison wants to work on Saturday.

b) Alison’s boss wants her to work on Saturday.

6. Late-comers are to report to the dean’s office.

a) It’s a good idea.

b) It’s the rule.

7. Astronauts must feel afraid sometimes.

a) They are supposed to.

b) It’s only natural.

8. You can’t come in here.

a) It isn’t allowed.

b) I don’t believe it.

9. We should be there soon.

a) I expect so.

b) It’s absolutely certain.

10. All motorcyclists have to wear crash helmets.

a) It’s a good idea.

b) It’s the rule.

Ex. 15. Choose the correct modal verb or its equivalent.

1. You (may/ought to/are to) take care of your parents. 2. My sight is getting worse. Next year, I’m afraid I (cannot/may not/won’t be able to) read without glasses. 3. Twelve delegates from several countries (can/have to/are to) meet at the end of February. 4. Excuse me, (could/may/must) you tell me the way to the Houses of Parliament? 5. The weather is getting worse. It (must/is likely/may) rain. 6. There are no people in the hall, we (must/can/need) have a talk there. 7. Although he felt ill, he (could/was able to/may) finish all the paperwork. 8. You (can/must/ought to) go and see that movie. It’s very interesting. 9. Don’t worry, you (don’t have to/mustn’t/may not) pay now.10 When we were at school, we (had to/ought to/must) wear a uniform.

Ex. 16. Give the proper English equivalents for the Russian expressions.

1. Нам пришлось perform the operation of addition to find the answer. 2. Ему предстоит specify the conditions of the experiment. 3. Им разрешают use a dictionary if necessary. 4. Я в состоянии solve this difficult problem myself. 5. Вам следует remember that multiplication is associative. 6. Ей не надо use this theorem. 7. Они могут apply their theories in practice. 8. Вы обязаны remember several rules about division. 9. Можно мне start the calculations now? 10. Вам следует to accept everything your parents say as an axiom.

Ex. 17. Translate from English into Russian.

Ex. 18. Translate from Russian into English.

1. Числа, которые нужно сложить, называются слагаемыми, а результат сложения называется суммой. 2. Эти числа предстоит перемножить. 3. Мы должны записывать результат справа от знака равно. 4. Число можно поделить на два без остатка (точно), если это четное число. 5. Деление обратно умножению. 6. Произведение любого числа, умноженного на ноль, равно нулю. 7. Никто не может сказать, когда люди начали считать. 8. Они обозначили (указали) операцию сложения знаком плюс. 9. Ни один студент не мог решить задачу, заданную профессором. 10. Им придется использовать двоичную систему счисления. 11. Данный элемент может быть обозначен тем же символом.

UNIT 5

Ex. 1. Compare Russian and English Tense forms.

Grammar Rules Patterns.

Ex. 2. Read and compare the following sentences. Explain the use of the English Tense forms. (Present Perfect, Past Indefinite, Past Perfect, Future Perfect, Future Indefinite, Future Continuous, Present Continuous).

1. a) He has enlarged his English vocabulary lately.

b) He enlarged his English vocabulary when he was in Great Britain.

c) Before he went to Great Britain he had enlarged his English vocabulary.