- •Grammar: the participle. Forms of the participle
- •Exercises
- •The group concept
- •Grammar and vocabulary exercises
- •IV. State the forms and the functions of Participle I in the following sentences and translate them.
- •Speech exercises
- •Grammar: the absolute participle construction exercises
- •V. Guess the meaning of the following words:
- •VI. Read and learn these words:
- •Grammar and vocabulary exercises
- •Speech exercises
- •Subsets
- •Ordinary differential equations
- •Forms of the gerund
- •Exercises:
- •X. Guess the meaning of the following words:
- •Coefficient [kouI'fISqn] theorem ['tIqrqm]
- •XI. Read and learn these words:
- •Ordinary differential aquations
- •Vocabulary and grammar exercises
- •Speech exercises
- •Integration
- •Grammar: the infinitive, its forms and functions
- •Equation and locus
- •Vocabulary and grammar exercises
- •Speech exercises
- •The equation of a locus
- •Grammar: the infinitive constructions (complex subject, complex object and for-phrases) exercises
- •Vocabulary and grammar exercises
- •Functions
- •Speech exercises
- •Grammar: condional sentences revision: the nominative absolute participal constructions exercises
- •Speech exercises
- •Surfaces grammar: conditional sentences
- •Grammar and vocabulary exercises
- •Contens
Speech exercises
I. Read and reproduce.
SUBGROUPS
We can find that some elements form a smaller group inside the big one. This smaller group within the larger is an example of a subgroup. If G is a group with operation *, then the subset H of G is a subgroup if H forms a group under the operation *.
Not every subset H is a subgroup. Subgroups are extraordinarily common. The group of integers, under addition, has subgroups having all even integers, all multiples of 3, all multiples of 4, all multiples of 5, … . Every group G is a subgroup of itself, as is the single element set {I}, which has the trivial multiplication table
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X
I
I
I
The number of elements in a group is called the order of the group. The order of a subgroup always divides the order of the group.
II. Topics for discussion:
1. Groups can arise in many quite distinct situations.
2. The concept of a group is abstracted from arithmetic.
II. Say this in English:
Подгруппы:
Подмножество S группы G называется ее подгруппой, если S является группой относительно определяющей операции группы G. Это справедливо I) в том и только в том случае, если множество G содержит все произведения принадлежащих ему элементов и все элементы, обратные его элементам, 2) в том и только в том случае, если для любой пары элементов а, в, из G множество S содержит и произведение ав-1. Если G – группа конечного порядка g, то порядок g1 любой ее подгруппы G1 является делителем порядка группы. Это теорема доказана Лагранжем.
T E X T II
Grammar: the absolute participle construction exercises
I. Read the following sentences, in which the Absolute Participle Construction is used at the beginning of the sentence. Translate them into Russian.
1. The weather being fine, we shall start tomorrow. 2. The dictionaries being brought, we were given articles for translating. 3. A novel being really good, you don’t have to be educated to like it. 4. The first part of the work having been finished, the results were published in a journal. 5. The article being well written, it was read with pleasure. 6. The article being difficult, I couldn’t translate it without your help. 8. Most of the work having been done, we decided to have a rest. 9. The lights going out, we stopped our work.
II. Read the following sentences in which the Absolute Participle Construction is used at the end of the sentence. Translate them into Russian.
1. My friend was asked many questions, some of them being very difficult. 2. The teacher gave me two articles yesterday, both containing interesting facts. 3. The professor spoke about the latest achievements in the national economy, his lecture being illustrated by diagrams. 4. The plan was discussed in detail, many workers taking part in this discussion. 5. Many results used before remain true for our case, the proofs being similar. 6. We may use two different methods, the first being the more general one.
III. Read the following sentences, translate them paying attention to the place of the Absolute Participle Construction.
1. The game having ended, the people went home. 2. Cybernetics is a new branch of science, it being developed in the twentieth century. 3. Nobody being there, I went away. 4. The play being very popular, it was difficult to get tickets. 5. Most of the students of our group go in for sports, many of us being fond of gymnastics. 6. The doctor having done everything possible, my sister began recovering. 7. The examinations being over, most of the students left the city. 8. My friend having returned from London, I went to see him. 9. The bridge having been repaired, we were able to cross the river.
IV. Translate the sentences into English, use the Absolute Participle Construction.
1. Так как погода была прекрасная, мы решили провести несколько дней в деревне. 2. Так как было воскресение, библиотека в университете была закрыта. 3. Когда занятия окончились, студенты начали обсуждать свои планы на выходной день. 4. Существует много методик обучения ино- странным языкам, причем данная методика – самая эффективная. 5.Если погода будет такой дождливой, вам придется купить новый плащ. 6. Так как мои часы отставали, я опоздал на 5 минут.