- •Contents
- •General comprehension questions:
- •Isaac Newton; Fibonacci; Lioville; Birkhoff; Hilbert; Archimedes; Pythagoras; Giloramo Cardano; Leibniz; Abraham de Moivre; Leonard Euler; Caspar Wessel; Hamilton.
- •General comprehension questions:
- •Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •Vocabulary
- •1. A list of words to remember:
- •2. Translate the following sentences into English:
- •3. Can you solve the following problems and explain how you obtained the solution?
- •Forms of the Infinitive
- •Functions of the Infinitive in the sentence
- •Attributive Clauses
- •Integrating Factors
- •Unit 3.
- •General comprehension questions:
- •Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •The Fundamental Theorem of Algebra
- •The Number I
- •Vocabulary
- •1. A list of words to remember:
- •2. Translate the following sentences into English:
- •3. Translate the following text into English.
- •Participles and their forms
- •Functions of participles in the sentence
- •The complex plane
- •1. General comprehension questions:
- •2. Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •8.1. Euclidean Linear Transformations
- •3. Translate the following text into English.
- •The Gerund and its forms
- •Functions of the Gerund in the sentence
- •Families of circles
Functions of the Gerund in the sentence
As the gerund combines features of a verb and a noun, it can perform a whole range of functions in the sentence.
as the Subject: Working with him was fun.
The gerund is more often used at the beginning of a sentence than the infinitive. Still, it is also common to introduce the gerund in a sentence with the help of pronoun it: It was difficult persuading him.
There are a few fixed phrases which begin with introductory it and are followed by the gerund or gerundial construction – it is fun, it is no/little use, it is no good, it is (not) worth: It is no use us trying to prove this theorem.
I don’t think it’s worth explaining it in more details.
It’s worth paying attention to what he says.
A single gerund as subject can also be introduced by there:
There is no denying his talent.
There is no telling which of them will get the results first.
as the Predicative (commonly after the link verb be):
Her only fun was reading books.
The example I gave was measuring a distance by arranging matches end to end.
It should be distinguished from participle 1 as a part of the progressive (continuous) verb tense:
She was reading a book. (participle 1)
as an Object used directly after verbs or after verbs with prepositions. The gerund, like the infinitive, is widely used in this function after certain verbs and expressions that you are supposed to remember:
to admit
to appreciate
to avoid
cannot help
to carry on
to consider
to delay
to deny
to dislike
to enjoy
to fancy
to finish
to give up
to imagine
to include
to involve
to justify
to keep (on)
to mention
to mind
to put off/to postpone
to require
to risk
to suggest
She kept (on) saying that she was worried.
She risks failing the exam.
I appreciated hearing from them.
He considered speaking at the conference.
In spite of the noise she carried on writing.
The gerund is also used after a number of verbs with prepositions:
to account for
to accuse of
to agree to
to aid in
to aim at
to approve of
to apologize for
to complain of
to depend on
to differ in
to dream of/about
to feel like
to insist on
to look like
to object to
to persist in
to prevent from
to rely on
to result from
to result in
to succeed in
to suspect of
to think of
He dreamed of solving the problem.
She apologized for disturbing us.
I object to their coming here.
The gerund is used after the following prepositional expressions:
to be aware of
to be capable of
to be fed up with
to be fond of
to be tired of
to be for/against
to be/get used to
to be happy about
to be proud of
to be sure of
to be surprised at
to be worth
to have difficulty in
to look forward to
there is no point in
what’s the use of…?
I am used to getting up early.
The risk is worth taking.
What’s the use of waiting?
I will be looking forward to speaking to him.
She had difficulty (in) finding the book.
*There are a number of verbs which can be followed by either the infinitive or the gerund with difference in meaning.
To remember: Remember to lock the door.
She remembered talking to him.
To forget: I forgot to ask him.
She forgot ever going there.
To regret: I regret to inform you that…
You will regret doing nothing in this situation.
To stop: He stopped trying to solve the problem.
He stopped to discuss the problem with a colleague.
To go on: He went on talking for hours.
He welcomed us and went on to offer us some drinks.
To prefer: in the affirmative we can use both the infinitive and the gerund with practically no difference in meaning: I prefer staying/to stay at home. To express a particular action in the past the infinitive is commonly used: I preferred to stay at home. Note also the usual patterns with prefer:
I prefer solving problems to proving theorems.
I prefer to solve problems than (to) prove theorems.
**Two options are possible with the verbs advise, intend, recommend:
1) verb + gerund: She advised talking to him.
He intended staying till the end.
He recommended limiting the number of equations considered.
2) verb+(pro)noun+infinitive:
He advised me not to insist on it.
The scientific advisor didn’t recommend him to change the
approach.
as an Attribute after nouns or pronouns with the preposition of
They had a feeling of being able to find the solution..
I considered the possibility of joining them.
They give the impression of not working hard enough.
as an Adverbial Modifier (also preceded by a preposition):
On closing the door she remembered that she hadn’t turned off the light.
The whole evening was spent in deciding whether to do it or not.
It turned out that this method was used for solving a number of equations.
You cannot make an omelette without breaking eggs. (a proverb)
Exercise 3. Find the gerund in the following sentences and identify its function.
1) Writing a sentence in algebraic form involves two steps.
2) It is no use calculating the norms of these operators for p=∞.
3) We cannot help acknowledging the importance of this statement.
4) The main part of the paper consists in determining all indecomposable objects in K.
5) Another alternative way of writing (4) is the following…
6) After multiplying by its inverse, we may use it to sweep out the other non zero elements of the first row and first column.
7) Eliminate Δ’n and w’n by equating the right hand sides of (26.1) and (26.2).
8) This kind of objects are capable of being deformed.
9) This will lead to the formulation of a general definition of a tangent and to a method of finding its slope.
10) Using the above procedure for each map gives us the desired homotopy Hi+1.
11) It is worth noting that none of these questions depends on the uniform algebra setting.
12) We postpone giving a definite answer.
Exercise 4. Translate the following sentences into English using the gerund.
1) Эффективность этого процесса привела к увеличению влияния данного метода.
2) Эта статья затрагивает проблему нахождения условий, при которых данные идеалы образуют группу.
3) Современные исследования нацелены на выведение новых классов формул для обобщенной функции от нескольких переменных.
4) Удобным способом изучения данных отношений было бы использование метода конечных элементов.
5) Он легко привел уравнение (17) к виду (18) без использования дополнительных теорем.
6) Знание свойств данного неравенства поможет вам решить, является ли утверждение истинным или ложным.
7) Мы попробуем разделить эти числа.
8) Возможно, следует уточнить, что эта терминология слегка отличается от общепринятой.
9) Таким образом, единственное решение, как кажется, заключается в доказательстве, что данная программа выполняется корректно.
10) В рамках доказательства корректности независимость концепции измеряется возможностью приводить отдельные доказательства для разных уровней.
11) Данные коэффициенты получены умножением выражения (7) последовательно на 1, cos(nx/λ), sin (nx/λ) и интегрированием по х в диапазоне между -πλ и + πλ.
Exercise 5. Identify the gerund or the participle 1 in the following sentences and translate the sentences into Russian.
1) In Anderson (1) a functor R:C→C is introduced which has the effect of localizing the homotopy groups of 1-connected space.
2) While the effect on π1 is not as pleasant as Hilton, Mislin and Roitberg’s localizing functor (6), R does have the advantages of being factorial on C.
3) In discussing characters of the orthogonal group, Littlewood gives six expansions of symmetric products that are basic for expressing the characters of irreducible representations of orthogonal and symplectic groups as series in those for the general symplectic group, and conversely.
4) We
could continue the process of squaring some number between 4 and 5
indefinitely and never get the exact value of
.
5) Some applications are given and several noteworthy types of restrictedness are introduced including ones which display compactness, connectedness and closedness as special cases of a more general concept.
6) The normal rules of probability can therefore be applied in making the choice.
7) Having a single theorem proven both for verifying Hoare’s conditions and for checking the program state at run time is one of the possibilities opened by the predicate calculus as a programming language.
8) Having fixed the sharp end of the compass we drew a curved line.
9) The approach to the problem being considered remained traditional.
10) In factoring as in all other algebraic processes the first step is always to make a careful study of the given expression.
Additional text. Read it and retell in English. You may need to write down the formulas and base your retelling on them. Pay attention to the vocabulary and correct pronunciation.
