- •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
Participles and their forms
There are two participles in English – participle 1 (Ving) and participle II (past or =ed participle; V3 for irregular verbs).
The forms of participle 1 coincide with the forms of gerund (*the difference is in functions, which will be dealt with later):
|
Active |
Passive |
Simple |
solving |
being solved |
Perfect |
having solved |
having been solved |
The perfect forms emphasize that the action expressed by the participle precedes the one expressed by the finite verb. Participle 1 perfect cannot be an attribute and expresses mostly temporal and causal relations. Participles are not used after prepositions, unlike Gerunds.
E.g. In this paper we survey the possibilities arising from the application of new high-precision instruments.
I am going to give a review of papers covering the most important problems.
Many new options are not being shown in this application.
Addressing the audience Prof.N emphasized the importance of direct contacts among scientists.
Dr. Smith showed a few slides, giving comments.
Having answered all the questions he left the room.
Participle II of most verbs has only one form. If the verb is regular, we add =ed to the infinitive; if the verb is irregular, it has its own “third” form (V3). However, some irregular verbs have two different forms of participle II:
Burn – burned/burnt; dream – dreamed/dreamt; get – got/gotten (AmE); hang – hanged/hung; leap – leaped/leapt; learn – learned/learnt; light – lighted/lit; show – showed/shown; spell – spelled/spelt; wake – waked/woken, etc.
E.g. The results presented here add to our knowledge of the mechanism.
A glance at the table shown in the article leads us to the conclusion that the result lies far beyond our expectation.
When approached from the classical point of view, this problem seems to be unsolvable.
Participle II of objective verbs is always passive in meaning.
Exercise 1. Read the text below and define the italicized verb forms.
In fact Cantor borrowed the paradox cited by Galileo and turned it into a means of comparing the size of infinite sets. He defined two sets as equivalent if one-to-one correspondence can be established between the members of each set. Such a correspondence provides a natural way of comparing size. For example, imagine a bucket filled with black and colored marbles, and suppose one want to compare the number of black marbles with the number of colored marbles. The simplest way is to remove the marbles from the bucket in pairs of one black and one colored marble. If every marble can be paired with a marble of a different color, the two sets are equivalent. Failing that, the marbles remaining in the bucket are the basis of the comparison.
Exercise 2. Put the verbs in parentheses into the correct participle form (participle 1 or participle II).
The introduction of the computer in science is comparatively recent. Already, however, computation is (establish) a new approach to many problems. It is (make) possible the study of phenomena far more complex than the ones that could previously be (consider), and it is (change) the direction and emphasis of many fields of science. Perhaps most significant, it is (introduce) a new way of thinking in science. Scientific laws are now (be) (view) as algorithms. Many of them are (study) in computer experiments. Physical systems are (view) as computational systems, (process) information much the way computers do. New aspects of natural phenomena have (be) (make) accessible to investigation.
