- •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.
- •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?
- •Vocabulary
- •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
Attributive Clauses
The attributive clause functions as an attribute (as an adjective) and stands after the noun that it modifies. Attributive clauses are introduced by the words who, whom, whose, which, that, when, where, why. One type of attributive clauses is relative clauses, which often present some difficulty for language learners, mostly in the choice of the right relative pronoun.
Who refers to persons; which refers to things; that refers to things or persons. To avoid possible mistakes, use who (not that) when referring to people.
That is more formal and cannot be used in non-restrictive clauses, which are separated with commas and function as parentheses.
For example:
My uncle, who now lives in Greece, invited us to spend next summer at his place.
The war, which lasted nearly ten years, brought devastation and suffering to both countries.
She lost his book, which made him angry.
Whom can be used after a preposition and refers to persons:
This is the speaker about whom we were talking.
Also possible: This is the speaker who we were talking about.
Or: This is the speaker we were talking about.
Whose is used to show possession, together with a noun, and may refer to people, objects and animals:
This is the equation whose roots we have obtained.
This is the speaker whose report I liked most of all.
When is used to refer to time, usually after nouns like time, period, moment, day, etc.:
I’ll never forget the day when I passed this exam.
It can either be replaced by that or can be omitted.
Where is used to refer to places:
The street where the University is located is very busy.
It can be replaced by which/that + preposition and, in this case, which/that can be omitted: The city (which/that) the University is located in is very big.
Why is used to give a reason:
The reason why I can’t meet you tonight is that I’m working overtime.
It can either be replaced by that or can be omitted.
Who/which/that can be omitted when they function as objects rather than the subjects of the attributive clause:
I spoke to the man (whom/who/that) I had met before.
That’s the book (which/that) I recommended to you.
They cannot be omitted if they are the subject of the relative clause:
I know a man who is a famous mathematician.
The equation which was solved during the seminar was quite difficult.
Exercise 1. Combine the sentences by using an attributive clause. Note when it is possible to omit who/which/that.
The radiation is present in small amounts in the air. We breath this air.
New statistical theories and methods take advantage of the high-speed digital computer. There has been an increase in the development of them.
The assumptions often involved he bell-shaped curve. It is also called the normal or Gaussian distribution, after the German mathematician Carl Friedrich Gauss.
The computer program is a medium. The algorithms can be expressed and applied in it.
The objects in a computer experiment follow the laws embodied in the computer program. These laws can be of any consistent form.
There are many scientific calculations. They can be done by conventional mathematical means, without the aid of the computer.
The equations of motion of an electron yield an algorithm. The trajectory of an electron can be determined from it.
The nature of the infinite appeared in the famous paradoxes of Zeno of Elea. He argued that motion is impossible because it requires an object to pass through an infinite number of points in a finite time.
In modern times problems associated with the infinite have appeared in the abstract theory of sets. This theory provides a foundation for virtually all contemporary mathematics.
The eminent French mathematician Henri Poincare condemned the theory of transfinite numbers as a “disease”. Mathematics would someday be cured from it, he thought.
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 sentences with conditional and attributive clauses.