2. Find in the text English equivalents to the following words and word combinations:

точне формулювання, впливати, складатися зі знаків, чіткий, стислий, науковий вік, удосконалюватися, абревіатура, словесна алгебра, символ рахування, головна причина, двозначність слова, обробка, якісний перехід.

3. Make up questions to the following answers:

Model: Human language is a system of symbols. (What ...)

What is human language?

1. Yes, it does. Algebra, the language of mathematics, consists of signs and symbols. (Does …)

2. Algebra is precise, concise and universal. (What …)

3. Algebra in its development has passed through three stages: verbal, abbreviated and symbolic. (How many …)

4. Yes, it is. Verbal algebra is characterized by the complete absence of any symbols. (Is …)

5. In medieval Europe the symbol “-” was denoted by the full word “minus”. (How …)

6. The turning point in the history of algebra was written in the sixteenth century by a Frenchman Viete. (When …)

7. Yes, they do. Symbols permit of concise, clear representations of ideas. (Do …)

8. Mathematics is so effective in problems, because it has a powerful technique, based upon the use of symbols. (Why …)

9. Mathematics is convenient, because the literal notation is free from all ambiguities of words. (Why …)

4. Make up word combinations from the following words:

universal abbreviated scientific symbolic to paraphrase convenient equivalent formal spoken to grasp

age sense stage shorthand form language statement meaning algebra logic

5. Answer the following questions:

1. What does algebra consist of?

2. What is a general belief in our scientific age?

3. What is the turning point in the history of algebra?

4. How many stages have algebra passed in its development? What are they?

5. What is one of the basic characteristics of modern mathematics?

Section 3

1. Read and translate the following text: the fields and uses of physics

The story of man's civilisation is the story of his study of nature and the application of his knowledge in his life. Primitive man was born, lived and died with little change in his manner of living from generation to generation. The laws of nature were not studied.

The use of tools, first of stone and later of metals, the domestication of animals, the development of writing and counting, all progressed slowly since rapid advance was not possible until man began to gather data and check theories. Till that time most of man's knowledge was based on the speculations of the Greeks.

Not until a little over three centuries ago did man adopt the scientific method of studying his environment. After this the development of civilisation has become increasingly more rapid. The advance of all the natural sciences has been almost simultaneous: in fact, many of the prominent scientists were working in more than one field of knowledge.

We shall limit our attention to the one field of physics. Probably more than any other science physics has changed the conditions under which man lives. Physics deals not with man himself, but with the things he sees and feels and hears. This science deals with the laws of mechanics, heat, sound, electricity, light, which have been applied in numerous combinations to build our machine age. Modern physics also deals with electronics, atomic phenomena, photo-electricity, X-rays, radioactivity, the transmutation of matter and energy and the phenomena associated with electron tubes and the electric waves of modern radio.

The practical application of the developments of physics continues at an ever increasing rate. “Practical physics” plays, therefore, no small role, for the laws of physics are applied in every movement we make, in every attempt at communication, in the warmth and light we receive from the sun, in every machine. Practical applications of physics are not all made, by physicists, for the majority of those who apply the principles of physics are called “engineers”.

In fact, most of the branches of engineering are closely related with one or more sections of physics: civil engineering applies the principles of mechanics; mechanical engineering utilises the laws of mechanics and heat; electrical engineering is based on fundamentals of electricity, etc. The relation between engineering and physics is so close that a thorough knowledge and understanding of physical principles is important for progress of engineering. One of the tools common to physics and engineering is mathematics.

If we are to make effective use of the principles and measurements of physical science, we must have a workable knowledge of mathematics. Physics and mathematics are thus the basic “foundations of engineering”.