4. Перепишите предложения и переведите их, обращая внимание на бессоюзное подчинение.

1. Computers today are running our factories, planning our cities, teaching our children, and can forecast the possible futures we may be heir to.

2. We think he will never drive in excess of the speed limit.

3. He was one of the greatest scientists the world had ever known.

4. The computer games you are asking for are on the top shelf.

5. The results you obtained using the New Maths agree, of course, with the results we obtained using the old classical Maths.

5. Перепишите предложения и переведите их. Подчеркните герундий и определите его функцию.

1. Maths method is reasoning of the highest level known to man, and every field of investigation- be it law, politics, psychology, medicine or anthropology- has felt its influence and has modeled itself on maths.

2. By applying your knowledge of geometry you can locate the point in the plane.

3. He hates being interrupted.

4. Analyzing information involves examining a source to determine what the author is trying to say.

5. Instead of being moved to the right the dot is moved to the left.

6. Maths has been of use to science in preparing men’s mind for new ways of thinking.

6. Перепишите предложения и переведите их, обращая внимание на различные функции инфинитива.

1. To explain this simple fact is not easy.

2. To correct the defects in Euclid’s ‘Elements’ many axiom systems were suggested and developed.

3. In each generation, men have developed new methods and ideas to solve difficulties.

4. Many events in physics can now be recognized as examples of mathematical catastrophes.

5. There are many problems to be solved later.

6. Mathematicians tried to measure a huge triangle on three peaks in Germany but failed to bring about a decisive conclusion.

7. Прочитайте текст, перепишите и письменно переведите 1, 2, 4, 5 абзацы.

MATHEMATICS

Mathematics has been called “the queen of knowledge”. A most important fact about the real, material world is that objects in it can be counted and their masses can be measured. Mathematics is a tool which helps the man know how much, how many, how large, how fast, in what direction, and with what chances. But mathematics is more than just a system of numbers (numeration). It is also a way of thinking and a form of logical reasoning.

From this manner of reasoning about numbers and space, ideas and conclusions can be developed.

Mathematics grew up with civilization as man’s quantitative needs increased. It arose out of practical problems and man’s needs to solve these problems. As soon as man began to count, even on his fingers, mathematics began. It was the first of the sciences to develop formally. It is growing faster today than in its early beginning. New questions are always arising, partly from practical problems and partly from pure, theoretical problems. In each generation, men have developed new methods and new ideas to solve these problems.

The Greeks elevated mathematics to the field of abstract thinking. In its higher form mathematics becomes a form of logic in which basic assumptions are laid down and results are then deduced within the framework of the system. The system, itself, is composed of (1) a few, elementary, undefined terms, such as number, point, and line, which are called primitives; and (2) rules which govern their operations. The primitives comprise the basic vocabulary of mathematics and provide the groundwork for a technical vocabulary within the system. The basic definitions are stated in terms of the primitives, as are the postulates, which are assumptions or evident truths. With these tools, then, statements and conclusions can be derived or proved. The results, in turn, assist in proving more statements. Thus, a large structure is built.

However, mathematics is much more than just a system of conclusions drawn from definitions and postulates that must be consistent. Even though the assumptions may be created by the free will of the mathematician, there must be a very strong relationship of the abstract mathematical principle to its physical counterpart in the real, material world. Otherwise, mathematics would be only an intellectual pastime or game without any real purpose.

Real progress in this science began only after the concrete pictures, emotions, and physical concepts were isolated from the numbers themselves. At this time pure mathematics emerged – the science of number and quantity unconnected with any material object. Arithmetic, algebra, geometry, trigonometry, and the more advanced branches of mathematics can each be considered as pure mathematics only if the concepts attach no real, tangible application.

Mathematics in the service of the physical sciences – such as mechanics, engineering, optics, astronomy, geodesy and electricity – is referred to as applied mathematics. The applied mathematician takes the pure mathematician’s findings and applies them to the varied concrete situations.