III. Заполните пропуски подходящими по смыслу словами

1. The basic concepts of the main branches of mathematics are … from experience.

a) abstractions b) notions

c) concepts c) functions

2. Irrational numbers,..., and so forth are not wholly abstracted from the physical experience.

a) functions b) negative numbers

c) quantitative values d) abstractions

3. The notion of... that represents the quantitative values of some changing physical phenomena, such as temperature and time, is also at least one mental step beyond the mere observation of change.

a) a function b) an abstraction

c) a variable d) an addition

4. The concepts of a..., or relationship between variable, is almost totally a mental creation.

a) irrational number b) negative number

c) multiplication d) function

5. The gradual introduction of new... in any field enables mathematics to grow rapidly.

a) notions b) concepts

c) functions d) quantitative values

Text II

The basic concepts of the main branches of mathematics are abstractions from experience, implied by their obvious physical counterparts. But it is noteworthy, that many more concepts are introduced which are, in essence, creations of the human mind with or without any help of experience. Irrational numbers, negative numbers and so forth are not wholly abstracted from the physical practice, for the man's mind must create the notion of entirely new types of numbers to which operations such as addition, multiplication, and the like can be applied. The notion of a variable that represents the quantitative values of some changing physical phenomena, such as temperature and time, is also at least one mental step beyond the mere observation of change. The concept of a function, relationship between variables, is almost totally a mental creation.

The more we study mathematics the more we see that the ideas and conceptions involved become more divorced and remote from experience, and the role played by the mind of the mathematician becomes larger and larger. The gradual introduction of new concepts which more and more depart from forms of experience finds its parallel in geometry and many of the specific geometrical terms are mental creations.

As mathematicians nowadays working in any given branch discover new concepts which are less and less drawn from experience and more and more from human mind the development of concepts is progressive and later concepts are built on earlier notions. These facts have unpleasant consequences. Because the more advanced ideas are purely mental creations rather than abstractions from physical experience and because they are defined in terms, of prior concepts it is more difficult to understand them and illustrate their meanings even for a specialist in some other province of mathematics. Nevertheless, the current introduction of new concepts in any field enables mathematics to grow rapidly. Indeed, the growth of modern mathematics is, in part, due to the introduction of new concepts and new systems of axioms.

IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.

1. What are the basic concepts of the main branches of mathematics?

a) abstractions from experience b) experience

c) physical abstractions d) quantitative values

2. What does the notion of a variable represent?

a) the quantitative values of some constant physical phenomena.

b) the quantitative values of some changing physical phenomena.

c) mathematical concepts.

d) functions.

3. Where does the gradual introduction of new mathematical concepts find its parallel in?

a) physics b) geometry

c) experience d) physical practice

4. Where are the new concepts remoted from?

a) experience b) human mind

c) geometry d) mathematics

5. Why are the new concepts more difficult to understand?

a) they are not defined in terms.

b) they are defined in terms of prior concepts.

c) they are defined in terms of physical concepts.

d) they involve many difficult notions.

6. What do new concepts enable mathematics to do?

a)to grow rapidly.

b) to grow slowly.

c) to stop the development.

V. Выберите заголовок для данного текста, в соответствии с его содержанием.

a. The basic and new concepts c. Modern mathematicians

b. The basic concepts d. Irrational numbers

VI. Укажите правильный перевод подчеркнутой части предложения.

1. But it is noteworthy, that many more concepts arc introduced which are, in essence, creations of human mind.

a) представлены b) были представлены

c) представляли

2. Irrational numbers, negative numbers, and so forth are not wholly abstracted from the physical practice.

a) не отделяются b) не отделяли

c) не были отделены

3. Later concepts are built on earlier notions.

a) строили b) строятся

c) были построены

4. The basic concepts of the main branches of mathematics are abstractions from experience, implied by their obvious physical counterparts.

a) подразумеваемые b) подразумевают

c) подразумевали

5. Irrational numbers, negative numbers and so forth are not wholly abstracted from the physical practice, for the man's mind must create the notion of entirely new types of numbers to which operations such as addition, multiplication, and the like can be applied.

a) можно будет применить b) могли применить

c) могут применяться

6. The more we study mathematics the more we see that the ideas and conceptions involved become more divorced and remote from experience, and the role played by the mind of the mathematician becomes larger and larger.

a) играла b) играемая

c) играющая

  UNIT III I. Найдите в тексте интернациональные слова, переведите их. II. Выберите в колонке В эквиваленты к словам колонки А.

A	B
1.axiom 2. concept 3. theorem 4. deduce 5. calculus 6. function 7. differential equation 8. prove 9. geometry 10. pure mathematics	а) концепция b) чистая математика с) геометрия d) аксиома e)дифференциальное уравнение f) доказывать g) выводить h) функция i) вычисления j) теорема