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
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III. Заполните пропуски подходящими по смыслу словами.
1.... constitute the second major component of any branch of mathematics.
a) geometries b) theorems
c) differential equations d)axioms
2. The objective of mathematical activity consists of the... deduced from a set of axioms.
a) functions b) theorems
c) concepts d) notions
3. The … of number give rise to the results of algebra.
a) axioms b) functions
c) calculus d) geometries
4. Mathematical... must be deductively established and proved.
a) axioms b) concepts
c) theorems d) numbers
5. Some mathematicians claim that... is the most original creation of human mind.
a) pure mathematics b) geometry
c) theorems d) concepts
Text III
Axioms constitute the second major component of any branch of mathematics. Up to the XIX century axioms were considered as basic self-evident truths about the concepts involved. We know now that this view ought to be given up. The objective of mathematical activity consists of the theorems deduced from a set of axioms. The amount of information that can be deduced from some sets of axioms is almost incredible. The axioms of number give rise to the results of algebra, properties of functions, the theorems of the calculus, the solutions of various types of dif0,ferential equations. Mathematical theorems mist be deductively established and proved. Much of the scientific knowledge is produced by deductive reasoning; new theorems are proved constantly, even in such old subjects as aglebra and geometry and the current developments are as important as the older results.
Growth of mathematics is possible in still another way. Mathematicians are sure now that sets of axioms which have no bearing on the physical world should be explored. Accordingly, mathematicians nowadays investigate algebras and geometries with no immediate applications. There is, however, some disagreement among mathematicians as to the way they answer the question: Do the concepts, axioms, and theorems exist in some objective world and are merely detected by man or are they entirely human creations? In ancient times the axioms and theorems were regarded as necessary truths about the universe already incorporated in the design of the world. Hence each new theorem was a discovery, a disclosure of what already existed. The contrary view holds that mathematics, its concepts, and theorems are created by man. Man distinguishes objects in the physical world and invents numbers and number names to represent one aspect of experience. Axioms are man's generalizations of certain fundamental facts and theorems may very logically follow from the axioms. Mathematics, according to this view-point, is a human creation in every respect. Some mathematicians claim that pure mathematics is the most original creation of the human mind.
IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.
1. What is the second major component of any branch of mathematics?
a) axiom b) concept
c) notion d) theorem
2. What was considered as the basic self-evident truth about concepts up to the 19th century?
a) proofs b) axioms
c) calculus d) theorems
3. What may very logically follow from the axioms?
a) functions b) axioms
c) theorems d) set of notions
4. How is scientific knowledge produced?
a) by deductive reasoning b) by experience
c) from a set of axioms d) by mathematical calculus
5. How do mathematicians nowadays investigate algebra and geometry?
a) with immediate application b) with no immediate application
c) without any application d) with one application
6. What was regarded as necessary truths about the universe in ancient times?
a) hypotheses of future knowledge b) experience
c) the axioms and theorems
d) conclusions of physical processes
7. What may very logically follow from the axioms?
a) notions b) calculus
c) theorems d) concepts
V. Выберите заголовок для данного текста, в соответствии с его содержанием.
a. Mathematical theorems
b. Axioms as the second major component of any branch of mathematics
c. Mathematical concepts
d. Geometry as the second branch of mathematics
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