VI. Укажите правильный перевод подчеркнутой части предложения.




1. Up to the XIX -century axioms were considered as basic self-evident truth about the concepts involved.

a) считались b) считаются с) считают

2. Mathematical theorems must be deductively established and proved.

a) должны будут основываться и доказываться

b) должны быть основаны и доказаны

c) должны были быть основаны и доказаны

3. Much of the scientific knowledge is proved by deductive reasoning.

a) обоснованиемb) были обоснованы

c) будут обоснованы

4. New theorems are proved constantly, even in such old subjects as algebra and geometry and the current developments are as important as the older results.

a) доказываются b) доказали

c) были доказаны

5. In ancient times the axioms and theorems were regarded as necessary.

a) рассматриваются b) рассматривались

c) были рассмотрены

6. The objective of mathematical activity consists of the theorems deduced from some sets of axioms.

a) выведенные b) выводили

c) выводят

 

 

UNSOLVED MATHEMATICAL PROBLEMS
 
UNIT I
I. Найдите в тексте интернациональные слова, переведите их. II. Выберите в колонке В эквиваленты к словам колонки А.
А Б
1. solution 2. replace 3. significance 4. methods a) заменить b) значение c) решение d) методы

III. Заполните пропуски подходящими по смыслу словами.

1. Every age has its own problems that it solves or … by new ones.

a) replaces b) seeks

c) requires d) tests

2. It is by the … of problems that the researcher tests the temper of his steel.

a) question b) solution

c) investigation d) generation

3. The deep … of certain problems for the advance of mathematical science are not to be denied.

a) glance b) advance

c) significance d) importance

4. What new … in the wide and rich field of math – cal thought can the new centuries disclose?

a) methods b) facts

c) solutions d) ideas

Text I

Who of us cannot be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals can there be which the leading mathematical minds of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought can the new centuries disclose?

History teaches the continuity of the development ofscience. We know that every age has its own problems, which the following either solves or casts aside as worthless and replaces by new ones. If we could obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass in our minds and consider the problems which the science of today sets and whose solution we expect from the future. To such a review of present-day problems, raised at the meeting of the centuries, I wish to turn your attention. For the close of a great epoch of the 19th century not only invites us to look back into the past but also directs our thought to the unknown future.

The deep significance of certain problems for the advance of mathematical science, in general and the important role which they play in the work of the individual investigator are not to be denied. As long as a branch of science offers an abundance of problems, so long it is alive, a lack of problems foreshadows extinction or the cessation of independent development. Just as every human undertaking seeks after certain objects, so also mathematical research requires its problems. It is by the solution of problems that the researcher tests the temper of his steel; he finds new methods and new outlooks, and gains a wider and freer horizon.

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

1. What does every age have?

a) its own problems b) its own secrets

c) its own purposes d) its own ideas.

2. How long is the branch of science alive?

a) As long as a branch of science offers an abundance of problems, so long it is alive.

b) The branch of science is alive only when all its problems are solved.

c) The branch of science is alive as long as it is interesting for people.

d) The branch of science is always alive.

3. What foreshadows a lack of problems?

a) extinction or the cessation of independent development.

b) Extinction or the cessation of dependent development.

c) The revival of independent development.

d) The disappearance of independent development.

4. What does mathematical research require?

a) the solution of its problems.

b) it requires new investigations.

c) it requires the disappearance of its problems.

d) it requires new methods and ideas.

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

a. Connection between mathematical problems in past and in future

b. Mathematical problem in past

c. Mathematical problems in future

d. Mathematical problems of our days



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