Vocabulary exercises

I. Translate the sentences into Ukrainian.

Model. This information is new. It comes regularly.

Эти сведения новые. Они поступают регулярно.

I. What is the news? There is some, but I am not sure if it is good news or bad. 2. He makes good progress in English. 3. Let me give you some advice. 4. It is a fine piece of music. 5. Sound knowledge can be obtained through study and research work. 6. Information that is wrong is not useful. 7. This theory shows much ingenuity and sophistication.

II. Say the verbs related to the following words.

Computation, representative, confused, preference, divisible, unde­fined, managerial, involvement, objectively, sophistication, insensitive, subtraction, minded, reasoning, introductory, claimant, application, com­puting, determination, designed, meaningfully.

III. Say what part of speech the following words belong to.

Additive, avoidance, countable, subjectively, inexperienced, divider, objectivity, perfection, determined, misconception, distinguishable, mul­tiple, conceptual, decimal, numerator, unsophisticated, applied, nonsense, perception, search.

IV. Paraphrase the following verbs or give their synonyms.

To reason, to subject, to relate, to claim, to sophisticate, to multiply, to divide, to count, to devise, to manage, to avoid, to mind, to subtract, to apply, to communicate.

V. Give all the derivatives of the following verbs.

To add, to calculate, to divide, to define, to mean, to deal with, to subtract, to object, to mind, to relate, to sense, to sophisticate, to subject, to represent, to involve, to multiply, to communicate, to avoid, to com­pute.

VI. Classify the prefixes and suffixes of the following words and give their Ukrainian equivalents.

Meaningfulness, sophistication, additivity, interrelationships, points (to), consistency, unambiguously, indistinguishable, involved, manage­rial, reasonlessly, mindedness, subjective, subtractor, variable, develop­ment, conclusion, multinational.

VII. Consult the dictionary and give the Ukrainian equivalents of the following- phrase verbs.

to be on

to be off

to be over

to be through

to stand for

to stand up

to stand over

to stand back

to make for

to make away

to make out

to make up

to point at

to point to

to point out

to point up

VIII. Give the Ukrainian equivalents of the following words adding the negative prefixes: un-, in-, ill-, dis-, im-, ir-,mis-, non-

defined, known, wanted, willing, familiar, accustomed, manageable, ambiguous, suitable, like, spoken, common, official, reasonable, avoidable, sophisticated; exact, complete, accessible, dependent, efficient, sensible, sensitive, divisibility, ability, accurate, correct, convenient, definable, atten­tion, adequate, determinate, different, distinct, formal, human, ele­gant, experienced, escapable, valid; precise, possible, perfect, proper; rational, regular, relevant; logical, legal, limitable.

IX. Give the Ukrainian equivalents of the following antonyms.

good — bad, inside — outside, encourage — discourage, true — false, right wrong, absolute relative, natural artificial, alike different, ancientmodern, lend — borrow, inward — outward, internal — external, interior — exterior, implicit — explicit, include — exclude, converge — diverge, divide — unite, increase — decrease, forget — remember, general — particular, simple — complicated, knowledge — ignorance, positive — negative, inner — outer.

X. Translate the sentences into Ukrainian paying attention to: "ra­ther", "rather than", "other than".

1. Maths is the study of relations between certain ideal objects such as numbers, functions, and geometric figures. These objects are not regarded as real but rather as abstract models of physical situations. 2. Mathematicians want from maths objects not their material or physical existence but rather the right to Use them in proofs. 3. The maths concept is a notion or method rather than content. 4. Maths is an active rather than a passive activity. 5. Maths not only aids in the design of musical instruments but sometimes maths rather than the ear is the arbiter of perfect design. 6. In this century the skill of reading is divided into many types among which intensive, extensive and silent are most commonly used. Extensive reading is aimed at ideas rather than grammatical structure and is definitely distinguished from translation. 7. For many physical phenomena no- exact concepts exist other than maths notions. 8. The concepts of number and space figure do not come from any source other than the world of reality.

XI. a) Choose the proper Ukrainian equivalent and translate the sen­tences into Ukrainian.

Model. Development(s) п. развитие; изложение; раскрытие;, разъяс­нение; преобразование; построение; становление, разработка; теория; событие; результат; совершенствование; достижение.

1. The maths theory of groups is a development of the last centuries. 2. The development of the rigorous maths (as opposed to the dictionary) type of definition is the product of the modern maths. 3. Educated people must be familiar with all the important scien­tific developments of their day. 4. In maths the basic development from concrete individual matter through abstraction and back again to the concrete and individual gives a theory its meaning and significance. 5. The concept of number and the process of counting developed so long before the time of recorded history that the manner of this development is largely conjectural. 6. The requirements for quicker aids to computa­tion lay at the root of the development of multiplication tables, tables of reciprocals and the like. 7. Maths ranks among the highest cultu­ral developments of man. 8. It is especially true that in maths the creative work is done by individuals mostly; nevertheless the results are the product of centuries of thought and development, 9. What we call "maths" consists of several discrete individual developments, each manifesting its own birth and growth. 10. No subject can be effectively learnt or taught without an adequate understanding of its historical de­velopment. The development of maths knowledge is essentially in a continuous evolution. II. The development of the means of mass com­munication in the modern world makes for greater understanding among nations. 12. Lab. practice and self-training make for the development of important language skills: listening, understanding, reproducing and im­provising.

b) Consult the dictionary and give all possible Ukrainian equivalents of the English words "division", "power", and "consideration" with illustra­tive examples.

XII. Express surprise, consent or disagreement with the statements given below. Try to prove your viewpoint or advocate the opinion of others. Summarize the discussion.

Model. Maths is an art, with a beauty of its own.

1. Is it really? It is too much to say that maths is an art, to my mind. It runs counter to common sense, indeed. I pre­fer a conventional definition of maths as one of the oldest sciences.

2. Exactly. Maths has nothing to do (= nothing in common) with art. There is no poetry and no beauty in maths. From a maths standpoint, it's nonsense to claim it.

3. I share this viewpoint. Science is not the object for art and beauty. It's, in fact, a meaningless statement.

4. You're all a bit wrong, I am afraid. To say that maths is an art is not to say that it is a mere amusement. The highest compliment to a maths work is to call it elegant, though it is not easy at all to define elegant maths.

5. Surely. The inclusion of maths among arts is apparently not illogical. Maths creations have design, symmetry, harmony and inner beauty, i. е., characteristics of art, in the long run.

6. One more remark seems reasonable, namely, in the search for a method of proof the mathematician must use not only his creative ability and insight but inspiration that we usual­ly associate with the creation of a piece of art or music.

7. Certainly. I quite agree to it. I may as well add that the role of maths as an art is especially emphasized when conjectu­res (hypotheses) are proved.

8. That's right. It's common knowledge that a rigorous and ele­gant proof is beautiful to maths eye. It's a poem and a delight for the mathematician.

9. There is one more point that I think is relevant. The ana­logy between maths and art makes sense only to a person who loves both.

10. Summing up the discussion, it seems correct to say that there may be different viewpoints, but maths is more than only a language or technique. It's an art in the broad sense of the word.

1. Most mathematicians are not insensitive to art and beauty. 2. Mathematicians see beauty where others find only confusion of signs and symbols. 3. Maths and art are intimately related. 4. Art is beyond the scope of a scientist's interests. 5. Poetry is read only by artistic-minded people — not by mathematicians. 6. Mathematicians pay no attention to the elegance of presentation. 7. Mathematicians' search for beauty and ele­gance likens them to artists. 8. The beauty of a theorem lies in its simp­licity and generality. 9. Maths ability is often classed with artis­tic ability. 10. A beautiful maths result is always non-trivial. 11. Elegant and beautiful ideas enrich maths. 12. The mathematician like an artist is a maker of patterns. The mathematician rarely chooses his patterns for beauty's sake. 13. In mathematicians' view the formula c² = a²+b² is elegant and beautiful.

XIII. Confirm or deny the following statements.

1. From the time of Pythagoras the study of music is regarded as maths in nature. 2. The relationship between maths and music is obvious. 3. Music — the most abstract of the arts — apparently appeals to mathematicians. 4, Not few mathematicians are excellent musicians. 5. Masters such as Bach constructed and advocated maths theo­ries for the composition of music. 6. In such theories cold reason rather than spiritual feeling gives the creative pattern. 7. Music lovers can en­joy beautiful music thanks as much to a mathematician Fourier as to Beethoven. 8. Unlike the sciences but like the art of music maths is a free creation of the mind.

XIV. Translate the text into English.

Что такое математика? Что она изучает? Существует ли математи­ка единая как система, органически связанных между собой знаний или она скопление научных дисциплин, изолированных друг от друга по своим методам, целям и даже по языку выражения своих результа­тов? Ответить на эти вопросы — совсем не легкое дело. Определение предмета и сущности математики, высказанное Ф. Энгельсом сто лет назад, сохраняет свою справедливость и актуальность. Чистая матема­тика имеет своим предметом пространственные формы и количествен­ные отношения действительного мира. Все объекты и процессы, реаль­но существующие в мире, обладают такими свойствами, которые выра­жаются в категориях количества и формы, т. е. они присущи всей дей­ствительности. Математики абстрагируют упомянутые количественные отношения и пространственные формы, устанавливают связи в реально протекающих процессах, формулируя их в виде логических высказыва­ний, записанных символами и формальными определениями. Дальней­шее развитие этих абстракций включает в себя доказательство теорем, образование новых понятий, построение новых теорий. Эти понятия, теоремы, теории применяются впоследствии к изучению действитель­ности. По мере восхождения к более высоким абстракциям связь тео­ретической математики с практикой, с действительностью становится все менее непосредственной и осуществляется во многом через другие науки. По отношению к этим наукам математика выступает как метод и язык формулировки количественных закономерностей, как средства решения задач, как аппарат для построения и разработки теорий. В них она также черпает новые понятия, задачи и импульсы для сво­его развития.

Математика есть лишь специфическая форма процесса человеческо­го познания. Математическое мышление — одна из форм этого общего процесса познания. Математики мыслят абстракциями. Математические абстракции имеют материальное происхождение, они представляют определенные свойства реальных вещей. Математические теории явля­ются не произвольными построениями ума, а отражением сущности ве­щей. Математика выделяется среди других наук своей универсально­стью. Методы математического исследования составляют неотъемле­мую часть всех наук. Применение математических методов исследования повышает объективную ценность научных теорий. Мате­матика должна рассматриваться в развитии. Развитие математики не означает добавление новых теорем; оно включает в себя качественные изменения содержания математики. Универсальность математики объ­ясняется широтой ее предмета. Трудно, если вообще возможно, прове­сти границу между математикой чистой и прикладной. Обособление этих частей математики не соответствует объективным закономерностям развития математической науки, противоречит им. Быстрый рост состава математики и ее приложений привели к ряду революционных преобразований содержания математики, к осознанию ее значимости. Борьба противоположных взглядов на природу и методы математики или отдельных ее частей обостряются в те периоды ее истории, когда происходит становление новой теории, ведущей к существенному пере­смотру сложившихся представлений, смысла основных понятий, опера­ций логического анализа, систем исходных высказываний (аксиом), средств вывода новых теорем и т. п. Подобные революционные преоб­разования были, например, в период создания математического ана­лиза, формирования неевклидовых геометрий, введения в математику теории множеств и создания кибернетики.

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