I. Learn the meaning and pronunciation of the following words:

Mathematics, ratio, arithmetics, tangent, algebra, series, calculus, graph, variable, zero, derivative, designate, area, infinitesimal, increments, integral, subscript, superscript, magnitude, insoluble, addition, multiplication, division, raising to power, limits, subtraction.

2. Find in the text the words which can form:

a) adverbs after the model A + -ly: full — fully;

b) adjectives after the model S + -ic: symbol — sym­bolic;

c) nouns after the model V + -ation: abbreviate — ab­breviation.

2. Form words with the opposite meaning by adding prefixes un-, mis-, in-, im-:

dependent, possible, known, understand, soluble, inter­pretation, successful, favourable, productive, precise, com­plete, careful, frequent, limited, calculation, exact, con­venient.

IV. Read and remember the Plural of the following Nouns: radius — radii datum — data

formula— formulae index— indices

V. Read, translate into Ukrainian and memorize the following pairs of

verbs and nouns:

to produce — product to superscribe — superscription

to choose — choice to calculate — calculus

to speak — speech to add — addition

to use — use[ju:s] to subtract — subtraction

to design — design to multiply — multiplication

to place — place to divide — division

VI. Read aloud and give the Ukrainian equivalents of the following words:

social, design, universal, operation, symbol (symbolic), sense, idea, illustrate,

problem, technique, interpretation, base, transform (transformation), equivalent.

VII. Read and learn by heart:

1 inch = 2.54 centimeters (cms)

12 inches = 1 foot

1 foot = 30.48 cms

3 feet = 1 yard

1 yard = 91.44 cms

1,760 yards = 1 mile

1 mile = 1609.3 metres

220 yards = 1 furlong

1 furlong = 201.16 metres

8 furlongs = 1 mile

VIII. Translate the following words of the same root into English:

використовувати — використовування — користь — корисний — некорисний;

ділити — поділ — подільність — подільний — неподільний;

різнитися — різниця — різний — розрізнення.

IX. Arrange the following words according to:

1. similar meaning: precise, identical, exact, similar, careful, complicated, complex, attentive, universal, recurrent, global, frequent, brief, entire, complete, concise;

2. opposite meaning: simple, free, different, chief, precise, minor, similar, dependent, complex, long, ambiguous, brief.

10. Read the following:

a) numerals: 30; 80; 100; 103; 3,200; 2,045,237;

2. mathematical expressions: З³, 4³, 5^б, 7³, 10¹⁰;

3. fractions; ½ (km), 1/3 (ton), 0.5 (km), 3.152 (ton);

4. dates: in 1985; January 22, 1919; in 1995.

10. Translate into English using words and word-combina­tions from the text:

    1. Математична мова — це мова знаків та символів. 2. Мова математики

проста і універсальна. 3. Люди різних країн перекладають знаки i

символи мови математики на свою рідну мову. 4. Алгебра — це мова математики. 5. В своєму розвитку алгебра пройшла декілька ступенів. б. Сучасна алгебра об'еднує велику кількість самостійних дисциплін.

7. Метод аналізу математичних моделей посідає провідне мicцe серед інших методів дослідження.

Text 4 B

THE VICTIM OF OVERWHELMING NUMBERS

1. Read and memorize:

to reward — винагороджувати, the game of chess — rpa в шахи,

chess-board — шахівниця, square — квадрат, a bag of wheat —мішок пшениці,

to double — подвоювати, to enjoy — насолоджуватися, радіти, treasure — скарб,

to order — наказувати, to count — рахувати, to account for — пояснювати,

to increase — збільшувати, to fulfil — виконувати, pretty big — досить великий,

assuming (that) — припускаючи, (що), to contain — вміщати, the amount

re­quested — потрібна кількість, incessant flow (of latter's demands) — безпе-

рервний (безконечний) noтік (вимог останнього).

King Shirham of India, according to an old legend, want­ed to reward his grand

vizier Sissa Ben Dahir for inventing and presenting to him the game of chess.

The desires of the clever vizier seemed very modest. "Majesty", he said kneel­ing in front of the king, "give me a grain of wheat to put on the first square of this chessboard, and two grains to put on the second square, and four grains to put on the third and eight grains to put on the fourth. And so, oh King, doubling the number for each succeeding square, give me enough grains to cover all 64 squares of the board". "You do not ask for much, oh my faithful servant", ex­claimed the king, silently enjoying the thought that his gener­ous proposal of a gift to the inventor of the miraculous game would not cost him much of his treasure. "Your wish will certainly be granted". And he ordered a bag of wheat to be brought to the throne. But when the counting began, with a grain for the first square, 2 for the second, 4 for the third and so forth, the bag was emptied before the twentieth square was accounted for. More bags of wheat were brought before the king but the num­ber of grains needed for each succeeding square increased so rapidly that it soon became clear that with all the crop of India the king could not fulfil his promise to Sissa Ben. To do so would have required 18,446,744,073,709,551,615 grains... That's not so large a number as the total number of atoms in the universe, but it is pretty big anyway. Assuming that a bushel of wheat contains about 5,000,000 grains, one would need some 4,000 billion bushels to satisfy the demand of Sissa Ben. Since the world production of wheat averages about 2,000,000,000 bushels a year, the amount requested by the grand vizier was that of the world's wheat production for the period of some two thousand years.

Thus King Shirham found himself deep in debt to his vi­zier and had either to face the incessant flow of the latter's demands or to cut his head off. What alternative did he choose ?