Answer the questions:

1. Why is it important to know mathematics? 2. What is the distinction between

common human language and the language of mathematics? 3. How is the language of mathe­matics designed? 4. Why is algebra called the language of mathematics? 5.What signs and symbols in mathematics do you know? 6. What three stages has algebra passed through in its development? 7. What event may be called the turning point in the history of algebra? 8. What sciences does mathe­matics embrace? 9. What can you say about the expression "mathematics is the language of science"?

Exercises

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.