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G."For the things of this world cannot be made known without a knowledge of mathematics."

Roger Bacon

H."Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

READING

5.A. Underline the stressed syllable in each word as in the example. Practise reading.

abbreviation, concise, purposefully, throughout, frequent, minus, precise, algebra, geometry, pervade, philosophy, magnitude, vowel, successful, successively, ambiguity, susceptible, technique

B. Tell what the following abbreviations or shortenings mean. If you don't

6.Read the text "MATHEMATICS − THE LANGUAGE OF SCIENCE" and answer the questions.

1.Is the language of mathematics universal? Why (not)?

2.What is algebra?

3.What three stages has algebra passed?

4.How is the language of mathematics designed?

5.What signs and symbols are there in mathematics?

6.What sciences does mathematics embrace?

7.What is verbal algebra?

8.What are examples of abbreviated algebra?

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7. Think of the other heading(s) to the text.

MATHEMATICS − THE LANGUAGE OF SCIENCE

1.Human language is capable of precise statements because it is a system of symbols. But common language is a product of social development, customs and traditions. Even by the most careful choice of words the meaning concealed in them may influence our reasoning. Algebra, the language of mathematics,

consists mostly of signs and symbols and is carefully and purposefully designed. It is precise, concise and universal, i.e. one and the same throughout the civilized world, though the people in each country translate it into their own spoken language.

2.Algebra in the broad sense of the term, deals with operations upon symbolic forms. In this capacity it not only permeates all of mathematics, but pervades practically all sciences including formal logic, philosophy, and even linguistics, poetry and music. In our scientific age there is a general belief that all science, as it grows to perfection, becomes mathematical in its ideas.

3. It is generally true that algebra in its development has passed successively through three stages: verbal, abbreviated and symbolic. Verbal algebra is characterized by the complete absence of any symbols, except, of course, that the words themselves are used in their symbolic sense. To this day verbal algebra is used in such a statement as "the sum is independent of the order of the terms", which in symbols is designated by a+ b=b + a.

4. Abbreviated algebra of which the Egyptian is a typical example, is a further development of verbal one. Certain words of frequent use are gradually abbreviated. The history of the symbols "+" and "−" may illustrate the point. In medieval Europe the latter was denoted by the full word ''minus'', then by the first letter "m" duly superscribed. Eventually the letter itself was dropped leaving

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the superscript only. The sign "plus" has passed through a similar metamorphosis.

The abbreviation has become a symbol.

5.The turning point in the history of algebra was an essay written late in the sixteenth century by a Frenchman; it was Viete who denoted the unknown magnitudes by vowels. The given magnitudes were designated by consonants.

6.Within half a century of Viete's death there appeared Descartes' Geometry. In it, the first letters of the alphabet were used for the given quantities, the last −

for those unknown. The Cartesian notation not only displaced the Vietan one, but

has survived to this day.

7.It is symbols that permit of concise, clear representation of ideas which are sometimes quite complex. Consider, for example, how much is involved in the calculus symbol "Dy". Once we have grasped the meaning and use of a symbol there is no need to think through the origin and development of the idea symbolized, each time it is used. It is due to a powerful technique based upon the use of symbols that mathematics is so effective in problems which are insoluble by other methods.

8.It is convenient because the literal notation is free from all ambiguities of words. The letter is susceptible of operations and this enables one to transform literal expressions and thus to paraphrase any statement into a number of equivalent forms. It is this power of transformation that lifts algebra above the level of a convenient shorthand.

9.It is symbolic language that is one of the basic characteristics of modern mathematics. And modern mathematics supplies a language for the treatment of the qualitative problems of physical and social sciences.

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8.Look through the list of words and phrases and check if you know their Ukrainian equivalents. Take turns to ask each other. Use the MINIDICTIONARY section to Unit 7 if necessary.

9. Explain the meaning of the words and phrases.

common language, universal, a similar metamorphosis, abbreviated algebra, ambiguity, the given quantities, literal notation, to permeate, magnitudes, to pervade, precise, concise

10.Cross the odd word out.

1)abase, abbreviate, shorten, compress;

2)concise, compact, brief, conclusive;

3)equivocacy, ambivalence, alternative, ambiguity;

4)permeate, perpetrate, spread through, penetrate;

5)metaphor, metamorphosis, transfiguration, conversion.

11.Find the words in the text to which the following ones are the antonyms. The first letter is given to make the task easier.

vowels (c), nonambiguous (a), occasional (f), minus (p), known (u), nonverbal (v), presence (a), dependent (i), different (s), written (s), weak (p), particular (g), inaccurate (p)

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12. Match the words (1−6) with their definitions (a−g).

13.Fill in the word from the list below. Use each word only once. Translate the phrases into Ukrainian.

magnitudes, gradually, pervade, use, designed, insoluble, ideas, symbolic, ambiguities, literal

14.Look through the text "MATHEMATICS − THE LANGUAGE OF SCIENCE". Pick up all the adjectives to the following words.

15. Match the phrases with their Ukrainian equivalents.

16. Fill in the table with the words derived from the given nouns.

symbol

mathematics

precision

concision

science

verb

frequency

similarity

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convenience

power

effect

17.Make up adverbs adding "-ly" to the given words. Translate these words into Ukrainian.

careful, purposeful, practical, mathematical, general, successive, verbal, independent, symbolic, typical, certain, frequent, effective, convenient, literal, powerful, basical, qualitative, physical, social

18.Fill in the gaps with the appropriate words / phrases from the list below.

massive systems; operations; lasting understanding; mundane; measurements; discoveries; records; galaxies; quadratic equations; calculations; complex theories; universe; predictions; abstract; real-world application

ancient people recording numbers in various ways dating back to 30,000 B.C. By

ancient civilizations used mathematics the way we do today to explain the way things work.

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19. Fill in the correct word derived from the word in bold.

Like Thales, Pythagoras is rather known for 1) _______ (mathematical) than for 2) _________ (philosophical). Anyone who can recall math classes will remember the first lessons of plane 3) _______ (geometrically) that usually start with the Pythagorean theorem about right-angled 4) ______ (triangular): a²+b²=c². In spite of its name, the Pythagorean theorem was not discovered by

Pythagoras. The earliest known 5) _______ (formulate) of the theorem was written down by the Indian 6) _____ (mathematics) Baudhāyana in 800BC. The principle was also known to the earlier 7) _______ (Egypt) and the Babylonian master builders. However, Pythagoras may have proved the theorem and 8)

________ (popularization) it in the Greek world. With it, his name and his philosophy have survived the 9) _________ (turbulent) of history.

20. Match 1−8 with a−h to make sentences.

21.Work in small groups. Arrange the following words and phrases in the correct order to make the sentences. The first word is underlined.

1. not / "Mathematicians / born, / are / made."

Henri Poincare

2. subconsciously / "All musicians / mathematicians. /are"

Thelonious Monk

3. "the key / the sciences. / Mathematics / to / the door and / is"

Roger Bacon

4."rules / on / certain simple / Mathematics / meaningless marks / played / is / a game / according to / with / paper."

David Hilbert

5.Uglification, and Derision." / Arithmetic / "The different / of / are / Ambition, Distraction, / branches

Lewis Caroll

6.want / "Mathematicians / they / are / like / managers − / change." / improvement / without

Edsger Dijkstra

22.A. Pronounce the following:

numerals: 30; 13; 2,000; 101,101; 12,020,987;

fractions and decimals: 2,5 ; 3 ; 10.4 ; 0,7 ; 2;

mathematical expressions: ; ; ; ;

dates: Dec. 5; Jan. 1, 2012; 1990; 1905; Sept. 3, 2000.

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B. Form the ordinal numerals from the cardinal ones: 3; 7; 13; 14; 22; 203;

44; 100; 1001; 100000.

23. A. Learn the examples of some mathematical equations.

1.

"Two plus x plus the square root of four plus x squared is equal to ten."

2.

"M" is equal to "R" sub one multiplied by "x" minus "P" sub one, round brackets opened, "x" minus "a" sub one, round brackets closed, minus "P" sub two, round brackets opened, "x" minus "a" sub two, round brackets closed."

B. Study Appendix 7. Give your own examples of equations or formulae

that you have to solve at your lessons of mathematics.

24.Find and correct mistakes.

1.My birthday is twenty-seven March.

2.My phone number is naught sixty-seven, double two, three, eighty-nine, twenty-four.

3.The population of Kyiv is about three millions.

4.I got twenty-five from forty in my test.

5.It was a second typical example of the rule.

6.We have done at least 70 per cents of the work.

7.Seven, five, three are even numbers.

25.This time you have to write three sentences about the past, present and future. Alex always solves mathematical

problems in the morning. It always takes him an hour, from 8.30 until 9.30 a.m. So:

1.At 9 o'clock yesterday morning Alex ............... .

2.It's 9 o'clock now. He ........................... .

3.At 9 o'clock tomorrow morning he ............................... .

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