1. Find international words in the text and guess their meaning.

2. Give the Russian equivalents to the following words and word combinations:

Revolutionary discoveries, to explain, Brownian motion, a great contribution, to equal, the speed, to realize, discovery, unified field theory, research work, mysterious, extremely.

1. Where did Einstein work when he was 21?

1. at an office

2. at a hospital

3. at a university

2. What did Einstein explain in his first paper?

1. Brownian motion

2. photoelectric effect

3. field theory

3. Where was his “Special Theory of Relativity” published?

1. mathematical journal

2. physical journal

3. medical journal

4. How many equations was unified theory expressed in?

1. 2 b) 3 c) 4

3. Speak about a. Einstein’s greatest discoveries. Signs used in Mathematics

+ plus

• minus

x – times; multiplied by

: divided by; the ratio of … to

= sign of equality; equals, is equal to

a=b a equals b; a is equal to b

2x3=6 twice three is six

4x5=20 four multiplied by five is twenty

15:5=3 fifteen divided by five is (equals) three

3:6=2:4 three is to six as two to four

⅜ three eighths

0.3 three tenths, nought point three

0.024 nought point nought two four

% per cent

( ) parentheses

[ ] brackets

{ } braces

∞infinity

< is less than

>is greater than

x – eks

x² - eks squared

x³ – eks cubed

x⁴ – eks to the fourth power

x^-1 – eks to the minus one

xⁿ – eks to the en

Text 10.

The students of mathematics may wonder where the word “mathematics” comes from. Mathematics is a Greek word, and, by origin or etymologically, it means “something that must be learnt or understood”, perhaps “acquired knowledge” or “knowledge acquirable by learning” or “general knowledge”. The word “mathematics’’ is a contraction of all these phrases. The celebrated Pythagorean school in ancient Greece had both regular and incidental members. The incidental members were called “auditors”; the regular members were named “mathematicians” as a general class and not because they specialized in mathematics; for them mathematics was a mental discipline of science of learning. What is ma­thematics in the modern sense of the term? There is no neat, simple, general and unique answer to this question.

Mathematics as a science, viewed as a whole, is a collection of branches. The largest branch is that which builds on the ordinary whole num­bers, fractions, and irrational numbers, or what, collectively, is called the real number system. Arithmetic, algebra, the study of functions, the cal­culus differential, equations, and various other subjects which follow the calculus in logical order, are all developments of the real number sys­tem. This part of mathematics is termed the mathematics of number. A second branch is geometry consisting of several geometries. Mathematics contains many more divisions. Each branch has the same logical structure: it begins with certain concepts, such as the whole numbers or integers in the mathematics of number, and such as point, line and tri­angle in geometry. These concepts must verify explicitly stated axioms. Some of the axioms of the mathematics of number are the associative, commutative, and distributive properties and the axioms about equalities. Some of the axioms of geometry are that two points determine a line, all right angles are equal, etc. From the concepts and axioms theorems are deduced. Hence, from the standpoint of structure, the concepts, axioms and theorems are the essential components of any compartment of ma­thematics. We must break down mathematics into separately taught sub­jects, but this compartmentalization taken as a necessity, must be com­pensated for as much as possible. Students must see the interrelation­ships of the various areas and the importance of mathematics for other domains. Knowledge is not additive but an organic whole and mathema­tics is an inseparable part of that whole. The full significance of mathe­matics can be seen and taught only in terms of its intimate relationships to other fields of knowledge. If mathematics is isolated from other provinces, it loses importance.

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