Passive Voice

to be + 3^rd form of a verb

a). For Irregular verbs one must use the Table.

Ex. to do (Active Voice) - to be done (Passive Voice)

b). For Regular verbs one adds the ending “– ed”.

Ex. to wait (Active Voice) - to be waited (Passive Voice)

Task 4 Remake the sentences from Active to Passive Voice and vice versa:

1. Our night vision is not troubled by red light.

2. Militaries adopted red light in the cockpits of all jet fighters.

3. Scientists generate a model.

4. They can suggest a hypothesis.

5. A theory describes the behavior of broad sets of phenomena.

6. A large number of hypotheses can be logically bound together by a single theory.

7. The results of an experiment were announced.

8. Independent researchers will double-check them.

9. The research was performed by him.

Plural

Most of words -s; -es

ex. an experiment - experiment s;

Greek and Latin borrowings - um - a; - on - a; - us - i; - is - es;

ex. an radius – radii

English original words (exceptions)

ex. a man - men; a woman - women; a child - children; a foot - feet; a tooth - teeth; a goose - geese; an ox - oxen; a mouse - mice; a louse - lice;

Words with no graphical signs of Plural. There are only three of them.

ex. an species - species;

a means - means;

a series - series;

Task 5 Give the Plural form of the following words:

a thesis ____________; a problem ___________; a man _________;

a phenomenon _______________; a millennium _____________;

a maximum ____________; a child ____________; a hypothesis _______________;

a criterion ______________; a research ____________; a basis ____________;

a mechanism _________________; a bacterium _____________; an axis ________________; a means ______________;

Lesson 9

“Mathematics”

Text A

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BC, in India in AD 100, and in the Muslim world in AD 800, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.

Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis).

Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".

Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal, established in 1936 and now awarded every 4 years. It is often considered the equivalent of science's Nobel Prizes. The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was introduced in 2003. These are awarded for a particular body of work, which may be innovation, or resolution of an outstanding problem in an established field. A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.

Task 4 Remake the sentences using Passive Voice:

1. Mathematics studies quantity, structure, space, and change.

2. They formulated new conjectures.

3. You have to establish truth.

4. People use mathematics throughout the world as an essential tool in many fields.

5. We subdivide Mathematics into the study of quantity, structure, space, and change.

6. Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".

7. Some thinkers have applied a version of falsificationism to mathematics.

8. They established the Fields Medal in 1936.

9. The Wolf Prize in Mathematics recognizes lifetime achievement.

10. David Hilbert compiled a famous list of 23 open problems.

11. Mathematicians have been solved nine of "Hilbert's problems".

12. Computation and simulation are playing an increasing role in mathematics.

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