8. Compose sentences with the words and word-combinations from Ex.7. Reading Comprehension

1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:

– The text deals with … (speaks about, presents, shows, points out, discusses, reviews, throws light on, traces the history of, etc)

– The subject matter of the text is …

– The text can be segmented into … paragraphs.

– The first (second, third, fourth, etc.) paragraph considers … (deals with, informs of, describes, etc.)

– The topic sentence of the first (second, third, fourth, etc.) paragraph is …

– The main idea of the first (second, third, fourth, etc.) paragraph is …

– The main idea of the text is …

– The conclusion the author came to is …

– The reasons for this conclusion are …

2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:

It’s right. Quite so.

I quite (fully) agree to it.

Certainly. Exactly.

I doubt that …

I don’t think so.

This is not the case.

It’s wrong, I am afraid.

Quite the reverse.

The definition is inappropriate.

1. Maths as a science, viewed as a whole, is a collection of branches.

2. Each branch has a different logical structure.

3. 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.

4. Each branch begins with axioms.

5. There do not exist the interrelationships of the various areas.

6. The basic concepts of the main branches of maths are abstractions from experience.

7. There are no concepts introduced with the help of experience.

8. The concept of a function is not a mental creation.

9. The mathematicians nowadays discover new concepts which are more and more drawn from experience.

10. The more advanced ideas are purely mental creations rather than abstractions from physical experience.

11. Theorems constitute the second major component of any branch of maths.

12. Math theorems must be deductively established and proved.

13. Maths ia a human creation.

3. Answer the following question:

1. Where does the word “mathematics” come from?

2. Does math knowledge come as a consequence (result) of studying and learning alone?

3. How many subject-fields (branches, domains, divisions, compartments) of maths do there exist nowadays?

4. What are the fundamental components of any branch of maths?

5. Can you name some new branches of modern maths?

6. What field of maths is the most interesting (important, essential, significant), to your mind?

7. Why are axioms necessary in a deductive system?

8. Why ought the mathematician to reason deductively?

9. Can we distinguish between whole numbers and irrational numbers from the viewpoint of their origin?

10. What are the factors that make possible the growth of maths?

11. What can research in maths mean?

12. Is the use of abstractions peculiar to maths alone?

13. Are the concepts of force, mass, energy, wealth, liberty, justice, democracy etc., mental creations?

14. Where do math concepts come from?

15. Most abstract math concepts have their physical counterparts, haven’t they?

16. Are math concepts discovered or invented?

17. What is a math postulate (axiom, theorem, proof, theory)?

18. What is meant by the phrases “pure maths”, “applied maths”?

19. What is more important: a math theory or practical applications?

20. Can a single person be a specialist in many if not all the branches of present day maths?

21. Where is progress more rapid: in pure or applied maths?