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?

4. Give the definitions of the terms “the real number system” and “the maths of number”:

The real number system is …

The maths of number is …

Conversational Practice

1. Disagree with the following negative statements and keep the conversation going where possible. Begin your answer with the opening phrases:

It’s not correct…

It’s not right, I am afraid…

It’s wrong,…

On the contrary…

Quite the reverse…

1. Scientists do not think and reason in terms of abstractions.

2. Maths is not a free creation of the human mind and reasoning.

3. Pure maths cannot be applied to the physical world.

4. Mathematicians do not seek useful applications of their theories.

5. Pure maths theories do not find any practical applications.

6. Pure maths theories are often not significant and they are entirely forgotten in say, 50 years.

 

2. Agree or disagree with the statements. Use the introductory phrases:

That’s right…

Exactly. Certainly…

I fully agree to it…

I don’t think so. This is not the case…

It’s wrong, I am afraid. Quite the reverse…

The definition is inappropriate…

 

1. A math formula has a direct real physical counterpart.

2. Mathematicians do not rely on their intuitive judgement – they seek to give a rigorous proof.

3. If you want to know what a math theorem states, see what its proofs prove.

4. Maths is both intelligible and enjoyable.

5. Mathematicians do not deal with applications of maths.

6. An idea expressed in symbols is more scientific than the same thought presented in words.

7. Most mathematicians are not incentive to art and beauty.

3. Compose questions and a) answer them in writing at home according to the model; b) practice them orally in class:

Model	If you asked	me			should	say that …
	Should you ask		would
If I were asked		що таке «множина»	I	could
Were I asked			might
If I were to be asked Were I to be asked		ought to

Should you ask me what a “set” is, I’d say that unless otherwise specified “set” is an undefined concept in modern maths.

1. … що таке «математика», …

2. … що таке «постулат», …

3. … що таке «прикладна математика», …

4. … яка різниця між «чистою математикою» і «прикладною математикою», …

5. … де і коли виникла перша математична школа, …

6. … що означає поняття «a variable», …

7. … які найбільш фундаментальні поняття сучасної математики, …

4. Practise problem questions and answers. Work in pairs. Change over!

1. What do you feel looking at a book page sprinkled with ’s and ’s, = ‘s and other math symbols and signs?

2. Does the mathematician write in the language of maths to hide his knowledge from the world at large?

3. Do new symbols often appear in maths?

4. When do mathematicians introduce new symbols and signs into the language of maths?

5. To whom is language of maths “foreign”?